Physics 491 Fall 2003

unmUniversity of New Mexico

Department of Physics and Astronomy


Quantum Mechanics I


Copenhagen Spring Conference 1936



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General Information


Lecture Schedule

Problem Sets


General Information


Instructor: Prof. Ivan Deutsch (my research group web page)

Phys/Astro Room 24, Phone: 277-1502


Office Hours: MW: 1:00-2:00 (or by appointment)


Teaching Assistant: Clark Highstrete (


Prequisites: Physics 330 and Math 312, 321 (or equivalents)


Lectures: MW 11:00-12:15, PandA room 5


Discussion Section: Friday 11:00-12:00, PandA room 184


Text (Required): Introductory Quantum Mechanics (Fourth Edition), by R. Liboff (Ed. Addison Wesley)

Other recommended texts: Introduction to Quantum Mechanics by D.J. Griffiths, A Modern Approach to QuantumMechanics by J. S. Townsend, Quantum Physics (3rd Edition) by S. Gasiorowicz, Quantum Mechanics vol. 1 by C.. Cohen-Tannoudji et al.


• Problem Sets: 25%
• Two “Midterms” 50% (25% each)
• Final Exam 25%


Problem Sets: Available on Tuesdays and due in one week on Tuesday in the grader’s mailbox by 5:00 PM. There will on order 10 assignments throughout the semester.


Exam Dates:

Mid. Exam 1: Oct. 14, 7:00-:900 PM, Room 184

Mid. Exam 2: Nov. 24

Final Exam: Dec. Dec. 17

Tentative Syllabus

I Foundations (4 weeks)
A. Review - Historical overview, fundamental concepts.
B. Mathematical foundation – Probability, statistics, waves and Hilbert space.
C. Structure of quantum mechanics - States, observables, measurements, and dynamics.

II Waves Mechanics in 1D (6 weeks)
A. Wave function, momentum space, wave packets, Schrödinger equation.
B. Bound states, one dimensional potentials, tunneling.
C. Simple harmonic oscillator.
D. Correspondence principle, Ehrenfest’s theorem, WKB.

III Beyond 1D Wave Mechancis (6 weeks)
A. Multiple degrees of freedoms.
B. Wave mechanics in 1D, 2D, 3D.
C. Angular momentum – spherical harmonics.
D. Central potentials.
E. The hydrogen atom.
F. Introduction to spin.


Tentative Schedule of Lectures




Aug. 25

  Overview: Historical context, blackbody, photons, the Bohr quantization rule, deBroglie waves, Schrodinger equation, the Born interpretation.

 Download 1

Liboff Ch. 2

 Aug. 27

Quantum vs. Classical Probability:

Motivating the Born rule. Axioms of probability theory. Quantum probability amplitude vs. classical probability.

 Download 2

Sep. 1

Labor Day: No Class


Sep. 3

Probability: Bayes rule, distribution functions, expectation values, moments, correlations.

Examples: Gaussian distribution, Binomial distribution.

 Download 3

 Sep. 8

Review of wave dynamics: Wave equation, superposition, wave packets, Fourier Transform.

Download 4

Gasiorowicz 2

Fourier notes

Sep. 10

Wave Mechanics: The Schrödinger equation, continuity equation,

 Download 5

Sep. 15

Momentum space, the uncertainty principle.


Download 5a

 Sep. 17

Eigenfunctions, Eigenvalues,

Time Indepedent Schrödinger Equation

Download 6

Gasiorowicz 3

Sep. 22

The infinite square well, time dependent solutions, probability interpretation.

Download 7

Liboff 4.1-4.4, 5.1

 Sep. 24

Introduction to Hilbert Space,

Completeness, inner product, orthonormal functions

  Download 8

Sep. 29

The General Structure of Quantum Mechanics

States, Observables, Measurements, Dynamics

Download 9

Liboff Ch. 3, 4.5-4.6

Gasiorowicz 5

 Oct. 1

Compatible Observavbles -

Commutators, Uncertainty, Conservation Laws

Download 10

Liboff 5.2-5.5 

Oct. 6

Mechicanics in Quantum Mechanics

Ehnrenfest Theorem, Classical Trajectories

 Download 11

 Oct. 8

No Class


 Oct. 13

1D Wave mechanics: General properties.

Bound vs. free energy levels. Symmetric finite square well.

 Download 12

 Oct. 15

Bound states in 1D continued

Parity, delta function poential.

Download 13

Liboff Ch.8.1

  Oct. 20

Unbound states -Scattering

Download 14

Liboff 7.1,7.5

 Oct. 22

Unbound States: Step potentials and barriers.


Download 15

Liboff 7.6,7.7

 Oct. 27

.Catch up...

 Oct. 29

Finite square well: Ramsauer-Townsend effect. S-matrix

Download 16

Liboff 7.8

 Nov. 3

Wave mechanics in 3D - separation of coordinates.

 Download 17

Lib. 8.5, 10.1

 Nov. 5

Central potentials - radial and angular momentum, radial and angular Schrödinger equation.

Download 18

Liboff 10.2, 9.2,9.3

 Nov. 10

Angular momentum in quantum mechanics: spherical harmonics, operator algebra, and commutation relations.

Download 19

Liboff 9.1

Nov. 11

Free particle in spherical coordinates -- Partial waves.

Download 20

Liboff 10.3

Nov. 12 

Spherical Wells.

Download 21

Nov. 17

Two-body central force problem: Hydrogen atom. 

Download 22

Liboff 10.5

Nov. 19

Hydrogen eigenvalue problem

Download 23

Liboff 10.6

 Nov. 24

Hydrogen: Energy spectrum, eigenfunctions, etc.

Download 24

 Nov. 26

Scattering - Unbound problems in 3D

Review of classical scattering: Cross-sections and scattering amplitudes.

Download 25

Liboff 14.1

 Dec. 1

Low Energy Scattering -

Partial Wave Expansion

Download 26

Liboff 14.1

Dec. 3

s-wave Scattering examples

Download 27

Liboff 14.1

 Dec. 8
Review Session with Clark Highstrete
Dec. 10
No Class

Dec. 15-19



Problem Sets


Problem Set #1

Due Sep. 9

 Problem Set #6

Due Oct. 29

 Problem Set #2

Due Sep. 16

Problem Set #7

Due Nov. 5

Problem Set #3

Due Oct. 1

 Problem Set #8

Due Nov. 12

Problem Set #4

Due Oct. 7

Problem Set #9

Due Nov. 19

 Problem Set #5

Due Oct. 29

Problem Set #10

Due Dec. 10


Exam I

Exam I Solutions

Exam II

Exam II Solutions

Final Exam

Final Exam Solutions