Office Hours: Monday 12:30-1:30 Room 30
Office Hours: TBA
Grading:
Problem Sets: 35%
Problem sets will be distributed once a week on the web on Tuesday and due in one week, to be placed in the grader's mailbox by 5:00 PM.
Two "Midterms" 40%
Final Exam 25%
"Recommended" Texts:
We will not be following any text directly. Copies of my lecture note will be available. The are many good texts out there; you should pick the one(s) that work best for you. Relevant material from the following recommended texts with be referenced throughout the course.
o Quantum Mechanics , vol. I and II, by C. Cohen-Tannoudji, B. Diu, and F. Laloë.
This text is a great reference book to have around, but very verbose and sometimes hard to wade through. Many classic problems are solved in the "Complements.
o Modern Quantum Mechanics, by J. J. Sakurai
Good advanced text with a modern perspective. It's somewhat terse, are there are few examples.
o Quantum Mechanics 3rd Edition, by E. Merzbacher
Every thing is here but in the organization is difficult. This is a new edition and contains many contemporary topics.
Other texts:
o Quantum Mechanics, by L. I. Schiff
The old advanced classic. Still a good reference. Somewhat old fashion
o Quantum Mechanics, vol. I and II, by A. Messiah
Another older classic and good reference
Quantum Mechanics , vol. I, by K. Gottfried.
Republished. Contains a reasonable coverage of measurements theory.
o Introductory Quantum Mechanics, R. L. Liboff
An upper division undergraduate text . Very clear.
I Foundations (4 weeks)
A. Mathematical foundation - Hilbert space, operators, eigenvalues, commutators.
B. Structure of quantum mechanics - States, observables, measurements.
C. Quantum dynamics - Schrödinger and Heisenberg pictures, conservation laws.
II Waves Mechanics in 1D (3 1/2 weeks)
A. Wave function, momentum space, wave packets, Schrödinger equation.
B. Bound states, one dimensional potentials, tunneling.
C. Correspondence principle, Ehrenfest's theorem, WKB.
D. Simple harmonic oscillator - Different representations, phase space in QM.
III Angular Momentum (3 weeks)
A. Angular momentum as the generator of rotations, commutation algebra.
B. Eigenstates, Spherical harmonics.
C. Spin and magnetic resonance.
IV Multiple Degrees of Freedom (4 1/2 weeks)
A. Entangled states, Einstein-Podolsky-Rosen paradox.
B. Addition of angular momentum - Clebsch-Gordan coefficients.
C. Wave mechanics in 3D.
D. Central potentials.
E. The hydrogen atom.
Tentative Schedule of Lectures
Date
Topic
Material
Aug. 19
Introduction to quantum notions - probability amplitude, wave/particle duality
Lecture 1
Podcast 1
Aug. 21
Math: Linear vector spaces, representations, inner product, Dirac notation
Lecture 2
Podcast 2
Aug. 26
Math: Operators, adjoints, change of basis, unitarity
Lecture 3
Podcast 3
Aug. 28
Math: Eigenvalues, eigenvectors, commutators
Lecture 4
Podcast 4
Sept. 2
Hermitian operators, Complete sets of commuting operators
Podcast 5
Sept. 4
Structure of quantum mechanics- States, observables, measurements
Lecture 5-6
Podcast 6
Sept. 9
Unitary reversible evolution vs. Irreversible stochastic evolution
Sept. 11
More on the mystery of quantum measurements
Sept. 16
Pure vs. mixed states - density operators
Lecture 7
Podcast 9
Sept. 18
Continuation
Sept. 23
Open Quantum Systems and Decoherence
Sept. 25
Quantum Dynamics:
Time evolution operator, conservation, and symmetries
Stationary-states: Time Independent Schrödinger Equation
Lecture 8
Podcast 12
Sept. 30
Time evolution: Schrödinger vs. Heisenberg
Lecture 9
Podcast 13
Oct. 2
Particle mechanics in 1D, Heisenberg picture,
x and p representations.
Lecture 10
Podcast 14
Oct. 7
Podcast 15
Oct. 9
FALL BREAK
Oct. 14
Wave mechanics, interpretation of the wave function:
Probability current, semiclassical limit (WKB), path integrals
Lecture 11, 11b
Podcast 16
Oct. 16
Time Independent Schrödinger Equation (TISE).
Free particle, scattering states, constant potentials
Parity, bound states
Lecture 12, 13
Podcast 17
Oct. 21
SHO, Review classical problem, a and a^\dag
Lecture 14
Podcast 18
Oct. 23
SHO, Energy eigenstates, x-p space
Lecture 15
Podcast 19
Oct. 28
SHO, Uncertainty relations
Position/Momentum, Number/Phase
Lecture 16
Podcast 20
Oct. 30
SHO, Coherent States, Phase Space
and the Classical Limit
Nov. 4
Multiple Degrees of Freedom:
Lecture 17a, 17b
Podcast 22
Nov. 6
Separability, Symmetries and Degeneracy
Rotations and angular momentum algebra
Lecture 18
Podcast 23
Nov. 11
Lecture 19
Podcast 24
Eigenvalue problem for angular momentum
Lecture 20
Podcast 25
Nov. 18
Oribtal angular momentum and spherical harmonics
Lecture 21
Podcast 26
Nov. 20
Central Potentials and the Radial Equation
Lecture 22
Podcast 27
Nov. 25
No Lecture -- to be made up
Nov. 27
THANKSGIVING
Dec. 2
Radial equation continued: Partial Waves and Spherical Wells
Lecture 23a
Lecture 23b
Dec. 3
Spin-1/2: Pauli algebra
Lecture 24
Dec. 4
Separability, entangled states, marginal density operator
Lecture 25a, 25b
Podcast 28
Dec. 8
Bonus Lecture
EPR, Hidden Variables, and Bell Inequalties
Lecture 26
Podcast 29
Problem Set #1
Due Sept. 2
Problem Set #6
Due Oct. 14
Problem Set #11
Due Dec. 5
Problem Set #2
Due Sept 9
Problem Set #7
Due Oct. 21
Problem Set #3
Due Sept. 16
Problem Set #8
Due Oct. 27
Problem Set #4
Due Sept. 23
Problem Set #9
Due Nov. 4
Problem Set #5
Due Oct. 7
Problem Set #10
Due Nov. 25