Download Course Syllabus

Physics 521
Syllabus
Textbooks:
•
J. J. Sakurai, Modern Quantum Mechanics (required)
•
C. Cohen-Tannoudji et al., Quantum Mechanics, Vol. 1
The conceptual flavor of the course is similar to Sakurai’s book, but not identical. The main
differences correspond to background material, which we cover in more detail, dealing with
the mathematical framework of Quantum Mechanics, and an early extensive discussion of
spin ½ and other two-level systems —the simplest systems for which the essential aspects of
Quantum Mechanics are most directly visualized. Cohen-Tannoudji will be used in
Homework assignment the first part of the course; the emphasis will switch almost
completely to Sakurai as the course progresses. Sakurai will also be the textbook for Physics
522, where the second volume of Cohen-Tannoudji will be used as occasional reference (the
latter contains many important problems worked out in great detail!)
There is a new book (which is actually a strongly-revised second edition of an old book)
which I like a lot, K. Gottfried and T.-M. Yan, Quantum Mechanics: Fundamentals. I have
thought about adopting this book as textbook, but I eventually decided against that, as the
book may seem a little too “advanced,” on a first reading. Still, I strongly recommend it,
especially for those students who are more theoretically inclined.
Note: I always recommend the Feynman Lectures on Physics, Vol. 3, as a most beautiful,
illuminating source of Quantum Mechanics at an “elementary” level. Volume 3 of the
Feynman Lectures represents a famous experiment at teaching Quantum Mechanics
“correctly” at the sophomore level. (There is actually a nice story in a recent issue of
Physics Today about that “experiment,” describing both the design of the course and the
putting together of the three-volume masterpiece.) In addition, the old Berkeley Physics
Course, Vol. 4, Quantum Physics, is a must-read piece for those who have not been trained
to think about basic things such as orders of magnitude, qualitative reasoning, and other key
aspects of “thinking like a physicist” —which is important for your Qualifying Exams, but
even more important for your proper education as a research physicist!
Overview of the course:
◊
Introduction: The Quantum Mechanical way of thinking about nature at the
microscopic level. We shall condense the essence of key empirical evidence
stemming from the Stern-Gerlach experiment and from a gedanken electrondiffraction experiment.
◊
The language of Quantum Mechanics: Dirac notation — bras, kets, operators, matrix
elements, etc.
◊
The postulates of Quantum Mechanics: Probability amplitudes, probabilities, mean
values, the measurement process, the uncertainty “principle,” time evolution.
◊
Spin 1/2 and other two-level systems. Chemical bonding by electron sharing. The
systems to be considered display the beauty and practical implications —e.g.,
masers, lasers— of Quantum Mechanics. This is achieved with a minimum of
mathematical complications (a great advantage of the two-level systems).
◊
The harmonic oscillator in Quantum Mechanics (solved by operator techniques), and
applications. The Mössbauer effect.
◊
Aspects of wave mechanics: Propagation in space, the Feynman path integral, the
Aharonov-Bohm effect.
◊
Theory of the angular momentum in Quantum Mechanics.
◊
The central potential problem; the hydrogen atom.
Any topic from the above outline which is not covered in the Fall semester will be covered in
the Spring semester. The Physics 521-522 sequence is really one course (one subject),
partitioned into two because of “practical” reasons.
Note: Elementary aspects of wave mechanics are assumed to be part of your background.
(The first Homework assignment deals with standard one-dimensional problems.) Sakurai
assumes that you have this background (he also assumes that you are familiar with typical
three-dimensional wave-mechanics problems, such as the hydrogen atom, which we will
cover in some detail). In Cohen-Tannoudji, Vol. 1, you will find many worked-out problems
in wave mechanics. Let me know right away if you have any questions/anxieties, about this
issue!
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A proper comprehension of Quantum Mechanics is a necessary (but not sufficient!) condition
for a successful research career in just about any area of physics of current interest. Thus, in
doing physics, you will find that you will use Quantum Mechanics “all the time.”
Homework will be assigned about once a week. It is extremely important that you view
each assignment as a challenge for your understanding of the subject. Attack your
homework individually, and as soon as possible. Don’t wait until the day before the
assignment is due to start thinking about it —you would not learn much. I recommend that
you ask for help from me, or from a classmate, only after you think about your question for a
while. But to that end, you need to give yourself quality time to think.
Office hours: To be determined after we agree on a final schedule for the course. Feel free
to contact me also by e-mail at any time. I am setting up a class e-mailing list which I will
use to send your assignments, and general information (e.g., some clarification of a
Homework problem) outside class hours. Please send me an e-mail right away so that I
can include you in the class list.
There will be a “mid-term” and a final exam.
Course Credit: 40% mid-term; 40% final; 20% homework.
Note: Both exams (mid-term and final) will reflect rather closely the material covered in
homework assignments, and in my lectures; there will be no big “surprises.” Thus, by doing
the homework well you will not only learn the subject (which is the main point), but that you
can expect to perform well in the exams! I emphasize that you should concentrate, on a daily
basis, on learning the subject, with your effort, and my help. Your grade will take care of
itself if you understand (as oppose to memorize) your physics!
Professor Adolfo G. Eguiluz
613 Science and Engineering Building
Phone: 974-9642; 574-5783 (ORNL)
e-mail: [email protected]
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