Physics 521 Fall 2014



Graduate Quantum Mechanics I


University of New Mexico

Department of Physics and Astronomy

Lectures: Tues. and Thurs. 9:30-10:45 PM, P&A Room 184
Problem Session: Friday 10:30-12:00 Room 190


Instructor: Prof. Ivan H. Deutsch

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

Teaching Assistant: Gopi Murleedharan

Office Hours: TBA


General Information



Problem Sets: 35%

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

Two "Midterms" 40%

Final Exam 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. I and II, by C. Cohen-Tannoudji, B. Diu, and F. Laloë.

This text is a great reference book to have around, but very verbose and sometimes hard to wade through. Many classic problems are solved in the "Complements.

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

Every thing 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.

Republished. Contains a reasonable coverage of measurements theory.

o Introductory Quantum Mechanics, R. L. Liboff

An upper division undergraduate text . Very clear.


Tentative Syllabus


I Foundations (4 weeks)

A. Mathematical foundation - Hilbert space, operators, eigenvalues, commutators.

B. Structure of quantum mechanics - States, observables, measurements.

C. Quantum dynamics - Schrödinger and Heisenberg pictures, conservation laws.


II Waves Mechanics in 1D (3 1/2 weeks)

A. Wave function, momentum space, wave packets, Schrödinger equation.

B. Bound states, one dimensional potentials, tunneling.

C. Correspondence principle, Ehrenfest's theorem, WKB.

D. Simple harmonic oscillator - Different representations, phase space in QM.


III Angular Momentum (3 weeks)

A. Angular momentum as the generator of rotations, commutation algebra.

B. Eigenstates, Spherical harmonics.

C. Spin and magnetic resonance.


IV Multiple Degrees of Freedom (4 1/2 weeks)

A. Entangled states, Einstein-Podolsky-Rosen paradox.

B. Addition of angular momentum - Clebsch-Gordan coefficients.

C. Wave mechanics in 3D.

D. Central potentials.

E. The hydrogen atom.


Tentative Schedule of Lectures




Aug. 19

 Introduction to quantum notions - probability amplitude, wave/particle duality

 Aug. 21

Math: Linear vector spaces, representations, inner product, Dirac notation

Lecture 2

Podcast 2

Aug. 26

Math: Operators, adjoints, change of basis, unitarity

Lecture 3

Podcast 3

Aug. 28

Math: Eigenvalues, eigenvectors, commutators

Lecture 4

Podcast 4

 Sept. 2

Hermitian operators, Complete sets of commuting operators

Podcast 5

Sept. 4

Structure of quantum mechanics- States, observables, measurements

Lecture 5-6

Podcast 6

 Sept. 9

Unitary reversible evolution vs. Irreversible stochastic evolution

 Sept. 11

More on the mystery of quantum measurements

Sept. 16

Pure vs. mixed states - density operators

Lecture 7

Podcast 9

 Sept. 18


 Sept. 23

Open Quantum Systems and Decoherence

 Sept. 25

Quantum Dynamics:

Time evolution operator, conservation, and symmetries 

Stationary-states: Time Independent Schrödinger Equation

Lecture 8

Podcast 12

 Sept. 30

Time evolution: Schrödinger vs. Heisenberg

Lecture 9

Podcast 13

 Oct. 2

Particle mechanics in 1D, Heisenberg picture,

x and p representations.

Lecture 10

Podcast 14

  Oct. 7


Podcast 15

 Oct. 9



 Oct. 14

Wave mechanics, interpretation of the wave function:

Probability current, semiclassical limit (WKB), path integrals

Lecture 11, 11b

Podcast 16

 Oct. 16

Time Independent Schrödinger Equation (TISE).

Free particle, scattering states, constant potentials

Parity, bound states

Lecture 12, 13

Podcast 17

 Oct. 21

SHO, Review classical problem, a and a^\dag

Lecture 14

Podcast 18

 Oct. 23

SHO, Energy eigenstates, x-p space

Lecture 15

Podcast 19

 Oct. 28


SHO, Uncertainty relations

Position/Momentum, Number/Phase

Lecture 16

Podcast 20

Oct. 30

SHO, Coherent States, Phase Space

and the Classical Limit

Nov. 4

Multiple Degrees of Freedom:

Lecture 17a, 17b

Podcast 22

 Nov. 6

Separability, Symmetries and Degeneracy

Rotations and angular momentum algebra

Lecture 18

Podcast 23

 Nov. 11



Nov. 13

Eigenvalue problem for angular momentum


Lecture 20

Podcast 25

 Nov. 18

Oribtal angular momentum and spherical harmonics

Lecture 21

Podcast 26

 Nov. 20

Central Potentials and the Radial Equation

Lecture 22

Podcast 27

 Nov. 25

No Lecture -- to be made up


 Nov. 27




 Dec. 2

Radial equation continued: Partial Waves and Spherical Wells

Lecture 23a

Lecture 23b

 Dec. 3

Spin-1/2: Pauli algebra

 Dec. 4

Tensor product

Separability, entangled states, marginal density operator

Lecture 25a, 25b

Podcast 28

Dec. 8

Bonus Lecture

EPR, Hidden Variables, and Bell Inequalties

Lecture 26

Podcast 29


Problem Sets



Problem Set #1

Due Sept. 2

Problem Set #6

Due Oct. 14

 Problem Set #11

Due Dec. 5

 Problem Set #2

Due Sept 9

 Problem Set #7

Due Oct. 21


Problem Set #3

Due Sept. 16

Problem Set #8

Due Oct. 27


Problem Set #4

Due Sept. 23

 Problem Set #9

Due Nov. 4


 Problem Set #5

Due Oct. 7

Problem Set #10

Due Nov. 25