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@info.phys.unm.edu
Office Hours: Tuesday and Thursday: 2:00-3:00 (or by appointment)
Teaching Assistant: Andrew Silberfarb
email: drews@unm.edu
Problem Session: To be determined
Grading:
Problem Sets: 25-33%
Problem sets will be distributed 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 Apr. 28-30
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 (3 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 (4 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.
E. Identical particles, spin, and permutation symmetry - application to multielectron atoms.
V. Scattering Theory (3-3.5 weeks)
A. Time-independent formulation: Cross-sections, scattering amplitudes, Lipmann-Schwinger equation, T-matrix, Green's functions.
B. Born approximation and optical theorem.
C. Partial waves expansions.
D. Resonances and bound-states.
E. Time-dependent formulation: The S-matrix. Møller operators, and propagator in the interaction picture.
VI. Time-Dependent Perturbations and Open Quantum Systems (3-3.5 weeks)
A. Transition Probabilities
B. Coherent Rabi Flopping
C. Fermi's Golden rule
D. System-reservoir theory: Exponential decay
E. Spontaneous emission
Tentative Schedule of Lectures
Date
Topic
Notes
Jan. 22
Review 521: Foundations of quantum theory.
Three important problems- SHO, Angular momentum, Hydrogen atom.
Download 1
Download 2
Jan. 27
Time independent nodegenerate perturbation theory (TINPT)
Download 3
Jan. 29
Applications of TINPT - Quadratic Stark effect.
Download 4
Feb. 3
Time independent degenerate perturbation theory (TIDPT)
Linear Stark effect.
Download 5
Feb. 5
Anticrossings and TIDPT
Download 6a
Application of TIDPT:
Relativitistic effects - Fine Structure in Hydrogen
Hyperfine Structure and the Zeeman effect
Feb. 17
Wigner's theory of symmetries, groups, and representations
Supplemental notes on antiuntary operators by Prof. Caves
Download 8
Feb. 19
Rotation group, SU(2),
Addition of angular momentum: Clebsch-Gordan coefficients
Dirac "Belt trick"
Supplement on SU(2) vs. SO(3)
Download 9
Feb. 24
Formal theory of angular momentum coupling.
Irreducible representations of SU(2)
Download 10
Feb. 26
Tensor Operators
Mar. 3
Wigner-Eckart Theorem
Dipole Selection Rules
Special Lectures Notes from UCB
Download 12
Mar. 5
More on irreducible tensors:
General multipoles and selection rules
Download 13
Mar. 10
Permutation symmetry:
Identical particles, spin, and statistics.
Download 14
Mar. 12
No Lecture
Mar. 16-22
Spring Break
Make up
Exchange degeneracy, singlets and triplets
Download 15
Mar. 24
Multielectron atoms, multiplets, spectroscopy.
Variational method: Helium
Download 16
Mar. 26
Introduction to scattering - Time-independent vs. time-dependent formulation, cross-section, scattering amplitudes.
Download 17
Mar. 31
Time Independent Picture:
First Born-Approximation, Born Series, Green's Function.
Download 18
Apr. 2
Formal Theory of Scattering -
Green's Operator, Lippmann-Schwinger Equation, S-matrix
Download 19
Apr. 7
Spherical symmetry and partial waves
Download 20
Apr. 9
Scattering eigenstates and phase shifts
Download 21
Apr. 14
Examples: Hard-sphere scattering, high and low energy limits.
Scattering resonances and bound states
Download 22
Download22a
Apr. 16
Time dependent perturbation - The interaction picture
Download 23
Apr. 21
Transition Probabilities:
Absorption and Emission. Resonance.
Apr. 23
Transition Probabilities Continued:
Time-energy uncertainty. Second-order perturbation theory - virtual transitions.
Apr. 28
Resonant sinusoidal perturbation - Rabi Flopping
Download 25
Apr. 30
Coherent evolution vs. rate equations - Fermi's Golden Rule
Download 26
May. 5
Exponential decay; Introduction to System-Reservoir Interaction
Download 27
May. 6
Introduction to the Quantized Electromagnetic Field
Vacuum Fluctuations as a Reservoir - Spontaneous emission
Problem Set #1
Due Jan. 31
Problem Set #6
Due Mar. 10
Problem Set #2
Due Feb. 7
Problem Set #7
Due Apr. 7
Problem Set #3
Due Feb. 16
Problem Set #8
Due Apr. 16
Problem Set #4
Due Feb. 21
Problem Set #9
Due Apr. 23
Problem Set #5
Due Mar. 03
Problem Set #10
Due May 2
Exam 1
Due Feb. 28
Exam 2
Due May 9