General Information
Syllabus
Lecture Schedule
Problem Sets
Instructor: Prof. Ivan Deutsch
Phys/Astro Room 24, Phone: 277-1502
email: ideutsch@tangelo.phys.unm.edu
Office Hours: Tuesday and Thursday: 2:00-3:00 (or by appointment)
Teaching Assistant: Tracey Tessier
email: tessiert@gluino.phys.unm.edu
Problem Session: To be determined
Grading:
o Problem Sets: 50-70%
Problem sets will be distributed in class on Tues., every other week. Generally assignments will be due in two weeks, on Friday in the grader's mailbox by 12:00 PM.
o One Midterm Exam 25-30%
Take home: March 6, 2001.
o 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 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.
Recently republished. Contains a reasonable coverage of measurements theory.
I. Review (1 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. 16
Review 521: Foundations of quantum theory.
Download 1
Jan. 18
Review 521: Quantum dynamics, rotations, etc.
Three important problems- SHO, Angular momentum, Hydrogen atom.
Download 2
Jan. 23
Time independent nodegenerate perturbation theory (TINPT)
Download 3
Jan. 25
Applications of TINPT - Quadratic Stark effect.
Download 4
Jan. 30
Time independent degenerate perturbation theory (TIDPT)
Linear Stark effect.
Download 5
Feb. 1
Symmetry breaking, degenracies, and anticrossings
Download 6
Feb. 6
No Lecture
Feb. 8
Application of TIDPT: Hyperfine Structure and the Zeeman effect
Download 7
Feb. 13
Wigner's theory of symmetries, groups, and representations
Feb. 15
Rotation group, SU(2),
Addition of angular momentum: Clebsch-Gordan coefficients
Download 9
Feb. 20
Formal theory of angular momentum coupling.
Irreducible representations of SU(2)
Download 10
Feb. 22
Tensor Operators
Download 11
Feb. 27
Wigner-Eckart Theorem
Dipole Selection Rules
Download 12
Mar. 1
More on irreducible tensors: General multipoles and selection rules
Download 13
Mar. 6
Permutation symmetry: Identical particles, spin, and statistics.
Download 14
Mar. 8
Exchange degeneracy, singlets and triplets
Download 15
Mar. 12-16
Spring Break
Mar. 20
Multielectron atoms, multiplets, spectroscopy.
Variational method: Helium
15 continued
Mar. 22
Introduction to scattering - Time-independent vs. time-dependent formulation, cross-section, scattering amplitudes.
Download 16
Mar. 27
Time Independent Picture:
First Born-Approximation, Born Series, Green's Function.
Download 17
Mar. 29
Formal Theory of Scattering -
Green's Operator, Lippmann-Schwinger Equation, S-matrix
Download 18
Apr. 3
Spherical symmetry and partial waves
Download 19
Apr. 5
Scattering eigenstates and phase shifts
Download 20
Apr. 10
Examples: Hard-sphere scattering, high and low energy limits.
Scattering resonances and bound states
Download 21
Apr. 12
Time dependent perturbation - The interaction picture
Download 22
Apr. 17
Transition Probabilities:
Absorption and Emission. Resonance.
Download 23
Apr. 19
Transition Probabilities Continued:
Time-energy uncertainty. Second-order perturbation theory - virtual transitions.
Apr. 24
Resonant sinusoidal perturbation - Rabi Flopping
Download 24
Apr. 26
Coherent evolution vs. rate equations - Fermi's Golden Rule
Download 25
May 1
Exponential decay; Introduction to System-Reservoir Interaction
Download 26
May 3
Introduction to the Quantized Electromagnetic Field
Vacuum Fluctuations as a Reservoir - Spontaneous emission
Download 27
May 7-11
Finals
Problem Set #1 Perturbation Theory (Feb. 5 )
Problem Set #4
Many-body physics (Apr. 2)
Problem Set #2
Symmetries (Feb. 19)
Problem Set #5
Scattering (Apr. 17)
Problem Set #3
Tensors/multipoles (Mar. 7)
Problem Set #6
Time-dependent perturbation (May 3)
Exam (Mar. 21)
Questions
Solutions