General Information
Syllabus
Lecture Schedule
Problem Sets
Lecture: Physics and Astronomy, Room 184, TR 9:30-10:45
Instructor: Prof. Ivan Deutsch
Phys/Astro Room 23, Phone: 277-8602
email: ideutsch@unm.edu
Problem Session: Monday, 12:30-1:20, Room 5
Office Hours: Wednesday, 10:00-11:00, Room 23
Teaching Assistant: Bob Keating
email: keatingt@unm.edu
Offices : To be determined
Grading:
Problem Sets: 34%
Problem sets will be distributed approimately once a week and due on Thursdays, to be placed in the grader's mailbox by 5:00 PM.
Three "Midterms" 66%
Exam I Feb. 24, Exam II Mar. 22, Exam III TBA
"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 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 , 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 Quantum Mechanics 3rd Edition, by E. Merzbacher
Everything is here but the organization is difficult. This 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. Many-body Physics (2 weeks)
A. Identical particles, spin, and permutation symmetry - application to multielectron atoms.
B. 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. 18
Review: Foundations - Structure of Quantum Mechanics.
States, Observables, Measurements, Symmetries
Download 1
Review: Schrödinger Equation: Dynamics/Spectra.
Examples: Simple Harnomic Oscillator, Hydrogen Atom
Time independent nondegenerate perturbation theory (TINPT)
Jan. 27
No lecture -- On Travel
Feb. 1
Applications of TINPT - Anharmonic Trapping. Quadratic Stark effect.
Download 4
Feb. 3
Time independent degenerate perturbation theory (TIDPT)
Linear Stark effect.
Download 5
Feb. 8
Anticrossings and TIDPT
Download 6
Continuation
Review: Addition of Angular Momentum
Feb. 15
Application of TIDPT:
Relativitistic effects - Fine Structure in Hydrogen
No lecture
Feb. 22
Hyperfine Structure in Hydrogen
Download 7b
Feb. 24
---
Mar. 1
Wigner's theory of symmetries, groups, and representations
Continuation of symmetries -- Lie Groups
Download 8
Mar. 3
Rotation Group:
SO(3) vs. SU(2)
Download 9
Supplement
March 8
Addition of Angular Momentum -- Clebsch-Gordan Coefficients
Reducible and Irreducible representations of SU(2)
Download 10
Mar. 10
Tensor Operators
Irreducible Tensors
Download 11
Mar. 15,17
Mar. 22
No lecture (on travel)
Mar. 24
Wigner-Eckart Theorem:
Download 12
Make up lecture:
Application -- Dipole selection rules
General multipoles and selection rules
Mar. 31
Permutation symmetry:
Identical particles, spin, and statistics.
Download 14
Apr. 5
Multielectron atoms, multiplets, spectroscopy.
Download 15
Apr. 7
Variational method: Helium
Apr. 12
Time dependent perturbation - The interaction picture
Download 22
Apr. 14
Transition Probabilities:
Absorption and Emission. Resonance. Time-energy uncertainty.
Download 23
Apr. 19
Second-order perturbation theory - virtual transitions
Apr. 21
Rabi flopping
Download 24
May 3
May 5
Spontaneous emission
Download 27
Problem Set #1
Due Feb. 1
Problem Set #6
Due March 31
Problem Set #2
Due Feb. 8
Problem Set #7
Due April 7
Problem Set #3
Due Feb. 15
Problem Set #8
Due April 29
Problem Set #4
Due March 3
Problem Set #9
Due May 5
Problem Set #5
Due March 10