Physics 522 Spring 2016


University of New Mexico

Department of Physics and Astronomy


Graduate Quantum Mechanics II

Eugene Wigner


Lectures: Tues. and Thurs. 9:30-10:45 PM, P&A Room 184
Problem Session: Friday 10:00-11:15 Room 5


Instructor: Prof. Ivan H. Deutsch

Office Hours: Monday 12:30-1:30 Room 30

Teaching Assistant: Gopi Muraleedharan

Office Hours: TBA





On this Page...

General Information


Lecture Schedule

Problem Sets


General Information


Problem Sets: 34%

Problem sets will be distributed approimately once a week and due on Tuesdays, to be placed in the grader's mailbox by 5:00 PM.

Two Exams 66%

"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. Intro to Structure of Matter (5 weeks)

A. From one to multiple degrees of freedom

B. Intro to Angular Momentum in Quantum Mechanics

C. Central potentials and 3D wave mechanics

D. Nonrelativistic Hydrogen Atom


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. Time-Dependent Perturbations (2 weeks)

A. Transition Probabilities

B. Coherent Rabi Flopping

C. Fermi's Golden rule


IV. Symmetries and Groups (5 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.




Tentative Schedule of Lectures




Jan. 19

Review of Quantum I

Basic Structure of Quantum Mechanics

Lecture 1

Podcast 1

Jan. 21

Review of Quantum I

From Hilbert Space to Physical Space

Lecture 2

Podcast 2

Jan. 26

Multiple Degrees of Freedom

Lecture 3

Podcast 3

Jan. 28

Continuation -- Separability

Podcast 4

Feb. 2


Symmetries and Degeneracy


Lecture 4

Podcast 5

Feb. 4

Continuation -- Complete Sets and Integrabilty


Podcast 6

Feb. 9

Rotations and angular momentum algebra

Eigenvalue problem for angular momentum

Lecture 5

Lecture 6

Podcast 7

Feb. 11


Oribtal angular momentum and spherical harmonics


Lecture 7

Podcast 8

Feb. 16

Central Potentials

Free particle in Spherical Coordinates

Lecture 8

Podcast 9

 Feb. 17

Partial Waves and Spherica Wells

Lecture 9a

Lecture 9b

Podcast 10

Feb. 23 Hydrogen Atom I

Lecture 10a

Podcast 11

Feb. 25 Hydrogen Atom II

Lecture 10b

Podcast 12

Mar. 1

Time independent nondegenerate perturbation theory (TINPT)

Lecture 11

Podcast 13

Mar. 3

Applications of TINPT

Anharmonic Trapping. Quadratic Stark effect.

Lecture 12

Podcast 14

Mar. 8

Time independent degenerate perturbation theory (TIDPT)

Linear Stark effect.

Lecture 13

Podcast 15

Mar. 10



Spring Break

Mar. 22

Time independent degenerate perturbation theory (TIDPT)

Avoided Crossings

Lecture 14

Podcast 16

Mar. 23

Addition of angular momentum -- elementary theory

Lecture 15

Podcast 17

Mar. 24

Application of TDPT:

Relativitistic effects - Fine Structure in Hydrogen

Lecture 16

Podcast 18

Mar. 29

Application of TIDPT:

Hyperfine Structure in Hydrogen

Lecture 17

Podcast 19

Mar. 31

Introduction to tensors

Rotation Group: SO(3) vs. SU(2)

Lecture 18

Podcast 20

Apr. 5

Addition of Angular Momentum -- Clebsch-Gordan Coefficients

Reducible and Irreducible representations of SU(2)

Lecture 19

Podcast 21

Apr. 7

Tensors, Irreducible Tensors, and the Spherical Basis

Lecture 20

Podcast 22

Apr. 12

The Wigner-Eckart Theorem

Lecture 21

Podcast 23

Apr. 13

Application -- Multipole selection rules

Lecture 22

Podcast 24

Apr. 19



Podcast 25

Apr. 21

Introduction to time-dependent perturbation :

Magnetic resonance and Rabi Flopping

Lecture 23

Podcast 26

Apr. 26

Time-Dependent Perturbation Theory

Formalism: Interaction picture and the Dysan Series

Lecture 24

Podcast 27

Apr. 28


Transition Probabilities:

Absorption and Emission. Resonance. Time-energy uncertainty

Lecture 25

Podcast 28

May. 4

Incoherent evolution: Fermi's Golden Rule

Lecture 26

Podcast 29

May. 5

Continuation: Absorption rates, stimulate and spontaneous emission

Podcast 30


Problem Sets and Exams

Problem Set #1

Due Jan. 26

 Problem Set #7

Due Mar. 24

 Problem Set #2

Due Feb. 2

Problem Set #8

Due Mar. 31

Problem Set #3

Due Feb. 11

Problem Set #9

Due Apr. 7

Problem Set #4

Due Feb. 18

 Problem Set #10

Due Apr. 14

 Problem Set #5

Due Feb. 25

 Problem Set #11

Due Apr. 21

 Problem Set #6

Due Mar. 3

 Problem Set #12

Due Apr. 28


 Problem Set #13