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 Radial Equation

Lecture 8

Podcast 11

Feb. 26
Two-body problem - Intro to hydrogen

Lecture 9a

Podcast 12

Feb. 28

Exam 1


Mar. 5

Solution to the TISE for the bound states of hydrogen

Lecture 9b

Podcast 13

 Mar. 7

Hydrogenic atoms continued

Intro to magnetic coupling: Normal Zeeman effect

Lecture 10

Lecture 11

Podcast 14

 Mar. 11-15

Spring Break

  Mar. 19

Introduction to spin - Pauli matrices,

Lecture 12

Podcast 15

 Mar. 21

Magnetic coupling: gyromagnetic ratio, spin magnetic moment, Larmor precession and rotations, Bloch Sphere

Lecture 13

Podcast 16

 Mar. 25


Stern Gerlach

Lecture 14

Podcast 17

 Mar. 26

Introduction to to the density matrix

Lecture 15

Podcast 18

 Mar. 28

NO CLASS (travel)

 Apr. 2

Introduction to perturbation theory

Avoided crossing

Lecture 16

Podcast 19

 Apr. 4

Time-dependent perturbation theory

Magnetic Resonance - Rabi flopping

Podcast 20

 Apr. 9

Time-dependent perturbation theory

Fermi's Golden Rule and rate equations

Podcast 21

 Apr. 11

Addition of Angular Momentum: Addition of two spins. Singlet and Triplets.

General theory of the addition of angular momentum

Lecture 17a

Lecture 17b

Podcast 22

Apr. 16

Spin-orbit and relativisitic corrections in hydrogen

Lecture 18

Podcast 23

Apr. 18

Hyperfine interactions

The real hydrogen atom

Lecture 19

Podcast 24

Apr. 23

Mutiple Degrees of Freedom formalized: Tensor product

Lecture 20

Podcast 25

 Apr. 25

Entanglement marginal state

Podcast 26

April 30
The EPR paradox
Lecture 21
Podcast 27
May 2
Bell's Inequalities
Podcast 28


Problem Sets


Problem Set #1

 Problem Set #5

 Problem Set #2

Problem Set #6

Problem Set #3

 Problem Set #7

Problem Set #4

Problem Set #8


Problem Set #9


Final project