Physics 522 Spring 2011

University of New Mexico

Department of Physics and Astronomy


Quantum Mechanics II


Eugene Wigner


Link to: Physics 521 Quantum Mechanics I, Fall 2002


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General Information


Lecture Schedule

Problem Sets


General Information


Lecture: Physics and Astronomy, Room 184, TR 9:30-10:45


Instructor: Prof. Ivan Deutsch

Phys/Astro Room 23, Phone: 277-8602


Problem Session: Monday, 12:30-1:20, Room 5

Office Hours: Wednesday, 10:00-11:00, Room 23


Teaching Assistant: Bob Keating


Offices : To be determined



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




Jan. 18

 Review: Foundations - Structure of Quantum Mechanics.

States, Observables, Measurements, Symmetries

 Download 1

Jan. 20

 Review: Schrödinger Equation: Dynamics/Spectra.

Examples: Simple Harnomic Oscillator, Hydrogen Atom

Jan. 25

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

Feb. 10


Feb. 14

Review: Addition of Angular Momentum

Feb. 15

Application of TIDPT:

Relativitistic effects - Fine Structure in Hydrogen

Feb. 17

No lecture


Feb. 22

Application of TIDPT:

Hyperfine Structure in Hydrogen

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)

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

Spring Break


Mar. 22

No lecture (on travel)

Mar. 24

Wigner-Eckart Theorem:

Download 12

Mar. 28

Make up lecture:

Application -- Dipole selection rules

Mar. 29

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

Apr. 26
Fermi's Goldern Rule
Apr. 26
Exponential Decay - System Reservoir

 May 3

No lecture (on travel)


May 5

Spontaneous emission

Download 27


Problem Sets and Exams

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