Physics 492 Spring 2004

unmUniversity of New Mexico

Department of Physics and Astronomy

 

Quantum Mechanics II

 

Paul A. M. Dirac

 

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General Information

Syllabus

Lecture Schedule

Problem Sets

 

General Information

 

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

Phys/Astro Room 24, Phone: 277-1502

email: ideutsch@info.phys.unm.edu

Office Hours: MW: 12:30-1:30 (or by appointment)

 

Teaching Assistant: Animesh Datta (animesh@unm.edu)

 

Prequisites: Physics 491 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.

 

Grading:
• Problem Sets: 30%
• Midterm Exam 30%
• Final Exam 30%
• Instructor Judgement 10%

 

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, 7:00-:900 PM, Room 184

Final Exam: Dec. Dec. 17

Tentative Syllabus


I Foundations
A. Review - Fundamental concepts: Hilbert Space, States, Observables, Measurements, Dynamics.
B. Mathematical foundation – Linear Algebra, Matricies.
C. Dirac Notion - Bras, Kets, Representations, Adjoints.


II Simple Harmonic Oscillator
A. Alegrabic formulation of the problem - Rasing and lowering operators.
B. Algebraic solution to the Time Independent Schrödinger Equation (TISE).
C. Wave functions - position and momentum space.
D. Correspondence principle, WKB.


III Angular Momentum Redux and Marix Mechanics
A. Angular momentum algebra.
B. Algebraic solution to eigenvalue equation - complete set of commuting operators.
C. Matrix representations - Matrix Mechanics.
D. Spin Angular Momentum: Pauli algebra, Magnetic coupling.
E. Stern-Gerlach: von Neuman Measurements, statistical mictures, density matrices.

IV Addition of Angular Momentum
A. Coupled vs. Uncoupled Representations
B. Addition of spins - singlet and triplet
C. EPR/Bohm, Entangled States, Bell's Inequalties.
D. Identical Particles and Spin Statistics: Helium Atom, Hydrogen Molecule.
E. Spin-Orbit Coupling -- real atomic spectra, introduction to perturbation theory.

 

V. Perturbation Theory
A. Nondegenerate bound state perturbation theory -- Linear Stark effect.
B. Degenerate perturbation theory -- Quadratic Stark effect.
C. Time dependent perturbation theory -- Absorption and emission of radiation.
D. Decoherence.

 

Tentative Schedule of Lectures

Date

 Topic

 Notes

Jan. 21

Review: The Structure of Quantum Mechanics

 Download 1

 Jan. 26

Foundations 1: Linear algebra, representations, dual space, adjoints, matricies

 Download 2

Jan. 28

Foundations 2: Outer product, Dirac notation, bras, kets

 Download 3

Feb. 2

Foundations 3: Hermitian operators, Diagonal representations, Position and Momentum space

Download 4

 Feb. 4

Simple Harmonic Oscillator -- Introduction

Classical review and quantization.

 Download 5

Feb. 9

Solution to TISE

Algebraic formulation, raising and lowering operators.

Download 6
Feb. 11

SHO: Wave functions in position and momentum space.

Download 7

 Feb. 16

Angular Momentum -- Review

Commutation relations, spherical harmonics, algebraic formulation

Download 8

Feb. 18

Matrix Representation of Angular Momentum

Matrix solutions of eigenequation.

Download 9

 Feb. 23
Magnetic Coupling: gyromagnetic ratio, Zeeman effect, spin magnetic moment, electron g-factor.

  Download 10
Feb. 25

Larmor Precession and Rotations

Download 11

 Mar. 1

Stern-Gerlach Experiment: Basic Quantum Measurement

Download 12

Mar. 3

Density Matricies -

Coherent superposition vs. statistical mixture

 Download 13

 Mar. 8

No Class

 

 Mar. 10
Midterm Exam

 

 Mar.14-20
SPRING BREAK

 

  Mar. 22

Mutiple Degrees of Freedom

Tensor Products, Entangled states, Marginals

 Mar. 24

EPR and Bell's Inequalities

Download 15

 Mar. 29
Addition of Angular Momentum - Coupled and Uncoupled Representations.

 Mar. 31

Addition of two spins. Singlet and Triplets. Generalizations

Download 17

 Apr. 5

Identical particles, spin, statistics

Download 18

 Apr. 7
Helium, larger atoms, molecules

Download 19

 Apr. 12

Perturbation theory, nondegenerate.

First order example

Download 20

Apr. 14

Second order nondegenerate perturbation theory.

Quadratic Stark Effect

Download 21

Apr. 19 

Degenerate perturbation theory.

Linear Stark Effect

Download 22

Apr. 21

Relativisitic effects:

Spin-orbit coupling, fine structure.

Download 23

Apr. 26

Time dependent perturbations

Coherent interaction - Rabi flopping

Download 24

 Apr. 28
Incoherent - Fermi's Golden Rule

Download 25

 May 3

Fermi's Golden Rule vs. Rabi Flopping

Examples: Absorption and Emission of Radiation by Atoms

Download 26
 May 5

Review

 

May 12
Final Exam

 

Problem Sets

 

Problem Set #1

 Problem Set #6

 Problem Set #2

Problem Set #7

Problem Set #3

 Problem Set #8

Problem Set #4

Problem Set #9

 Problem Set #5

Problem Set #10

 

Midterm Exam

Midterm Exam Solutions

Final Exam

Final Exam Solutions