Download Wave Equation

Quantum Mechanics
as a
first physics course
M. Anthony Reynolds
Department of Physical Sciences
16 October 2003
Collaborators
Tristan Hubsch, Howard University
Per Berglund, University of New Hampshire
Birth of the “quanta”
Quantum Theory was born on December 14, 1900, when
Max Planck delivered his famous lecture before the
Physikalische Gesellschaft
(Berlin Physical Society)
“Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum”
“On the Theory of the Law of Energy Distribution in the Blackbody Spectrum”
 3

exp(h / kT )  1
1875
“Physics is a branch of knowledge that is just about complete.
The important discoveries, all of them, have been made.
It is hardly worth entering physics anymore.”
-Head of the physics department,
University of Munich,
to Planck at age 17
1917, Nobel Prize
The Nobel Prize in Physics 1918
"in recognition of the services he rendered to the advancement of Physics by
his discovery of energy quanta"
Max Karl Ernst Ludwig Planck
Germany
b. 1858
d. 1947
http://www.nobel.se/physics/laureates/1918/
Quantum difficulty
“If anybody says he can think about
quantum problems without getting giddy,
that only shows he has not understood the first thing about them.”
- Max Planck
Quantum difficulty II
“Anybody who thinks they understand
quantum physics is wrong."
- Niels Bohr
Quantum difficulty III
“You never really know a subject unless
you can prepare a freshman lecture on it.”
- Richard Feynman
Quantum difficulty IV
“You do not really understand
something unless you can explain it to your grandmother.”
- Albert Einstein
Quantum difficulty V
“For an idea that at first does not look preposterous,
there is no hope”
- Freeman Dyson
Standard intro course outline
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Mechanics
Fluids
Sound
Heat
Electricity & Magnetism
Optics
Modern Physics
> 125 years old!
Previous attempts
• Six Ideas that Shaped Physics
– Thomas Moore
• Matter & Interactions
– Chabay & Sherwood
Goals
• Ambitious: restructure the entire sequence
– Quantum mechanics should play a fundamental
role
• Modest: create “Physics 0”
– Teach quantum first
Problems
MATH
Pedagogical challenge
Convey conceptual understanding
without requiring the student to master all the
mathematical details.
Approaches
• Historical
– Newtonian mechanics, then quantum
• Idea-based
– unifying physical concepts
• Deductive approach
– Fundamental formulation, then classical mechanics
“Physics 0” Outline
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Qualitative overview
Basic concepts (mathematical and physical)
Waves
Measurements
Axioms of quantum mechanics
Examples
Classical limit
Qualitative overview
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Powers of ten, hierarchy of universe
Simple vs. collective phenomena
Quantitative and qualitative differences
Systems of units
– Including “natural”: speed-action-gravitation
• Order-of-magnitude
Basic concepts - math
• Limit, derivative
– Product rule, chain rule
• Integration, anti-differentiation
– Integration by parts
• Complex numbers
» Calculus I taken concurrently
Basic Concepts - physics
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Position & time
Mass vs. weight (force)
Work & energy
Linear momentum
Action:
– Potential-to-kinetic energy transfer over time
– Angular momentum x rotated angle
Waves
• Plane traveling wave
– not point particle
new
paradigm
• Superposition (qualitative)
– Wave packets
– Wave-particle duality (e.g., electron diffraction)
• Waves (quantitative)
– amplitude, wavelength, frequency
– wave number, phase velocity
– beats, group velocity, wave packets
Measurements
• Probabilistic nature
– Example: dice statistics
• Principle of complementarity (historical)
– E = h
– p = h/l
Axioms
• Y(x,t) describes object’s state (database)
– Hilbert space = databank
• Observables are assigned real operators
– Extracts values
• Time evolution is given by
• Average value is
Y
ih
 HY
t
Q   Y *QY
Examples
• Quantitative
– Free particle
– Particle-in-a-box
• infinite square well
finite square well
(qualitative)
• Qualitative
– harmonic oscillator
– hydrogen atom
elucidate strange features:
wave packets,
superposition,
indeterminacy principle
Classical Limit
• Ehrenfest’s theorem:
d p
V

dt
x
• Computer simulations of high n states
• Estimate action
– If S ? h , then classical physics applies
Ancillaries
• Historical digressions
– How quantum physics came to viewed as correct
• “observe-represent-predict” cycle of modeling
• Symmetries
• Connection with current physics (e.g., strings)
Implementation
• Pilot test – Fall 2004
– ERAU
– Howard University
– University of New Hampshire
• Evaluation
– pre/post test
– track students through Physics I, II, III
• Dissemination
– publish text on web (“open source”)