Physics 492 Spring 2019

Department of Physics and Astronomy


Quantum Mechanics II


Paul A. M. Dirac


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General Information


Lecture Schedule

Problem Sets


General Information


Instructor: Prof. Ivan Deutsch

Phys/Astro Room 23, Phone: 277-8602


Office Hours: TBA


Teaching Assistant: Anupam Mitra (

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.


• 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
Quantum computing

Tentative Schedule of Lectures




Jan. 15

Review: The Structure of Quantum Mechanics

Lecture 1

Podcast 1

 Jan. 17


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


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


Operator Algebra for Angular Momentum

Podcast 10

Feb. 19



 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



 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




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