General Information
Syllabus
Lecture Schedule
Problem Sets
Lecture: Physics and Astronomy, Room 5, 11:00-12:15
Instructor: Prof. Ivan Deutsch
Phys/Astro Room 24, Phone: 277-1502
email: ideutsch@unm.edu
Problem Session: Tuesdays, 5:00-6:00, Room 5
Office Hours: Thursday, 10:00-11:00, Room 30
Teaching Assistant: Alexandre Tacla
email: tacla@unm.edu
Problem Session: To be determined
Grading:
Problem Sets: 25-33%
Problem sets will be distributed approimately once a week and due on Fridays, to be placed in the grader's mailbox by 3:00 PM.
Two Take-Home "Midterms" 50-66%
Exam I Mar. 10-12, Exam II May. 7-8
Final Exam (optional oral) 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. II, by C. Cohen-Tannoudji, B. Diu, and F. Laloë.
Vol II of this text is not quite as good vol. I. It is a bit elementary for this course, but has some very good material, especially on atomic physics.
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
Everything is here but 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.
Recently republished. Contains a reasonable coverage of measurements theory.
I. Review (1/2 week)
II. Time-Independent Perturbation Theory (4 weeks)
A. Nondegenerate theory - examples from atomic/molecular spectra.
B. Degenerate theory - examples: quadratic stark effect, band structure in solids, relation to symmetries.
III. Symmetries and Groups (3 weeks)
A. Symmetries and group theory in quantum mechanics.
B. SU(2) and irreducible representations.
C. General theory of addition of angular momentum.
D. Tensor operators, Wigner-Eckart theorem, multipole selection rules.
V. Manybody Physics (2 weeks)
E. Identical particles, spin, and permutation symmetry - application to multielectron atoms.
F. Introduction to Second Quantization
V. Scattering Theory (2 weeks)
A. Time-independent formulation: Cross-sections, scattering amplitudes, S-matrix.
B. Partial waves expansions.
C. Resonances and bound-states.
VI. Time-Dependent Perturbations and Open Quantum Systems (3 weeks)
A. Transition Probabilities
B. Coherent Rabi Flopping
C. Fermi's Golden rule
D. System-reservoir theory: Exponential decay
Tentative Schedule of Lectures
Date
Topic
Notes
Jan. 23
Review 521: Foundations - Hilbert space.
Download 1
Review 521: Foundations - Structure of Quantum Mechanics.
Postulates of Quantum Mechanics: States, Observables, Measurements
Review 521: Schroedinger Equation
Three important problems- SHO, Angular momentum, Hydrogen atom
Feb. 4
Time independent nondegenerate perturbation theory (TINPT)
Download 3
Feb. 6
Applications of TINPT - Anharmonic Trapping. Quadratic Stark effect.
Download 4
Feb. 11
Time independent degenerate perturbation theory (TIDPT)
Linear Stark effect.
Download 5
Feb. 13
Anticrossings and TIDPT
Download 6a
Application of TIDPT:
Relativitistic effects - Fine Structure in Hydrogen
Feb. 20
No Lecture (on travel)
Hyperfine Structure and the Zeeman effect
Feb. 27
Wigner's theory of symmetries, groups, and representations
Download 8
Feb. 29
Special Day
Make up: Continuation of symmetries -- Lie Groups
Download 9
Supplement
Mar. 3
Irreducible representations of SU(2)
Download 10
Mar. 5
Tensor Operators
March 7
Make up: Wigner-Eckart Theorem
Special Lectures Notes from UCB
Download 12
Mar. 10
No Lecture (March meeting)
---
Mar. 12
Mar. 17-21
Spring Break
Wigner-Eckart continued
Mar. 26
More on irreducible tensors:
General multipoles and selection rules
Download 13
March. 31
Permutation symmetry:
Identical particles, spin, and statistics.
Download 14
Exchange degeneracy, singlets and triplets
Apr.4
Make up:
Multielectron atoms, multiplets, spectroscopy.
Variational method: Helium
-----
Apr. 7
Introduction to scattering - Time-independent vs. time-dependent formulation, cross-section, scattering amplitudes.
Download 16,17
Apr. 9
Formal Theory of Scattering
Download 18
Apr. 14
Continuation
Taylor - 2
Taylor - 8
Apr. 16
Spherical symmetry and partial waves
Download 19
Apr. 21
Scattering eigenstates and phase shifts
Download 20
Apr. 23
Examples: Hard-sphere scattering, high and low energy limits.
Scattering resonances and bound states
Download 21
Download21a
Apr. 28
Time dependent perturbation - The interaction picture
Download 22
Apr. 30
Transition Probabilities:
Absorption and Emission. Resonance. Time-energy uncertainty. Second-order perturbation theory - virtual transitions.
Download 23
May 5
Resonant sinusoidal perturbation - Rabi Flopping
Download 24
May 7
Coherent evolution vs. rate equations - Fermi's Golden Rule
Download 25
Problem Set #1
Due Feb. 1
Problem Set #6
Due Apr. 7
Problem Set #2
Due Feb. 8
Problem Set #7
Due Apr. 23
Problem Set #3
Due Feb. 22
Problem Set #8
Due Apr. 30
Problem Set #4
Due Feb. 29
Problem Set #9
Due May 14
Problem Set #5
Due Mar. 31