Download Quantum Mechanics (Part II)

Department of Physics
UC Berkeley
Spring 2015
"Those who are not shocked when they first come across quantum theory
cannot possibly have understood it yet."
—Niels Bohr
PHYSICS 137B lectures 2&3
Quantum Mechanics (Part II)
Instructor:
Office:
Telephone:
E-mail:
Office Hours:
GSI:
Office:
E-mail:
Office Hours:
Andrew E. Charman
445 Birge Hall
(510) 642-4846
acharman (AT) physics (DOT) berkeley (DOT) edu
andy (DOT) charman (AT) gmail (DOT) com
currently Thu. 3 pm – 4 pm; Fri. 2 pm – 3 pm; or by appointment
(held in 429 Birge unless otherwise announced)
We may experiment with an online "virtual" office hour as well.
Mudassir Moosa
421 Birge (TA's office hours will be held here unless otherwise noted)
mudassir (DOT) moosa (AT) berkeley (DOT) edu
tentatively Wed. 11 am – 12 pm, Thu. 4 pm – 5 pm
(held in 421 Birge unless otherwise announced)
All scheduled office hours are of course open to all students.
Course Website:
Electronic forum:
https://bcourses.berkeley.edu/courses/1298330
piazza.com/berkeley/spring2015/physics137blectures23
Consultation Room:
429 Birge
Physics 7C/137AB
Course Center:
(find graded homework…)
109 LeConte
Units:
Final Exam Group:
4 (standard for a required, upper-division, non-lab, physics core course)
Lecture 2: group 10 (Wednesday, May 13, 2015, 11:20 am – 2:30 pm)
Lecture 3: group 18 (Friday, May 15, 2015, 11:30 am – 2:30 pm)
Catalog
Description:
(instructor’s office hours will be held here)
Physics
Reading Room:
(find colleagues…)
251 LeConte
Physics 137B: Quantum Mechanics (Part II)
Introduction to the methods of quantum mechanics with applications to
atomic, molecular, solid state, nuclear, and elementary particle physics.
Homework:
Due weekly, by 6 pm on Fridays in the box labeled "Physics 137B lectures 2&3"
in 251 LeConte, unless otherwise announced.
Grading:
Approximately 50% Homework, 20% Midterms (2), 30% Final Exam
(But see below for specific details—assignments on which you perform better
will be weighted more heavily, and an optional enrichment activity can boost
your overall numerical score).
Course Format:
3 hours of lecture and 1 hour of discussion per week, plus: encouraged but
optional office hours, and of course several hours outside of class expected for
reading, thinking, discussing, and problem-solving (+12–15 hours per week)
Lecture 2:
TeleBears info:
Tue./Thu.
LEC: 002
9:30 am – 11:00 am
CCN: 69450
210 Wheeler Hall
Discussion Section:
TeleBears info:
Thursday
SEC: 201
1:00 pm – 2:00 pm
CCN: 69453
110 Barker Hall
Discussion Section:
TeleBears info:
Tuesday
SEC: 202
4:00 pm – 5:00 pm
CCN: 69456
179 Stanley Hall
Lecture 3:
TeleBears info:
Tue./Thu.
LEC: 003
5:00 pm – 6:30 pm
CCN: 69459
20 Barrows Hall
Discussion Section:
TeleBears info:
Monday
SEC: 301
3:00 pm – 4:00 pm
CCN: 69462
6 Evans Hall
Discussion Section:
TeleBears info:
Tuesday
SEC: 302
4:00 pm – 5:00 pm
CCN: 69465
4 Evans Hall 179 Stanley Hall
???
If enrolled in Lecture 002, you must also enroll in either Section 201 or 202;
If enrolled in Lecture 003, you must also enroll in either Section 301 or 302;
You may attend any of the four discussion sections.
Discussion sessions will meet weekly starting in the first week.
Prerequisites:
Physics 7A, 7B, 7C (introductory mechanics, waves, fluids,
thermodynamics, electromagnetism, optics, and modern physics);
Math 1A, 1B (differential and integral calculus), Math 53 (multivariable
calculus), Math 54 (linear algebra and differential equations);
Physics 137A (quantum mechanics, part I); or prior consent of the instructor.
Physics 105 (classical mechanics) or Physics 110A (electromagnetism) are not
required, but could enrich your perspective.
Textbooks:
John S. Townsend, A Modern Approach to Quantum Mechanics (2nd Edition),
Mill Valley, CA: University Science Books, 2012.
[required]
David J. Griffiths, An Introduction to Quantum Mechanics (2nd Edition),
Harlow, UK: Pearson, 2004.
[recommended]
(supplemental): David A.B. Miller, Quantum Mechanics for Scientists and Engineers,
Cambridge, UK: Cambridge University Press, 2008.
[online]
(supplemental): G. Auletta, M. Fortunato, and G. Parisi, Quantum Mechanics,
Cambridge, UK: Cambridge University Press, 2009.
[online]
(supplemental): Bernd Thaller, Visual Quantum Mechanics: Selected Topics with ComputerGenerated Animations of Quantum-Mechanical Phenomena
New York: Springer-Verlag, 2000.
[online]
.
THEMATIC and HISTORICAL OVERVIEW:
"I think I can safely say that nobody understands quantum mechanics."
—Richard Feynman, The Character of Physical Law
Physics 137B is an upper-division, second-semester course (and indeed a required core course for
physics majors) building on Physics 137A and providing further introduction to and exploration of the
concepts, principles, procedures, tools, and elementary applications of quantum mechanics. Following
up on our work in Physics 137A, we take a closer look at some foundations, fundamentals, and
formalisms, introduce some further concepts and methods, and apply these to additional examples
involving particle, atomic, nuclear, molecular, crystalline, optical, and other systems, in preparation for
still more in-depth applications in specialized upper-division elective courses such as solid state
physics, atomic physics, quantum and nonlinear optics, and elementary particle physics.
In the spring of 1900, one of the most illustrious physicists of the 19th century, Lord Kelvin, delivered a
now-famous address in which he declared that only two small "clouds" obscured the "beauty and
clearness" of the worldview informed by the classical physics of Newton and Maxwell: the failure to
detect the luminiferous aether, and the inability of the equipartition principle to predict the spectrum of
blackbody radiation. As if right on cue, these small conceptual clouds were soon to portend the two
most tumultuous tempests encountered in our exploration of the physical world at least since
Copernicus — relativity theory and quantum mechanics, respectively. A century later, these dual
frameworks continue to undergird our understanding of nature and serve as the primary pillars
supporting much of our modern science and technology, while challenging deeply-entrenched
intuitions about the way we believed the world ought to behave. (In the middle part of the 20th
century, quantum mechanics and special relativity were unified within the formalism of quantum field
theory. The synthesis of quantum mechanics and general relativity remains the holy grail of 21st century
physics).
Quantum mechanics is an account of the dynamics and measurable properties of both matter and fields
at atomic and sub-atomic scales, superseding and in some sense subsuming the classical mechanics of
Galileo, Newton, Lagrange, and Hamilton, as well as the classical electromagnetism of Lorentz, Faraday
and Maxwell. Quantum theory is essential to the understanding of the very small and very cold, but is
also indispensable in apprehending the characteristics and even existence of the atoms making up
ordinary matter and engineered materials, the nature of chemistry and chemical reactions, and many
fundamental biological processes such as photosynthesis.
With more than one hundred years of diverse and detailed experimental success behind it, quantum
mechanics is the most far-reaching and successful theoretical edifice in all of natural science. One way
or another, it seems to encompass and account for virtually all of the everyday and esoteric things and
phenomena around us, from the very small—elementary particles—to the very large—neutron stars—and
everything in between, including atoms, molecules, liquids, and solids. It describes both matter and
light, and the interactions between them, with fantastic accuracy.
So it is all the more surprising that at is core, quantum theory seems far removed from and foreign to our
intuitions and everyday experience. Quantum theory might seem too strange to be believed were it not
for the fact that it accurately predicts so many phenomena that simply cannot be understood classically.
But Kelvin himself reminded us that "science is bound, by the everlasting vow of honor, to face fearlessly
every problem which can be fairly presented to it," and follow the facts wherever they may lead.
The facts seem to be leading us into a strange but beautiful — or perhaps strangely beautiful — quantum
world, where things are not quite what we expect based on our expectations and intuitions evolved in
our noisy, course-grained, macroscopic environment. Newton thought that light was made of particles,
but his rival Leibniz instead argued that light was some sort of wave. The debate persisted down the
decades. By the mid-to-late 19th century, with the maturation of physical optics and electromagnetic
theory, it seemed settled that light indeed behaved like a wave, but then in the early 20th century, in
considering phenomena such as the photoelectric and Compton effects, it was found that light
sometimes seemed to behave like a particle after all. Perhaps even more perplexing, in the early
twentieth century, it was then realized that matter, by then universally thought to be made up of
particles, sometimes behaved like a wave, confounding our intuitions about the working of the world,
but also holding out the hope that since both matter and light exhibited this so-called wave-particle
duality, both might be described in fundamentally similar ways at a microscopic level.
Soon physicists were forced to confront the unsettling truth that a microscopic "thing" sometimes
behaved something like a particle or beam of particles, and sometimes like an extended wave, apparently
depending on the sort of observations we make or experiment we chose to perform. Such wave-particle
duality is not really a question of "either/or" or "both/and," but rather "neither/nor." Microscopic things
really behave neither like classical particles, nor classical waves — nor like billiard balls, nor fluids, nor
a masses on a spring, nor any of the familiar idealized things studied in classical physics. For lack of a
better name, we call these bits of microscopic stuff quantum particles, but our everyday language rooted
in classical physics is apparently inadequate to capture their full logic. With a sly nod to Shakespeare,
David Mermin once quipped that quantum mechanics describes the "dreams that stuff is made of."
Facing the failure of classical physics to explain things like blackbody radiation, the photoelectric effect,
and the spectra and very stability of atoms, in the first years of the 20th century various scientists such as
Planck, Einstein, Bohr, Sommerfeld, and de Broglie attempted to contain the crisis with a number of
bold and insightful, if somewhat ad hoc, ideas now collected under the moniker "old quantum theory."
Despite much ingenuity, confusion seemed to outpace clarity until the 1920's, when a more complete
theoretical structure was supplied by the so-called "matrix mechanics" of Heisenberg, Born and Jordan,
and the alternative "wave mechanics" of Schrödinger. The notion of intrinsic particle spin was
incorporated by Pauli, Uhlenbeck, Goudsmit, and others, and shortly Schrödinger, Dirac, and von
Neumann were able to establish the equivalence of the matrix and wave mechanics, and helped cast the
now unified theory of "quantum mechanics" in its modern, Hilbert-space language.
In subsequent decades, the likes of Dirac, Jordan, Klein, Fock, Pauli, Bogoliubov, Schwinger,
Tomonoga, Feynman, Yang, Mills, and others reconciled quantum mechanics with special relativity
within quantum field theory, but that is a story for another class. At the same time, many physicists,
chemists, and electrical engineers continued to apply, extend, elaborate, and refine quantum theory,
and develop and apply important techniques for calculation and approximation, in order to understand
the implications and predictions of quantum mechanics for many diverse systems and materials.
Despite its theoretical elegance and unparalleled experimental successes, the full formalism of quantum
mechanics has in no way resolved all of the mystery. The things of our world simply behave on a small
scale like nothing with which we have intuition or experience in our lived world of large objects, and
hence it is difficult for anyone to wrap one's mind around the quantum universe. While virtually
universal consensus underlies the application of the theory to physical phenomena, controversy
continuous to surround the interpretation of the theory. Quantum mechanics' foundations seem as
shaky as its results are solid.
Quantum mechanics is essentially simple but subtle in its theoretical foundations, beautiful in its
mathematical structure, ubiquitous in applications, unambiguous and accurate in its observable
predictions, yet also deeply perplexing, challenging deeply-held convictions of objectivity, causality,
determinism, and continuity at the core of classical physics and everyday experience. We have
expectations and intuitions about how macroscopic objects should act, but things on the atomic-scale
just do not act that way, and our best theory of nature seems intrinsically disconnected from our
ordinary experience of objects with definite properties and trajectories. Even as quantum theory
elucidates, it also seems to elude and elide.
Einstein, who actually did more than any other individual to prod quantum thinking in its early days,
was never satisfied with quantum theory, for some time fearing it was logically inconsistent, then
continuing to argue that it must be incomplete and would be replaced ultimately by some more
fundamental, non-statistical theory. Other pioneers such as Schrödinger and de Broglie also recoiled
from the very thing they helped create, reminiscent perhaps of Victor Frankenstein and his monster.
Bohr on the other hand seemed to embrace a world-view suggested by quantum theory, and would
apply his philosophy of "complementarity" inspired by quantum mechanics to other areas, such as
psychology, sociology, and the nature of biological life.
Throughout the last century, even as physicists gained facility and confidence in applying quantum
mechanics, they still debated the meaning behind the equations. Because quantum mechanics seems so
foreign to our everyday experience of things ann their motions, no other physical theory has engendered
so much demand for introspection and interpretation. Attitudes range from a positivistic "stop-worryingand calculate" approach sometimes associated with the Copenhagen interpretation, to speculation that
quantum mechanics is telling us something deep and important about the nature of human
consciousness itself. Two approaches that are gaining currency in recent years are the Everett or "Many
Worlds" interpretation, which argues that the infamous "collapse of the wave function" is an illusion,
and the "Informational" or "Quantum Bayesian" sorts of interpretations, which emphasize that quantum
mechanics seems less a theory about photons and atoms than a method for optimal information
processing and inference making, that in some sense generalizes classical probability theory in
microscopic settings.
The struggle to make sense of quantum mechanics has been at times convoluted and arduous, and still
is not entirely free of controversy. To this day, if you want to start an argument amongst physicists, just
gather a few in one place and ask them about their pet interpretations of quantum mechanics. This
semester you will continue to cultivate your own understanding and interpretation, and can debate
persistently if politely with your peers.
Still, quantum mechanics is a true gem of human thought, and so, inspired by the "Four C's" of actual
diamonds: carat (size), cut, color, and clarity — fundamental characteristics which together determine
the all-important "fifth C," cost, or value, of the stone — we shall highlight the "Sixteen C's" of quantum
mechanics — thematic features which together help inform the character, cogency, consilience, and
comprehensibility, and hence value, of this theory:
Causality: to what extent is the future determined by the past? Do effects have causes? And do unique
causes lead to unique effects?
Chance versus determinism: on a related note, is nature fundamentally random or stochastic? How and
why exactly does quantum mechanics make probabilistic predictions? Are these probabilities intrinsic
and fundamental, or merely epistemic?
Certainty and uncertainty: in the realm of the microscopic, what can be know with certainty, and why?
What are the fundamental limitations on the accuracy with respect to which we can make predictions or
perform measurements? When can a system be said to possess certain properties?
Compatibility: on a related note, when can we know or measure things jointly or simultaneously?
Which measurements interfere with or preclude other measurements?
Commutativity and non-commutativity: and what turns out also to be a related question — what does it
mean for physical observers to be associated with "q"-numbers, where the order of multiplication matters,
instead of the usual "c"-numbers of classical physics, which can be multiplied together in any order?
Classicality and the correspondence principle: how is classical physics used to guide the choice of the
quantum description? And how does the classical limit emerge from the quantum mechanics?
Coherence and superposition: one of the most distinctive features of quantum mechanics is that it is
linear: the superposition of two quantum states is also a possible quantum state, and it is probability
amplitudes, not probabilities themselves, that are added together, leading to the possibility of
constructive or destructive interference between different possibilities.
Correlation and entanglement: quantum systems can also exhibit entanglement, a sort of correlation
which is evidently stronger than is allowed by any sensible classical theory. Even particles which are
widely separated in space must be described as part of a single, non-separable system.
Continuity versus clumpiness: quantum mechanics owes its name to the fact that properties like energy
or angular momentum which take on any of a continuous range of values classically, often assume only
quantized, or discrete, values according to quantum theory. When are physical observables quantized,
and what determines the allowed set of possible values?
Conservation and symmetry: as in classical mechanics, in quantum mechanics there are deep
connections between dynamical conservation laws (of things like energy or linear momentum or angular
momentum) and symmetries or invariances of the system under translations, rotations, etc. And in
quantum mechanics, the roles played by discrete symmetries (such as parity inversion, time reversal, or
charge conjugation) are even more prominent than in classical physics.
Contextuality and non-contextuality: how does a measurement result depend on the physical apparatus
and arrangement chosen to measure it? How, and why, do observables fail to have well-defined values
until we measure them? What is the relationship between the system and the measuring apparatus?
Completeness and incompleteness: Is quantum mechanics a complete theory of nature, or is it an
approximation to something with more ontological assertiveness, a so-called hidden variable theory? Is
quantum mechanical probability all there is, or is there a deeper description?
Collapse: does the wave function collapse at all? If so, how, when, and why? Is collapse a physical,
mental, or merely mathematical process? What might this mean for the nature of reality?
Cardinality and countability: the formalism of quantum mechanics is simplest when dealing with finitedimensional vector spaces, and therefore with observables taking on values from a finite, discrete set of
possibilities. Much of the structure carries over to the more typical case involving vector spaces with
countably-infinite dimensions, but some additional mathematical care may be needed, particularly when
dealing with observables that can take on values from a continuous range of possibilities. Some of this
mathematically i-dotting and t-crossing can be saved for more advanced graduate classes, but we will
need to confront a few results from functional analysis, which is the generalization of linear algebra to
these infinite dimensional spaces. Some pitfalls appear and surprises ensue.
Computation and information: what limitations are imposed or opportunities afforded on information
gathering and processing by quantum as compared to classical physics? How do classical and quantum
information differ?
Complementarity: Bohr stressed that (i) scientists need to resort to classical language to communicate the
setup and results of any measurement, and (ii) that the non-zero value of the quantum of action
(Planck's constant) implies the impossibility of any sharp or absolute separation between the behavior of
microscopic objects and their interaction with the macroscopic measuring instruments that serve to
define the conditions under which the phenomena can be said to appear. As a result, evidence
acquired under different experimental contexts or conditions cannot be synthesized into one holistic
classical picture, but serves to illuminate complementary features of the system. For example,
complementary pairs of concepts include position and momentum, components of spin along
orthogonal directions, and wave-like versus particle-like behavior, or more specifically "which-path"
information versus interference fringe visibility.
We should definitely keep the "16-C" quantum conceptual categories in mind as we proceed, with both
curiosity and caution.
Finally, in furthering our exploration the physical world, this course will rely heavily on various
mathematical tools, techniques, and formalisms, a few of which may be new to you. As Galileo himself
wrote, “Natural Philosophy is written in that great book which lies ever before our eyes — I mean the
Universe — but we cannot understand it if we do not first learn the language and grasp the symbols, in
which it is written. It is written in the language of mathematics, … without whose help it is impossible
to comprehend a single word of it, and without which one wanders in vain through a dark labyrinth.”
A few centuries later, Feynman would concur: "To those who do not know mathematics it is difficult to
get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about
nature, to appreciate nature, it is necessary to understand the language that she speaks in."
Mathematics provides a natural quantitative and symbolic language for physics as well as powerful
practical tools for tackling specific type of problems, but mathematical formalism itself is intended to
enhance, not replace, our physical understanding and intuition. We should neither be so intimidated
by nor enamored with the math that we lose sight of the physical content, even if that content in the
case of quantum mechanics does not always conform to our intuitions. “Any mathematical formalism
must keep the physical problem clearly in focus,” advised Maxwell. We shall try to build both physical
intuition and analytic facility.
Over the course of the semester, we hope that you will enjoy your continuing and increasingly in-depth
look at these fascinating if challenging topics, and gain: a working understanding of key concepts and
themes in quantum theory; insight into not just the what but some of the how and why of the
underlying principles, some facility with the associated conceptual, logical, mathematical, and
experimental tools and problem-solving techniques; an appreciation for the great theoretical ideas and
great experiments that drove progress in quantum physics; an awareness of how this material relates both
to your previous studies and to the workings of the natural and manufactured world around you; and a
solid preparation for further upper-division or graduate study in physics, chemistry, biophysics, materials
science, or engineering.
Also, after some of the details inevitably fade, we hope you are left with a deeper sense, more generally,
of how one can “think like a physicist" — the combination of rationalism and empiricism, rigor and
creativity, abstraction and practicality, simplicity and complexity, mathematical and non-mathematical
expression, collective and individual effort, that characterizes our approach to critical-thinking, sensemaking, and problem-solving.
BACKGROUND and PREPARATION
We shall definitely presume knowledge of classical mechanics at the level of Physics 7A,
electromagnetism and thermal physics at the level of Physics 7B, and optics and elementary quantum
theory at the level of Physics 7C. On one or two occasions, we may make use of a few simple results
from the theory of special relativity, which you may or may not have studied in Physics 7C, but do not
worry if this is new.
Various high-level mathematical tools, particularly involving linear algebra, differential equations, and a
bit of group theory, functional analysis, and orthogonal polynomials and special functions, will be
introduced or reviewed as needed, but we will definitely presume some working familiarity with:
complex arithmetic and algebra; differential and integral calculus of one variable; functional limits and
Taylor expansions; simple first-order and second-order differential equations; partial differentiation,
multiple integration, a bit of probability theory, and perhaps most importantly, basic linear algebra
(inner products, matrix multiplication and all of that).
As Physics 137B is a continuation of Physics 137A, we shall certainly build upon rather than merely
recapitulate much of the material covered during the first semester. But Physics 137A syllabi vary from
semester to semester and professor to professor, and my version of the course perhaps introduced
students to both greater depth and breadth of material than most, so we will review and refine certain
important concepts and tools briefly as needed, and if anything does not sound familiar, please speak to
me as soon as possible.
So If you are already looking for things to do, reviewing some mathematical and physical topics from
previous courses before or during the first weeks of the semester may be useful.
Although not required by us or by the physics department, taking Physics 105 (classical mechanics), and
also perhaps Physics 110A (electromagnetism), before taking Physics 137 would likely enrich your
appreciation of quantum mechanics and facilitate your understanding and mastery of this material.
Quantum mechanics is conceptually radical in many ways, but sometimes beginning students receive an
exaggerated sense of the nature of its break with classical mechanics and an inaccurate impression of
exactly where the true novelty lies, because Physics 137 is also the first place they learn about
Hamiltonians, canonical momentum, Noether's Theorem, etc., all theoretical constructs which actually
play key roles in classical mechanics as well.
In addition, for those seeing upper-division quantum physics before upper-division classical physics,
many mathematical tasks, such as finding eigenvalues and eigenvectors, performing Fourier transforms,
solving boundary-value problems, complex contour integration, etc, are demanded for the first time in
the quantum setting, and students can become a bit overwhelmed with all the new mathematics and can
tend to lose sight of the genuinely new physics.
However, we will not presume background from Physics 105 or 110 in general, but may briefly
introduce a bit of classical mechanics or electromagnetism beyond the Physics 7 level, as needed, and
will discuss and illustrate the use of various mathematical tools at a level possibly beyond your previous
math or physics courses. And if you are taking Physics 137 first, do not fret, as subsequently your
appreciation of courses like Physics 105 will be enhanced as you spot retroactively the connections to
quantum mechanics.
COURSE SYLLABUS
Please see the separate Schedule and Syllabus document posted online (in the Resources section on our
bCourses website) for a more detailed, if still tentative, course syllabus and weekly schedule. This is our
first educated guess at our timeline, but may be revised as we proceed, based on our assessment and
your questions and feedback. Be sure to pay attention to any announcements and suggested reading
mentioned in class or on the weekly homework assignments to get an up-to-date sense of where we are
and where we are headed topically.
We shall try to split our time between explicating the abstract formalism and mathematical tools,
examining more concrete physical examples, extending our intuition for the behavior of the quantum
state (and perhaps also the microscopic system it describes), and exploring some questions regarding the
interpretations and foundations of the theory. We will often rely on the very useful Dirac bracket
notation, but will also make liberal use of standard matrix notation, Pauli spinors, or position-space or
momentum-space wavefunctions.
After a few logistical preliminaries, and a quick conceptual and historical overview to orient ourselves
and highlight several recurrent themes, we will briefly review the principal axioms and formalism of
quantum mechanics. Then we will look more carefully at the quantum theory of measurement, and the
so-called "Measurement Problem," segueing into an overview of a few of the most influential
interpretations of quantum mechanics and how these interpretive structures deal with the measurement
problem and other conceptual challenges, and an exploration of some of the famous "paradoxes" and
puzzles of quantum theory, involving measurement, superposition, uncertainty, wave-particle duality,
and especially quantum entanglement.
Next, we will engage in a bit of a refresher on the theory of angular momentum, and extend these ideas
by analogy to other special unitary groups like isospin and color symmetries in particle physics.
We will then look in more detail at time-independent approximation methods, particularly nondegenerate and degenerate perturbation theory, focusing on spin systems and hydrogenic atoms. We
will consider the most important perturbations to the Coulombic energy levels of the hydrogen atom,
known collectively as fine structure and hyperfine structure, as well as the effects of external static
magnetic and electric fields on the spectrum, known as the Zeeman effect and Stark effect, respectively.
Then, we will turn to the analysis of systems containing multiple indistinguishable particles, the
associated symmetrization/anti-symmetrization postulate, and explore fundamental differences between
identical fermions and bosons. We may also look at Fock space and the so-called second-quantization
formalism, which is a powerful framework and notation with which to treat systems of identical particles
in quantum theory.
As a prototypical example of a multi-electron system, we will first look at the Helium atom, primarily via
variational approximations, and then more broadly, if briefly, explore further along the periodic table,
motivating the so-called Hund's rules.
After spring recess, we will turn to time-dependent approximation methods, particularly perturbation
theory, focusing on magnetic resonance in spin systems, unstable particle decays, and electric and
magnetic dipole transitions in atomic systems, and discuss the notion of selection rules and the famous
Fermi's golden rule.
Then we will study scattering theory, primarily time-independent scattering from central potentials. Most
of what we know about sub-atomic physics has been obtained via scattering experiments. We will
introduce the total and differential cross section, scattering length and scattering phase shift, and focus
on two prevalent approximation techniques, the Born approximation and the partial wave expansion.
We will next briefly look at some applications of quantum mechanics to molecular physics (rotovibrational levels, the Morse potential, Born-Oppenheimer approximation, ortho-hydrogen and parahydrogen), and solids (crystal symmetries and Bloch's theorem), before turning to a brief introduction to
quantum optics. Finally, we will take a quick tour of the relatively new field of quantum computation.
Throughout, we will endeavor to cultivate simultaneously a careful conceptual understanding, a facility
with fundamental mathematical machinery, and familiarity with important models and fundamental
experimental examples and systems.
Because of Berkeley’s revised calendar, with a shortened instruction period making room for the “RRR”
week, several interesting but advanced sub-topics, such as the Hartree-Fock, Thomas-Fermi, and densityfunctional schemes for many-electron atoms, the Dirac equation and relativistic quantum mechanics,
quantum electrodynamics and spontaneous emission, path integral methods, Wigner and other quasidistribution functions, multi-dimensional WKB theory, etc., will be saved for your graduate classes, to
make room for important modern topics like Bell's Theorem and quantum computation.
We will mostly spend RRR week reviewing material and doing practice problems in preparation for the
final examination, but we will use one day to explore an advanced topic just for fun (not tested) and
general interest. The class will be polled later in the semester; but possible topics are mentioned below.
COURSE ORGANIZATION, REQUIREMENTS, and GRADING POLICIES
Lectures:
While there is no official contribution to your course grade, you are responsible for all material and
methods covered in lectures unless otherwise noted, regardless of whether it is discussed explicitly in
the textbooks. At least lectures do not occur at 8 am — at worst we might get a little hungry around
breakfast time (lecture 2) or dinner time (lecture 3), but if there are sufficient volunteers, we can plan for
a “Snack Friday,” which has been a tradition in my courses.
Lectures provide an opportunity for us to elaborate, explicate, and explore together the course material,
hopefully see some fun animations and demonstrations, and of course most importantly seek
clarifications and ask questions in a dynamic, interactive way. You are definitely encouraged to ask
questions at any time in lecture — if you are confused by something, or interested in hearing more
about something, someone else probably is too.
We will also present a bit of context and history, to give you some appreciation for the key figures in our
drama, the great experiments and theoretical ideas, and how they arose. I believe learning a bit about
the development and context helps to clarify the material and deepen your appreciation and
understanding of it. This is perhaps particularly important in quantum mechanics, where it can help to
look carefully at some of the experimental facts that compelled physicists to take seriously this radical
and counterintuitive theory.
I also believe it is important for students to realize that physics is not all about canned problems with
answers in the back of a book—that science is accomplished by real people, who first have to perceive
even which questions to ask, and then tentatively grope forward toward the uncertain answers. Of
course, with the benefit of hindsight, we do not have to slavishly follow the historical arc of the subject.
We can save time by glossing over some of the inevitable false leads and missteps, and the inspired if
incomplete ideas that gradually brought some clarity to a subtle subject.
Reading:
While there is also no official contribution to your grade, we shall expect you to keep up with all the
required reading, listed in the syllabus as well as on each week’s homework assignment. Material
discussed in the assigned reading may appear on homework or exams even if not explicitly covered in
lectures.
All required reading will be from our required textbook or else posted or linked online. We will also list
recommended reading that we think could enhance your understanding of certain topics, and
suggested reading that may be helpful, or at least interesting, for students wishing to learn about certain
topics in greater depth. Specific relevant readings may be mentioned in class, but always at the
beginning of each week's homework assignment.
There is really no substitute for careful, deliberate, and active reading (and re-reading!) in studying
physics, and that takes time. In a perfect world, you should try to complete the reading before the
material is covered in lecture, and bring up questions or points of confusion during lecture, then re-read
after lecture but before or while attempting homework problems to solidify your understanding. This
gives you a chance to use the potential for feedback and interaction possible in lecture to discuss those
aspects of the textbook presentation which were less than clear.
To get the most from your time spent reading, reflect carefully about what you are seeing, constantly ask
yourself questions, make connections with what you already know, push and stretch your
comprehension, and have paper and pencil handy to work through some of the calculations and try out
examples as you go through the text. Simply following along passively will not work as well.
For Physics 137A last semester, I decided to experiment with a new book, A Modern Approach to
Quantum Mechanics, by John S. Townsend, who teaches at Harvey Mudd. It received somewhat mixed
reviews from students, but in the interests of maintaining pedagogical continuity and avoiding textbook
sticker shock, I am going to continue using Townsend as our primary text for Physics 137B. For those of
you who used and enjoyed Griffiths last semester, do not despair, as we will make use that as a
recommended text. Perhaps you all can find colleagues with whom to share or swap these books.
In addition, I have also chosen some supplementary texts — which are freely (and legally) available
online for Berkeley students, so that you do not have to pay for yet another textbook. Each text has its
strengths and weaknesses, and additional reading will be suggested from time to time to round out the
presentation and supplement our main texts. Needless to say, we will not read every chapter in every
book. David Miller's Quantum Mechanics for Scientists and Engineers will provide a useful alternate
look at many of the topics in Townsend or Griffiths, while offering introductions to a few topics they
omit. Another new-ish text, Quantum Mechanics by G. Auletta, M. Fortunato, and G. Parisi, treats many
recent developments in quantum measurement theory and quantum information theory. We will
occasionally use Visual Quantum Mechanics by Bernd Thaller for some illuminating visualizations and
animations. The accompanying software has been made available to us courtesy of the author.
We will also distribute or link to various lecture notes from time to time on bSpace, and post other
notes, commentaries, chapters, or papers. These readings will all be intended to supplement, not
supplant, the required textbook.
Many of the readings posted on bCourses will contain copyrighted material, and are available
electronically to members of the UC Berkeley academic community only through special agreements
with the publishers. Please respect the intellectual property of other scholars, and do not re-distribute
these materials to anyone outside of our class.
Discussion Sections:
All students are required to enroll in one of the two discussion sections associated with the
corresponding lecture, and are highly encouraged to attend regularly and participate fully in the
discussions. You may attend any of the four discussion sections, provided there are seats available..
In section, You can pose questions to us about the homework or other areas of interest or concern. We
may give some tutorials to supplement the regular lectures, students may present solutions to their peers
(see below), and you will work together as a class or in small groups on examples and problems, under
our guidance.
Sections will be mostly question-driven and problem-based, and will provide a forum for us to work
together to put into practice material from the readings and lectures. Just like learning how to play a
sport like tennis, or a musical instrument such as the saxophone, learning how to do physics requires a
lot of practice. To benefit most from the discussion sections, some preliminary reading and grappling
with the week’s homework may be useful before you arrive, but the most important thing is to attend
regularly and be prepared to engage with the material and with your fellow students.
Lecture offers insufficient time to go through many examples in depth, so we regard discussion section
as an essential part of the course, giving students the opportunity to ask questions, discuss ideas, and
think about problems in an active way. While the lectures will tend to be a bit ore conceptual and
theoretical, in discussion section, we will work through some examples, and reinforce some important
tools and approaches, illustrate calculational and problem-solving tips, and point out common mistakes
and potential pitfalls. Remember that merely watching the instructor solve a problem on the board is
not an effective or efficient way to learn physics, so we will give you some time to discuss the problems
with your peers as well.
Office Hours:
Office hours are of course optional, but everyone is welcome and encouraged to come. Even if you do
not have a specific question in mind, you may benefit from the discussion, or be inspired by others'
enquiries. Based on some suggestions from last semester, I will also experiment with some "virtual" office
hours, where I will be available to answer questions online.
If you wish to discuss your grades or speak privately, we will probably need to schedule an individual
appointment.
RRR Week:
We expect to meet for both lectures and discussion sections during RRR week. Lectures will include a
combination of review and practice, as well as one topic purely for fun and enrichment — it will not be
tested. Currently I am thinking about one of the following:
Towards relativistic quantum mechanics: the Dirac and Klein-Gordon equations
Supersymmetry, integrability, and shape invariant potentials
Open quantum systems and decoherence
"Pictures" of quantum mechanics: the Heisenberg, Schrödinger, Dirac, Feynman, and Bohm formulations
Computational quantum mechanics.
We will vote on a topic later in the semester.
Homework:
Problem sets will be assigned on an approximately weekly basis, approximately one week in advance.
Assignments will be posted electronically, and will be due in the box labeled "Physics 137B lectures
2&3" in 251 LeConte on the following Friday by 6:00 pm, unless otherwise noted. Each assignment
will include optional practice problems in addition to required problems. Some of these practice
problems will just provide extra opportunities to explore the material and solidify your skills, and others
will be problems considered to be especially challenging, or to cover supplementary subjects. Ideally,
homework will explore material covered during the previous week’s lectures and reading, but with our
tight schedule this will not always be possible in practice.
You are welcome, even encouraged, to use computational environments such as Mathematica or
MATLAB to assist with algebra or integration, making series expansions, plotting, exploring solutions to
differential equations, etc.—just acknowledge resources where appropriate in your solutions.
Grappling with challenging homework is at the heart of the educational experience, and is essential to
solidifying your own understanding of the course material and to developing your own critical-thinking
and problem-solving skills. As we see it, the purposes of the homework assignments are multifold: to
give you specific practice on the material covered in lectures, discussions, and the readings, to help you
better understand the concepts and become more facile with the calculations; to provide you and us
with meaningful feedback on your comprehension, revealing what you are finding difficult or easy, and
what we may be communicating effectively or not; and to improve your general skills of thinking clearly
and carefully about physics, of creative and technical problem-solving within physics, and effective
communication to others of your understanding of physics.
Working earnestly on the homework is one of the best ways to learn the material and prepare for the
exams. That being said, what makes a good homework problem is not necessarily what makes a good
in-class exam problem, so exam problems may not be exactly like homework problems. Homework
problems serve to reinforce, integrate, develop, or extend your understanding, while exams are intended
primarily to measure or reflect your knowledge applied in slightly novel situations.
We will grade the homework with these goals in mind. Specifically, on each graded homework
problem, 50%, but only 50%, of your score will be directly based on how well and completely you
solved the problem, using a holistic grading scale. An additional 30% of your score will be based on
the clarity, organization, and effectiveness of your written presentation and explanations, and an
additional 20% will be based on your assessment and analysis of the problem — a brief discussion as to
whether your answer makes sense, and why, or what you learned from it, or how it connects to other
things you have learned in this class or in other physics classes. In this way we hope to encourage you
to use the homework as a means to improve your skills of critical thinking and problem solving,
analytical reasoning, and cogent writing.
The GSI’s time is best spent talking with you in person or online, and doing problems with you, rather
than spending countless hours assessing the minutiae of your problem sets. Therefore, you will not find
a lot of red ink on your individual assignments, and each week he may grade in detail only a
representative sub-sample of the required problems, chosen at the discretion of the GSI or me. Of
course, you do not know which problems will be graded, so you should try to complete all the required
problems. To help mitigate some sampling error, each assignment’s score will also include some points
based on our assessment of the overall completeness of your submission. Success in a class like this is
typically highly correlated with conscientious effort put into the homework.
For more details on this grading scheme, see the Homework Grading Philosophy, Rubric, and Feedback
Policies document posted on bCourses.
You do not have to turn in any of the optional practice problems, but you are encouraged to look at
them if you have the time. We will post detailed solutions online for all of the required problems, so
you can see what we had in mind, compare with your own work, and ensure that you understand all
the assigned problems, not just those that were graded in detail.
Your homework score H (expressed as a percentage of the maximum points possible) will be based on a
weighted average of your homework percentages, after your lowest-performing homework is dropped,
using specified weights reflecting the estimated length and/or difficulty of the assignment (not just the
raw number of total problems or graded problems). Otherwise, no late homework will be accepted for
credit without prior consent of the instructor (me) or your GSI.
Generally, we tend to be disinclined to accept late homework solutions from students, except for
reasons of official university activities, unavoidable medical problem, graduate school visits, or scientific
conferences.
Online Presence:
Homework assignments, solutions, handouts, notes, suggested reading, some fun applets or videos and
interesting websites, etc., will all be posted on our main website hosted on bCourses. Important
announcements will be made in class and on bCourses, which should also send out email notifications
when assignments or other important handouts are posted. You should check our site regularly for
additions or updates. Our Courses site also has chat and forum capabilities will allow you to interact
online, but we have also set up messaging through piazza.com, so that students can post questions and
comments on homework or other subjects, arrange study groups, etc., there if desired. In past semesters,
students have also set up Facebook pages. Please be inclusive if you do, and invite all students to join.
Examinations:
Midterms:
There will be two timed, closed-book “midterms” [sic], tentatively planned to be administered in the
evening to allow for somewhat less time pressure.
Midterm #1 (expected during the second week of October) will cover the basic formalism applied to
finite-dimensional Hilbert spaces. Midterm #2 (expected during the second week of November) will
cover topics discussed since the first midterm, particularly observables with continuous spectra, various
systems moving in one spatial dimension, and general features of orbital and total angular momentum.
—but obviously must also build on foundational material.
To each midterm, you are allowed to bring an electronic calculator without wireless capabilities, and
one double-sided, 8.5" X 11" sheet of handwritten notes.
You should also bring a pen or pencil (we recommend pencils) and a blank, large-format bluebook. A
straightedge/ruler can be useful fro sketching graphs or diagrams. Quiet snacks or drinks are allowed.
On exams, we will not grade explicitly on presentation as in the homework, but to maximize your
chances at partial credit, it is of course helpful to offer concise explanations for what you are doing, and
be as clear and organized as possible within the constraints of a timed exam. Whenever a "what?" or a
"when?" is asked in physics, keep in mind that, implicitly, we are also asking "how?" and why?”
Each part of each problem on each midterm will be graded holistically, and your midterm scores M1
and M2 will reflect the points earned as a percentage of the maximum number of points possible.
Final Exam:
A comprehensive, cumulative, closed-book, final exam will be given during the scheduled exam session
Actually, you will be given a full three hours to complete the exam starting so expect that the exam will
run a few minutes late.
You will be allowed an electronic calculator (without wireless capabilities) and three double-sided 8.5"
X 11" pages of handwritten notes. You must bring pencils or pens and one or two blank, large-format
bluebooks. A straightedge may also be useful.
Everything covered in the class (in lecture, discussion, required reading, or required homework) is fair
game on the final, unless otherwise indicated, although the exam will likely tend to emphasize
fundamental concepts and themes stressed repeatedly throughout the semester, and may include in
somewhat excess proportion any material covered after the second midterm.
Each part of each problem on the final will be graded holistically, and your final exam score F will
reflect the points earned as a percentage of the maximum number of points possible.
“Re-Grade” Requests
When we return your exams or assignments in discussion section, please look it over together with the
solutions posted online, and ask one of us if you have any questions. Any errors of accounting or
arithmetic (e.g., not adding up your points correctly), should be brought to our attention immediately,
and any such mistakes discovered by you and brought to our attention will never lower your grade.
Any disagreements of interpretation can be discussed with us. Actual requests to re-evaluate a response
to an exam question may be considered, but keep in mind that when you ask us to take a second look
and re-judge your performance, we will look critically at the entire exam, and your score can go down as
easily as up.
Exam Score:
Your total exam score X will be calculated as follows:
First, your Midterm Score M will be calculated as the weighted average of your two midterm
percentages, such that your higher-scoring exam counts for twice as much as your lower-scoring exam:
M=
1
3
min[M1 , M2 ] +
2
3
max[M1 , M2 ] ,
giving you the opportunity to make up some points on one midterm if you do less well on the other.
Your exam score X will then be calculated as the following weighted sum of your midterm score M and
your final exam score F:
X = 35 F + 13 M +
1
15
max[F, M ] ,
meaning your final exam will contribute 2.0 as much to your exam grade as your combined midterms if
you score better on the final exam, but only 1.5 times as much otherwise.
These nonlinear weightings are intended to alleviate a bit of inevitable exam anxiety and to offer you a
little extra breathing room on any one assignment, or an opportunity to make up for earlier stumbles.
These weightings can only improve your numerical score. Our hope is that we can spend our energies
exploring cool physics, and not worrying over much about point totals.
Optional Enrichment Activity:
In order to take some pressure off of you during in-class exams, and hopefully to enrich your
understanding of quantum mechanics and its role in understanding the universe, we offer you an
opportunity (but not an obligation) to replace some of your exam points with points earned on an
optional enrichment activity.
This is intended to give you the opportunity to explore a specific topic of interest to you in somewhat
greater depth, to see how important quantum mechanics has become in essentially all of contemporary
physics and much modern technology, and alleviate some pressure viz the in-class exams. It can only
help your grade, and omitting it cannot actually lower your grade, so if you feel too busy to complete it,
you will not be penalized, only your exams scores will not be tempered. Hopefully you will enjoy
exploring some aspect of classical mechanics on your own. If you choose a technical topic, it may also
help you in preparing for the final exam.
Each participating student will be assigned a holistic enrichment activity score A, which can replace up
to 8% of your exam points, if higher than the latter. Again, this activity is optional in that you will not
be penalized if you choose not to do it, but it can definitely help to boost your overall class score if you
do a reasonable job. Unlike standard extra credit, it does not add to your exam points, or otherwise
automatically lower your class score in absolute or comparative terms if you choose not to participate,
but it could be a relatively painless and even fun way to improve your score and obviate some stress.
Your optional section activity score A, expressed as a percentage of the maximum points possible, will
replace up to 8% of your exam score, and be factored into your final course score as described below,
in a way that will not penalize you if you choose not to do it, but can definitely help to boost your
overall class score if you do a halfway reasonable job. An 8% contribution may not sound like a lot,
but this is often enough to boost your grade by a half-step — for example from a B+ to an A–.
For any purely written assignments, your score will be based 50% on accuracy and completeness of
content, and 50% of clarity and style of communication, and expressed as a percentage of the maximum
points possible. The written assignment should be about 800 – 1800 words, and will be due in PDF
format via email attachment on the last day of RRR week. The section presentation option will include
both an oral and written sub-score, as discussed below.
Option A: Book Review
You may read a technical or semi-popular book of your own choosing, and write a short review or
critique of the book, as if for American Scientist, Physics Today, Scientific American, the American Journal
of Physics, or Physics Education, or similar pedagogical or general interest journal. Was the organization
of the book effective? Was the presentation clear? Were its arguments persuasive? Was the book
enjoyable or interesting, and why? Was the physics correct? Were important topics omitted? For what
level of readers, or what type of class, might the book be useful?
The book can be, for example, another textbook on quantum mechanics, a semi-popular or popular
account of related physics, or a biography of some key player in our drama, such as Planck, Einstein,
Bohr, Schrödinger, Heisenberg, Dirac, von Neumann, Bohm, Feynman, etc.
Option B: Puzzling Problem
American Journal of Physics and other pedagogical journals often include in-depth analyses of
particularly subtle, puzzling, counterintuitive, or controversial textbook physics problems in quantum
mechanics. Read a few of these articles to get a sense of how such questions are approached, then write
up a brief analysis of such a problem, as if it were to be submitted to AJP.
Option C: Mr. Tompkins at the Exploratorium
Mr. Tompkins is a character introduced by physicist George Gamow in the 1940s in a series of books in
which the counterintuitive results of special relativity and quantum mechanics become apparent in
everyday life (in effect, by envisioning changing the value of the speed of light and/or Planck's
constant). Imagine Mr Tompkins visits the San Francisco Exploratorium, with its fantastic collection of
hands-on demonstrations and exhibits, but in an alternate universe in which Planck's constant is much,
much bigger. Analyze and describe how one of the demonstrations would behave differently. Doing
this with complete consistency may not be possible — after all, our eyes and ears would change size as
well, as would the atoms of which we are constituted, and various forms of everyday matter might
become unstable. But do your best, in the sprit of the original books, or else explain why the
phenomena would no longer be possible at all. (You might also find a suitable exhibit at the Lawrence
Hall of Science, the Chabot Science Center, or, if you happen to find yourself traveling, at one of the
other science museums around the continent, such as those in San Diego, Los Angeles, Seattle,
Portland, Anchorage, Denver, Chicago, Columbus, St. Paul, Pittsburg, Boston, New York City, etc.)
Option D: The Quantum Century
Quantum mechanics continues to perplex and intrigue working scientists as well as other intellectuals
and the broader public. Whether understood or misunderstood, quantum mechanics has often captured
the imagination of authors and artists, playwrights and philosophers, and others. Choose a piece of
either “popular” or “high” culture—a book, play, film, TV show, comic book, album, etc., that involves
quantum mechanics in some way—and analyze carefully what role the physics plays, and how they get
the physics right or wrong.
Option E: Quantum Weirdness a la Wikipedia
Try to add an entry to Wikipedia on some quantum mechanical topic. You may want to start with one
of the quantum physics "stubs" listed here:
http://en.wikipedia.org/wiki/Category:Quantum_physics_stubs,
while information on how to go about submitting an article can be found here:
http://en.wikipedia.org/wiki/Wikipedia:Article_wizard
if you are unfamiliar with the process. Be sure to properly attribute your paper-based or online sources,
and remember to email me a pdf copy even if your article is not accepted.
Option F: Attempt an Applet
For those of you with computational interests, try creating an online educational applet illustrating some
aspect of quantum mechanics. Do some internet sleuthing first, to avoid re-inventing the wheel, but
there seems to be plenty of room to either branch out with new examples or improve on the usability or
visual appeal of existing applets. Provide a working applet as well as a brief "instruction manual" and
discussion of the illustrated physics.
Option G: Interesting Interpretation
Perhaps in no other area of physics have both working scientists and philosophers felt so strongly the
need to offer some interpretation of the theory on top of its mathematical prescription. Practically
everyone has their favorite interpretation — or two or three. Choose one interpretation, and briefly
summarize its main features, and strengths and weaknesses. Compare and contrast it with at least one
competing interpretation.
Option H: Peer Presentation
Learning physics requires more than passively listening to lectures or reading textbooks. Exactly like
learning to play a sport or a musical instrument, it requires practice, more practice, and active
engagement. With large lectures and sections, it is difficult to give you the opportunities for the kinds of
active, peer-driven learning that education research shows are most effective, but we are going to
experiment with one idea in this direction. During the first 15 minutes of discussion section, a student
or pair of students will discuss and present to the class a solution to one of the previous week’s
homework problems and take questions from the audience.
Here is how it will work. Individual students or pairs of students will sign up in advance for available
slots. (We should have opportunities for every student who is interested to participate). The week
before, the student(s) should discuss with us and agree upon which problem is to be tackled. Students
should photocopy their relevant work before turning it in that Friday, using their write-ups as a starting
point for more extensive notes for their blackboard presentation in section the following week. Based
on their notes and perhaps questions and comments during their presentation and consultation with the
instructors, students will write up and submit a detailed solution and analysis by the end of the week,
which will be shared with the class after any needed further corrections are made. You should plan out
your presentation in advance, and presentations should last about 15 minutes.
Each student will be assigned a holistic grade based on both the in-section presentation (50%) and
write-up (50%) sub-scores. If you are working in pairs, both students should contribute. As long as we
feel you made a good effort and put in a respectable amount of time, grading should be reasonably
generous.
Further Grading Policies and Philosophies:
To receive credit in this course, you must be enrolled in a lecture and in one of the corresponding
discussion sections. Do NOT take the course if you cannot attend the scheduled final exam for any
reason other than official university business or excused religious activities.
If, due to some severe illness, family emergency, or official university or scientific activity, you cannot
make one of the scheduled exam times, please contact us before the exam if at all possible. We will be
reluctant to offer opportunities for make-up exams after the fact, except in the most extenuating
circumstances, but for excused absences we may shift weight to other exams.
Holistic Grading:
Homework and exam problems (or distinct parts of longer problems), the optional assignment, etc., will
all be graded “holistically,” where we assign you positive points based on our overall, course-grained
assessment of your performance on, and demonstrated understanding of, a given problem. This is
contrast to the traditional subtractive, or "nickel-and-dime" approach, where you are penalized points
here and there for various mistakes or errors of commission or omission. While the description as
“holistic” might strike you as vague and new-age-ish, much education research shows that this approach
is actually more fair and more reproducible, less prone to random drifts in grading standards as the
instructors grow tired, or to false claims of precision far beyond any reasonable psychometric
justification.
So on your individual assignments you will not see a lot of red ink and fine print offering detailed
explanations of what went wrong, and why. It is your responsibility to look at your assignment and
compare it to the solutions posted online, where we will offer more detailed explanations, derivations,
and calculations. If you still do not understand the problem, or what you did right and wrong, come
and talk to one of us.
Each problem (or possibly part of a longer problem) will therefore receive a score from zero (0) to five (5)
points, typically based on the following 5-point holistic grading scale:
5 = student shows essential mastery of the material and answers all aspects of the question
with essentially no meaningful errors;
4 = student shows good understanding, with some minor or moderate errors or mistakes or
omissions in execution;
3 = student shows reasonable understanding, but with a significant error or omission or major
conceptual misunderstanding, or many minor ones;
2 = student shows some partial understanding, but with notable errors or several large
omissions or major conceptual misunderstandings;
1 = student attempted the problem but shows heavily flawed understanding or execution, or
omits a significant portion of the explanation or write-up;
0 = student made virtually no meaningful attempt to solve the problem.
You can still receive five points even if your answer is not perfect, but will receive zero points only if
you essentially include nothing at all relevant. Sketch a diagram, tell us what is known and unknown,
or offer any other meaningful attempt at starting a problem, and you can at least earn one point.
Overall Score:
You overall numerical score S for the course will involve a weighted average of your homework score H,
exam score X, and possibly your optional section activity score A.
First, the exam score will be augmented by the enrichment activity score A if this would help your grade:
X� =
23
25 X
+
2
25
max[X, A] ,
and then this adjusted exam score is combined with your homework score as follows:
S=
�
9
20 X
+
9
20 H
+
1
10
max[X � , H] ,
meaning that the exam/homework split is 55%/45% if you score better on the (adjusted) exams than on
homework, but 45%/55% if you do better on homework compared to (adjusted) exams.
These nonlinear formulae may sound complicated, but they are merely designed to weigh somewhat
more heavily those assignments on which you perform best, and encourage us to avoid getting too
distracted by numerical grades so we can focus on the physics.
Letter Grades:
Your course letter grade G will be based on your total numerical score S. In assigning these letter grades,
I do not believe in grade cutoffs based on percentages fixed a priori, (e.g., where an A is strictly 90% or
above, a B is 80%, etc.), because it is virtually impossible to calibrate reasonable expectations and to
assess the length and difficulty of assignments without looking critically at the performance of the class
as a whole. Nor do I believe in pre-arranged percentiles (i.e., "grading on a curve”), where a fixed
fraction of the class necessarily receives A’s, B’s, etc., based on students’ relative ranking but without
regard to their absolute performance. In principle, your grade ought to reflect how well you learned the
material and demonstrated and communicated your understanding to us, not on how the person sitting
next to you might have scored. But in practice, how everyone actually did does inform how individuals
performed. So we do both consider the nature of the various assignments and look to how the class as
a whole performed on the various assignments in order to assess in a reasonably fair way what
constitutes excellent, good, and acceptable performance, etc., and then assign corresponding numerical
cutoffs mapping numerical scores to letter grades.
At UC Berkeley, the officially-stated meaning of the letter grades in terms of academic performance is as
follows:
A =
Excellent
B =
Good
C =
Fair
D =
Barely Passing
F =
Failed
We will further sub-divide these letter grades using +/– distinctions within each grade category for grades
of D or better, so that, for example, an A+ grade will indicate exceptionally strong performance, and an
A– will indicate very good performance. In our opinion, if a straight D already indicates barely passing
performance, then anything below that constitutes a failing grade, so for example a D– or an F+ grade
would make little sense.
If taking a class pass / no-pass (P/NP), note however that a "P" grade will correspond to the equivalent of
a C– letter grade or better. That is, passing a class taken pass/fail is harder than passing a class taken for
a letter grade. (No, this does not necessarily make much sense to us, either).
Out of a desire to maintain and signal the high standards for education at the University of California,
and to uphold fairness and maintain meaningfulness of grades to students, instructors, other institutions,
and others, UC Berkeley and the Physics Department have established "strongly recommended"
guidelines for the approximate distribution of A's, B's, and C's in any one course. For required upperdivision courses like Physics 137B, these recommendations suggest approximately 35% A+/A/A– grades
and 40% B+/B/B– grades. (Berkeley being Berkeley, together these are lower than the national average
amongst four-year universities, which is currently over 80% Be proud of the grades you earn here).
That being said, we hope that all students ultimately feel that they are being graded based on their own
performance as we can best assess it, and are not in direct competition with their peers. Typically, in a
moderately large physics course like this one, when the spectrum of assignments tests a diversity of
knowledge and skills and provides appropriate challenges, course grades will tend to fall into something
resembling a bell-curve pattern naturally, if for no other reason than due to the mathematical exigencies
of the Central Limit Theorem.
Earning a straight “A” grade will not be easy, but getting a C grade or worse typically requires some
deliberate lack of effort in terms of not keeping up with the reading or homework. This course will
demand careful thinking and serious work, move at a fast pace, presume a lot of reading, and offer
challenging homework assignments and exams, but the overall grading is not intended to be punitive or
onerous. If I feel that students have worked hard (which is almost always the case), then I will give as
many A’s and B’s as I can without facing too many admonishing memos from the administration or
uncomfortable meetings with our department chair.
Note that letter grades will not be directly assigned or suggested for individual assignments, but very
approximately, in terms of our holistic grading scale, for a typical exam or homework question, 5 points
corresponds to an A+, 4 to an A, 3 to a B, 2 to a C, 1 to a D, and 0 to an F, but the actual letter grade
correlates will depend on the difficulty of the problem — more challenging problems will tend to have a
more relaxed grading structure. To help you assess your performance in context, we will post some
class-wide statistics after each midterm, and unofficially offer some approximate cutoffs for corresponding
letter grades.
Note that by university decree, a course grade of "Incomplete" ( I ) can only be considered under dire
circumstances beyond a student’s control, and only when these circumstances have prevented the
student from completing certain assignments, not merely because performance suffered — and then,
according to official university policy, only when work already completed is of at least "C" quality or
better. Students should contact us directly in the event of any problems or emergencies, as soon as is
possible.
Students may also contact the instructor directly to discuss final course grades, but in the absence of
demonstrable errors, usually very little can be done after the fact to justify changes to the officially
posted letter grades. If you are having difficulties keeping up with the material, PLEASE talk to us as
soon as possible, preferably well before an exam, not after the grades are submitted to the university.
Although grades naturally cause much anxiety, and inevitably are imperfect, sometimes inaccurate
metrics of aptitude, effort, or accomplishment, grades are nevertheless something of a necessary evil
which attempt (admittedly, not always successfully) to serve many educational purposes:
* to provide objective information and feedback on how well students are learning;
* to describe as unambiguously as possible the merit, quality, or value of the work accomplished;
* to improve the capacity of students to assess and and identify good work, that is, to improve
their self-evaluation or discrimination skills with respect to work submitted;
* to stimulate and encourage effort and completion of quality work by students;
* to inform the instructors as to what students have and have not learned;
* to ensure the quality, reputation, and meaning of an official educational program or degree;
* to communicate the instructor's judgment of the student's progress and preparation
for subsequent instruction or employment;
* to help provide selection criteria for employment, continued education, or
other professional, academic, economic, or intellectual activities or rewards.
Why are tests so difficult? Exams and certain homework problems will be quite challenging by design,
not out of a desire to cause you anxiety or frustration, but to: (i) help push you to deeper
comprehension and appreciation of the subject and its subtleties, and (ii) help us accurately assess your
learning. An exam is, in effect, a measurement device (subject, of course, to measurement error), but like
any good instrument, it should take advantage of its full “dynamic range” to spread out results so as to
help better make distinctions.
In other words, if an exam is too easy, then most scores tend to fall in a narrow range, and rather trivial
mistakes can end up having outsized effects. Exam and homework problems are supposed to be
challenging. You are not expected to score 100% on any exam.
Keep in mind that your grades in this class — or any physics class — are not a reflection of our personal
approval or disapproval, nor our opinions of your personal worth, nor some definitive assessment of
your promise as a future scientist. Many very successful scientists earned less than stellar grades as high
school, undergraduate, or graduate students. Everyone who truly grapples with the material and works
hard in a fast-paced and conceptually and mathematically difficult course like Physics 137A will earn
our gratitude and respect.
COLLABORATION and INTELLECTUAL HONESTY
Science is simultaneously both a solitary and collective enterprise. To make progress, we must stand on
the shoulders of giants and mortals alike, and work effectively as part of a team and community, but to
gain deep understanding, we must also ponder alone and calculate and work out some things for
ourselves. It probably takes an entire career to figure out an appropriate balance between collaboration
and individual effort. In this class, we strongly encourage you to study with, interact with, and work
with other students both in and outside of official sections or office hours. Some of the best ways to
learn physics include conversing, brainstorming, and problem-solving with your colleagues about things
you do not understand, and trying to explain to them things you do understand. Research shows that
talking, and even just siting, with others improves learning outcomes, Individuals and overlyhomogeneous groups are often blind to their own biases, but heterogeneous groups can bring to bear a
diversity of ideas. Please go about these activities in a collegial manner, in the spirit of a shared quest.
That being said, you should never just copy material from another student, or book, journal, or website.
This serves little educational purpose, and if unacknowledged, constitutes academic dishonesty. After
engaging and discussing, think about a solution on your own, and write up what you believe you
understand in your words. If you do make use of outside resources, give appropriate credit where credit
is due. You may find it useful to use additional books or internet webpages, but cite any additional
written or electronic materials (other than the assigned readings, reference to which is implied) used to
complete your problem sets, and list any students with whom you worked closely. Do not plagiarize
through slavish copying or unreferenced borrowing. It is relatively easy to find solutions to almost any
textbook problem with a few minutes of google searching, but remember that the point of homework is
not for you write down the correct answer, but for you to reinforce or extend your own understanding of
and facility with the material.
During any exam, any discussion with anyone but an instructor or proctor, or use of resources other
than those explicitly listed, or starting the exam early or stopping late, shall constitute academic
dishonesty, and you will receive no credit for the test, and such incidents may be reported for possible
further disciplinary action by the university.
UC Berkeley has now also adopted the following academic honor code:
As a member of the UC Berkeley community, I act with honesty, integrity, and respect for others.
Though the findings of science may be ethically neutral, the activity of science is not: it demands that
those who practice it successfully conform to a strict set of values and virtues. The hope is that we, as
scholars and scientists, will always adhere to the values alluded to by this honor code, while engaging
our passion for learning and our eagerness to discuss and debate.
ACCOMMODATIONS:
If you require special accommodations due to a persistent medical condition or disability, please first
contact the DSP office, and then contact us as early in the semester as possible so that we can try to
make arrangements.
Normally, assignments can be postponed or re-scheduled only for official university-sponsored activities
(such as team athletic competitions, or artistic performances), for religious observances, for unavoidable
medical situations, or for graduate school admissions or academic conferences. If an issue does arise,
please speak with us at your earliest possible convenience.
OTHER RESOURCES:
With strange physical ideas that not infrequently strain credulity, and many mathematical tools which
are often new to the students, Physics 137A can be conceptually and mathematically challenging, and
we will have to cover a great deal of material very quickly — too quickly, if truth be told.
The course will likely be challenging to all, but If you are experiencing anxiety or having difficulties
keeping up with the work, please do talk to one of us in regularly-scheduled office hours, or make an
appointment to meet with one of us privately at some other time. My best advice is to address potential
troubles as early as possible, before the exam is upon us or the homework is due, to maximize our
opportunities to discuss and work things out in a meaningful way before it is too late.
Before paying for a tutor, we suggest first making maximal use of our own discussion sessions and office
hours, since your tuition has already paid for these. The Student Learning Center (SLC) typically offers
drop-in tutoring and study groups only for lower-division physics classes, but Claudia Trujillo in the
Student Affairs Office in 368 LeConte, or the Society of Physics Students (SPS) in 275 LeConte, may be
able to provide a list of recommended tutors qualified for Physics 137A, or suggest additional resources.
Some of your best resources are your peers. Wrestling with the same new material, they may be well
situated to offer helpful suggestions, perspectives, hints, and insights. And there is no better way to
detect shaky skills or solidify your own understanding than to try to explain a concept or a technique to
someone else. Talk to colleagues in or after office hours, arrange your own regular or ad hoc study
groups, post questions or comments online, or stop by the Physics 137A Course Center (109 LeConte)
or the Physics Department Reading Room (251 LeConte) to find colleagues.
FEEDBACK & QUESTIONS:
If you find any of our course policies to be unclear, ambiguous, confusing, or unfair, or if you have
questions or concerns, feel free to contact us. Come to an office hour, or make an appointment. Also
contact us with constructive feedback about how the course is going or how it could be improved, even
via an anonymous emailer if you prefer.
SUPPLEMENTARY READING
When confused about physics, sometimes all it takes is to read or hear the same material in a different
voice, or in slightly different language, and something clicks. Different books approach the material in
profoundly or subtly different ways, and what works well for one student may not be the best
presentation for another.
There are many, many, many books and online resources on quantum mechanics, in addition to our
required and recommended texts. Some textbooks will be put on reserve in the department library, or
else made available online — check out Berkeley's extensive list of e-books made available on OskiCat
through agreements with publishers such as Springer-Verlag, World Scientific, and the Oxford and
Cambridge University Presses.
Occasionally, we will also post links to particularly useful websites, applets, videos, blogs, or articles.
Feel free to search for other materials that might be helpful to you, but remember to read materials with a
somewhat critical eye — mistakes, misunderstandings, and misinformation have been known to find
their way onto the world wide web.
Here are a few suggestions:
Introductory Textbooks [first-year level, possibly useful for review of Physics 7C material]:
David Halliday, Robert Resnick, Robert and Jearl Walker, Fundamentals of Physics
Douglas Giancoli, Physics for Scientists and Engineers
S. Borowitz and A. Beiser, Essentials of Physics
Paul Tipler, Modern Physics
“Introductory” Textbooks [rather more challenging than perhaps originally envisioned]
Richard Feynman, Robert Leighton, Matthew Sands, The Feynman Lectures on Physics Volume III
E. Wichmann, Quantum Physics (Berkeley Physics Course Volume 4)
Intermediate Textbooks [more or less comparable to our texts, and intended for physics majors]:
David Griffiths, Introduction to Quantum Mechanics (2nd Edition)
R. Shankar, Principles of Quantum Mechanics (2nd Edition)
B.H. Brandsen and C.J. Joachain, Quantum Mechanics (2nd Edition)
Nouredine Zettili, Quantum Mechanics: Concepts and Applications
Gennaro Auletta, Mauro Fortunato, and Giorgio Parisi, Quantum Mechanics
Richard Robinett, Quantum Mechanics: Classical Results, Modern Systems, and Visualized Examples
Leslie E. Ballentine, Quantum Mechanics: A Modern Development
Mark Beck, Quantum Mechanics: Theory and Experiment
David McIntyre, Corinne A Manogue, and Janet Tate, Quantum Mechanics: A Paradigms Approach
James Binney and David Skinner, The Physics of Quantum Mechanics
John D. McGervey, Quantum Mechanics: Concepts and Applications
Robert Scherrer, Quantum Mechanics: An Accessible Introduction
D. ter Haar, Problems in Quantum Mechanics
Phillip James Edwin Peebles, Quantum Mechanics
P.T. Matthews, Introduction to Quantum Mechanics
David S. Saxon, Elementary Quantum Mechanics
Vishnu S. Mathur and Surendra Singh, Concepts in Quantum Mechanics
Amit Goswani, Quantum Mechanics
Richard Liboff, Introductory Quantum Mechanics
Stephen Gasiorowicz, Quantum Physics (3rd Edition)
L.I. Schiff, Quantum Mechanics
Eugen Merzbacher, Quantum Mechanics
David Park, Introduction to Quantum Theory (3rd Edition)
Cameron Reed, Quantum Mechanics
David Beard, Quantum Mechanics
David A.B. Miller, Quantum Mechanics for Scientists and Engineers
Gary E. Bowman, Essential Quantum Mechanics
Walter Greiner, Quantum Mechanics: An Introduction
Daniel Bes, Quantum Mechanics: An Introduction
Advanced / Graduate Textbooks in Quantum Mechanics [more in-depth or more mathematical]:
L. Landau and E. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (3rd Edition)
J.J. Sakurai and Jim J. Napolitano, Modern Quantum Mechanics (2nd Edition)
Claude Cohen-Tannoudji, Bernard Diu, and Frank Laloë, Quantum Mechanics (Volumes 1 and 2)
Eugene D. Commins, Quantum Mechanics: An Experimentalist's Approach
Keith Hannabuss, An Introduction to Quantum Theory
Alberto Galindo and Pedro Pascual, Quantum Mechanics (Volumes I and II)
Steven Weinberg, Lectures on Quantum Mechanics
Franz Schwabl, Quantum Mechanics
Franz Schwabl, Advanced Quantum Mechanics
Visualization-Based Textbooks in Quantum Mechanics [with accompanying software]:
Bernd Thaller, Visual Quantum Mechanics: Selected Topics with Computer-Generated Animations
Bernd Thaller, Advanced Visual Quantum Mechanics
Siegmund Brandt, Hans Dieter Dahmen, and Tilo Stroh, Interactive Quantum Mechanics
Siegmund Brandt and Hans Dieter Dahmen, The Picture Book of Quantum Mechanics
Classic TextBooks and Monographs [still worth a careful look]
Max Planck, The Origin and Development of the Quantum Theory
P.A.M. Dirac, Principles of Quantum Mechanics
P.A.M. Dirac, Lectures on Quantum Mechanics
John von Neumann, Mathematical Foundations of Quantum Mechanics
David Bohm, Quantum Theory
Erwin Schrödinger, Collected Papers on Wave Mechanics
W. Heisenberg, C. Eckart, and F.C. Hoyt, The Physical Principles of the Quantum Theory
Max Born, The Problem of Atomic Dynamics
Hans Bethe and Edwin Salpeter, Quantum Mechanics of One and Two-Electron Atoms
Richard Feynman, Albert Hibbs, and Daniel Styer, Quantum Mechanics and Path Integrals
Eugene Wigner, Group Theory and its Applications to the Quantum Mechanics of Atomic Spectra
Herman Weyl, The Theory of Groups and Quantum Mechanics
Albert Messiah, Quantum Mechanics
Edward and Philip Condon, Quantum Mechanics
Mathematical Methods [for more detailed treatments, more careful statements, and more proofs]
J.D. Jackson, Mathematics for Quantum Mechanics: An Introductory Survey
Kevin Cahill, Physical Mathematics
Thomas F. Jordan, Linear Operators for Quantum Mechanics
F. Strocchi, Introduction to the Mathematical Structure of Quantum Mechanics
Belal E. Baaquie, The Theoretical Foundations of Quantum Mechanics
George Arfken, Hans Weber, and Frank Harris, Mathematical Methods for Physicists
Mary Boas, Mathematical Methods in the Physical Sciences
Donald McQuarrie, Mathematical Methods for Scientists and Engineers
Jon Mathews and Robert Walker, Mathematical Methods for Physics
G. Shutz Geometric Methods of Mathematical Physics
Nadir Jeevanjee, An Introductions to Tensors and Group Theory for Physicists
Eberhard Zeidler: Applied Functional Analysis: Applications to Mathematical Physics
Michael Reed and Barry Simon, Methods of Modern Mathematical Physics (Volumes I and II)
Peter Lax, Functional Analysis
Bryan Rynne and M.A. Youngson, Linear Functional Analysis
F. Riesz and B.Sz. Nagy, Functional Analysis
Carlo Alabiso, A Primer on Hilbert Space Theory
Chris Isham, Lectures on Quantum Theory: Mathematical and Structural Foundations
R. Mirman, Group Theoretical Foundations of Quantum Mechanics
H.F. Jones, Groups, Representations, and Physics
Michael Tinkham, Group Theory in Quantum Mechanics
Interpretations and Foundations of Quantum Mechanics [for the philosophically inclined]
R.I.G. Hughes, The Structure and Interpretation of Quantum Mechanics
J.A. Wheeler and W.H. Zurek, Quantum Theory and Measurement
Franck Laloë, Do We Really Understand Quantum Mechanics?
Bernard d'Espagnat, Conceptual Foundations of Quantum Mechanics
Bernard d'Espagnat, On Physics and Philosophy
Bernard d'Espagnat, In Search of Reality
Bernard d'Espagnat, Reality and the Physicist: Knowledge, Duration and the Quantum World
Bernard d'Espagnat, Veiled Reality: An Analysis Of Present-day Quantum Mechanical Concepts
Asher Peres, Quantum Theory: Concepts and Methods
J.S. Bell, Speakable and Unspeakable in Quantum Mechanics
David Albert, Quantum Mechanics and Experience
Max Jammer, The Philosophy of Quantum Mechanics
Max Jammer, The Conceptual Development of Quantum Mechanics
Reinhold Blumel, Foundations of Quantum Mechanics: From Photons to Quantum Computers
Hans Reichenbach, Philosophic Foundations of Quantum Mechanics
Roland Omnes and Arturo Sangalli, Quantum Philosophy
Alisa Bokulich and Gregg Jaeger, Philosophy of Quantum Information and Entanglement
Jonathan Aliday, Quantum Reality: Theory and Philosophy
Richard A. Healey and Geoffrey Hellman, Quantum Measurement: Beyond Paradox
Tim Maudlin, Quantum Non-Locality and Relativity: Metaphysical Intimations of Modern Physics
Bas C. van Frassen, Quantum Mechanics: An Empiricist View
Arthur Fine, The Shaky Game; Science and its Conceptual Foundations
Vladimir B. Braginsky, Farid Ya Khalili and Kip S. Thorne, Quantum Measurement
Howard M. Wiseman and Gerard J. Milburn, Quantum Measurement and Control
Kurt Jacobs, Quantum Measurement Theory and its Applications
Paul Busch, Pekka J. Lahti, and Peter Mittelstaedt, The Quantum Theory of Measurrment
Orly Alter and Yoshihisa Yamamoto, Quantum Measurement f a Single System
Richard Healey, Philosophy of Quantum Mechanics: An Interactive Interpretation
Roland Omnes, Understanding Quantum Mechanics
Roland Omnes, The Interpretation of Quantum Mechanics
James Evans and Alan S. Thorndike, Quantum Mechanics at the Crossroads
Niels Bohr, Atomic Physics and The Description of Knowledge
James Cushing, Quantum Mechanics: Historical Contingency and the Copenhagen Hegemony
Malcolm Longair, Quantum Concepts in Physics: An Alternative Approach
Niels Bohr, Causality and Complementarity
David Bohm, Wholeness and the Implicate Order
David Bohm and Basil Hiley, The Undivided Universe: An Ontological Interpretation of Quantum Theory
Leslie Ballentine, Foundations of Quantum Mechanics Since the Bell Inequalities
Thomas Kuhn, Black-Body Theory and the Quantum Discontinuity
B. Wheaton and T. Kuhn, The Tiger and the Shark: Empirical Roots of Wave-Particle Dualism
Werner Heisenberg, Philosophical Problems of Quantum Physics
Max Born, The Natural Philosophy of Cause and Chance
Quantum Information and Quantum Computation [many books have appeared recently]
Michael A. Nielson and Isaac L. Chuang, Quantum Computation and Quantum Information
Scott Aaronosn, Quantum Computing Since Democritus
Mark Wilde, Quantum Information Theory
Christopher G. Timpson, Quantum Information Theory and the Foundations of Quantum Mechanics
Moses Feyngold and Vadim Fayngold, Quantum Mechanics and Quantum Information
Benjamin Schumacher and Michael Westmoreland, Quantum Processes, Systems, and Information
Dirk Bouwmeester, Artur K. Ekert, and Anton Zeilinger, The Physics of Quantum Information
Stephen Barnett, Quantum Information
Greg Jaeger, Entanglement, Information, and the Interpretation of Quantum Mechanics
Greg Jaeger, Quantum Information: An Overview
Jonathan A. Jones and Dieter Jaksch, Quantum Information, Computation, and Communication
Masahito Hayashi, Quantum Information: An Introduction
M. Hayashi, S. Ishizaka, A. Kawachi, and G. Kimura , Introduction to Quantum Information Science
Eleanor G. Rieffel and Wolfgang H. Polak, Quantum Computing: A Gentle Introduction
G. Benenti, G. Casati, and G. Strini, Principles of Quantum Computation and Information
Dagmar Bruss and Gerd Leuchs, Lectures on Quantum Information
N. David Mermin, Quantum Computer Science: An Introduction
Christopher A. Fuchs, Coming of Age With Quantum Information: Notes on a Paulian Idea
Miko Nakahara and Tetsuo Ohmi, Quantum Computing: From Linear Algebra to Physical Realizations
Miko Nakahara and Yoshitaka Sasaki, Quantum Information and Quantum Computing
Erika Andersson and Patrik Ohberg, Quantum Information and Coherence
MIchael Redhead, Incompleteness, Nonlocality, and Realism
Some Semi-Popular Books and Biographies [a few recommendations amongst hundreds]
Abraham Pais, Genius of Science: A Portrait Gallery
Abraham Pais, Subtle is the Lord: The Science and the LIfe of Albert Einstein
Abraham Pais, Niels Bohr's Times, in Physics, Philosophy, and Polity
Abraham Pais, Maurice Jacob, David I. Olive and Michael F. Atiyah , Paul Dirac: the Man and his Work
Max Born, The Restless Universe
Max Planck, Where is Science Going?
Niels Bohr, Atomic Physics and Human Knowledge
David Bohm, Causality and Chance in Modern Physics
Erwin Schrödinger, My View of the World
Werner Heisenberg, Physics and Philosophy: The Revolution in Modern Science
George Gamow, Thirty Years Which Shook Physics: The Story of Quantum Theory
Albert Einstein and Leopold Infeld, The Evolution of Physics
Roger Penrose, The Emperor's New Mind
Banesh Hoffman, The Strange Story of the Quantum
Leonard Susskind and Art Friedman, Quantum Mechanics: The Theoretical Minimum
Clifford Pickover: From Archimedes to Hawking: Laws of Science and Great Minds Behind Them
A. Douglas Stone, Einstein and the Quantum: The Quest of the Valiant Swabian
H. Thomas Milhorn, The History of Physics
David Park, The How and the Why
William H. Cropper, Great Physicists
C.P. Snow, The Physicists
Walter Isaacson, Albert Einstein: His Life and Universe
James Gleick, Genius: The LIfe and Science of Richard Feynman
Nancy Thorndike Greenspan, The End of the Certain World: The Life and Science of Max Born
Manjit Kumar, Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality
Graham Fermelo, The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom
David Lindley, Uncertainty: Einstein, Heisenberg, Bohr, and the Struggle for the Soul of Science
Nick Herbert, Quantum Reality
Michael Eckert, Arnold Sommerfeld: Science, Life, and Turbulent TImes 1868–1951
David C. Cassidy, Uncertainty: The Life and Science of Werner Heisenberg
David C. Cassidy, Beyond Uncertainty: Heisenberg, Quantum Physics, and the Bomb
Walter J. Moore, Schrödinger: Life and Thought
John Gribbin, Erwin Schrödinger and the Quantum Revolution
John Gribbin, In Search of Schrödinger's Cat
John Gribbin: Computing With Quantum Cats: From Colossus to Qubits
Helge Kragh, Niels Bohr and the Quantum Atom
S. Leialoha and J. Parker, Suspended in Language: Niels Bohr's Life, Discoveries, and Century
Bruce Rosenblum, Quantum Enigma: Physics Encounters Consciousness
Jim Baggott, The Quantum Story: A History in Forty Moments
Kenneth W. Ford and Diane Goldstein, The Quantum World: Quantum Physics for Everyone
Alistair Rae, Quantum Physics: A Beginner's Guide
Jim Al-Khalili, Quantum: A Guide for the Perplexed
Gennaro Auletta and Shang-Yung Wang, Quantum Mechanics for Thinkers
Bruce Gregory, Inventing Reality
David Lindley, Where Does All The Weirdness Go?
Amir Aczel, Entanglement
Nicholas GIsin and Alain Aspect, Quantum Chance: Nonlocality, Teleportation, and Other Marvels
Louise Gilder, The Age of Entanglement: When Quantum Mechanics Was Reborn
Brian Cox and Jeff Forshaw, The Quantum Universe: (And Why Anything that Can Happen, Does)
Vlatko Vedral, Decoding Reality: The Universe as Quantum Information
Robert Gilmore, Alice in QuantumLand: An Allegory of Quantum Physics
Tom Siegfried, The Bit and the Pendulum: From Quantum Computing to M-Theory
Maximillian Schlosshauer, Elegance and Enigma: The Quantum Interviews
Fred Wolf, Taking the Quantum Leap: The New Physics for Nonscientists
John Polkinghorne, Quantum Theory: A Very Short Introduction
David Deutsch, The Fabric of Reality
Oscar Zarate, Introducing Quantum Theory: A Graphic Guide to Science's Most Puzzling Discovery
Seth Lloyd, Programming the Universe
F. David Peat, Einstein's Moon