Physics 492 Spring 2019

Department of Physics and Astronomy

 

Quantum Mechanics II

 

Paul A. M. Dirac


 

On this Page...

General Information

Syllabus

Lecture Schedule

Problem Sets

 


General Information

 

Instructor: Prof. Ivan Deutsch

Phys/Astro Room 23, Phone: 277-8602

email: ideutsch@unm.edu

Office Hours: TBA

 

Teaching Assistant: Anupam Mitra (anupam@unm.edu)

Office Hours: TBA

 

Prequisites: Physics 491 and Math 312, 321 (or equivalents)

 

Lectures: Tues&Thurs 11:00-12:15, PandA room 184

 

Discussion Section: Friday 9:00-9:50, PandA room 184

 

Text : None required. Lecture Notes and Podcasts Distributed.

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%
• 2 Midterm Exam 50%
• Final Project 20%

Problem Sets: Available on Tuesdays and due in one week on Tuesday in the grader’s mailbox by 5:00 PM.

 

Tentative Syllabus


I Foundations
A. Review - Fundamental concepts: Hilbert space, states, observables, measurements, dynamics.
B. Mathematical foundation – Linear algebra, matricies, Dirac notation
C. Continuous variables, symmetries


II Beyond 1D Wave Mechancis
A. Multiple degrees of freedoms
B. Wave mechanics in 2D, 3D
C. Angular momentum – spherical harmonics
D. Central potentials
E. The hydrogen atom

III Spin and Angular Momentum in Quantum Mechanics
A. Angular momentum algebra and algebraic solution to eigenvalue equation
B. Spin Angular Momentum: Pauli matrices
C. Magnetic coupling: Magnetic dipoles, Stern Gerlach, Larmor precession
D. Introduction to perturbation theory: Zeeman splitting and avoided crossings

IV Addition of Angular Momentum
A. Coupled vs. uncoupled representations
B. Spin-orbit and hyperfine interactions -- the real hydrogen atom
C. Formal theory of composite systems: tensor product
D. Addition of spins - singlet and triplet
E. Identical particles and spin statistics: helium atom and the periodic table

V. Quantum Information Science
A. Density matrices
B. EPR/Bohm, Entangled states, Bell's inequalties
C. Decoherence and open quantum systems
D. Introduction to Quantum Information Science (QIS)
E. Quantum communication: quantum teleporation, quantum cryptography
F.
Quantum computing


Tentative Schedule of Lectures

Date

 Topic

 Notes

Jan. 15

Review: The Structure of Quantum Mechanics

Lecture 1

Podcast 1

 Jan. 17

Continuation

Podcast 2

Jan. 22

Foundations 1: Linear algebra, representations, Dirac notation

Lecture 2

Podcast 3

Jan. 24

Foundations 2: Hermitian operators, Eignevalues and Diagonalization

Lecture 3

Podcast 4

 Jan. 29

Foundations 3: Position and momentum space, Continuous Symmetries

Lecture 4

Podcast 5

Jan. 31

Continuation

Podcast 6

Feb. 5

Quantum Mechanics beyond one degree of freedom

Separability, Symmetry, Degeneracies

Lecture 5

Podcast 7

 Feb. 7

Quantum Mechanics in 2D

Central potentials and introduction to angular momentum

Lecture 6

Podcast 8

Feb. 12

SQuInT -- no class

 
Feb. 14

Spherical Symmetry

Eigenstates of Angular momentum

Lecture 7

Podcast 9

Feb. 15

Makeup

Operator Algebra for Angular Momentum

Podcast 10

Feb. 19

SNOW DAY

 

 Feb. 21

Position Representation of Angular Momentum

Spherical Harmonics and the Radia Equation

Lecture 8

Podcast 11

Feb. 26
Two-body problem - Intro to hydrogen
 

Feb. 28

Exam 1

 

Mar. 1

Make up

Hydrogenic atoms continued

 

Mar. 5

Magnetic coupling: gyromagnetic ratio, spin magnetic moment, electron g-factor, Stern Gerlach

 

 Mar. 7

Introduction to spin - Pauli matrices, Bloch Sphere

 

 Mar. 11-15

Spring Break
 

  Mar. 19

Larmor precession and Rotations

 

 Mar. 21

Inroduction to perturbation theory - Zeeman splitting and avoided crossings
 

 Mar. 26

Addition of Angular Momentum - Coupled and uncoupled representations.

 

 Mar. 28

Continuation

 

 Apr. 2

Spin-orbit and hyperfine interactions

The real hydrogen atom

 

 Apr. 4

Mutiple Degrees of Freedom formalized: Tensor products

Introduction to entanglement

 

 Apr. 9

Addition of two spins. Singlet and Triplets. Generalizations
 
Apr. 16
Identical particles, spin, statistics
 

Apr. 11

Helium, larger atoms, molecules

 

Apr. 18 

Introduction to density matrices
 

Apr. 23

The Bloch sphere = quantum bits

 

Apr. 25

Entanglement redux

 

 Apr. 30

EPR, Bohm, and Bell's Inequalities

 

 May 2

Decoherence and the measurement problem
 
 May 5

Slack

 

 


Problem Sets

 

Problem Set #1

 Problem Set #5

  • Questions
  • Solutions

 Problem Set #2

Problem Set #6

  • Questions
  • Solutions

Problem Set #3

 Problem Set #7

  • Questions
  • Solutions

Problem Set #4

Problem Set #8

  • Questions
  • Solutions