Course information

**Textbook:**

R. Shankar, Principles of Quantum Mechanics
(2nd Edition, Springer, 2008).

**Learning Objectives**

Axiomatic theory of quantum mechanics (state vectors, operators, Hilbert space, measurement theory);
the uncertainty principle;
position, momentum, and linear
translations; time evolution and quantum dynamics;
wave equation for a particle in a classical electromagnetic field;
harmonic oscillators; path-integral
formulation of quantum mechanics; theory of rotations and angular momentum; density
matrix and quantum ensembles; addition of angular momentum.

**Office hours:** Wednesday, 2-4pm,
or contact me

Grades available on d2l

**Homework (due in class):**

**HW1** due 9/5: Shankar 1.1.3, 1.1.4, 1.3.4, 1.6.2, 1.6.3, 1.8.5, 1.8.10, 1.9.1

**HW2** due 9/12: Shankar 1.10.1, 1.10.2, 1.10.3, 4.2.1, 4.2.2, 5.3.1, 5.3.4

HW3 due 9/19

**Solutions:**

HW1
HW2

**Lecture notes:** (under construction!)

Lec 1: Chronology of Quantum Mechanics

Lec 2: Uncertainty principle

2-Slit Gedankenexperiment (Feynman lectures III.1)

Experiment with an Atom Interferometer

Lec 3: Wave mechanics

Lec 4: The postulates of QM

Lec 5: The state vector; bras and kets

Lec 6: Inner products and operators

Lec 7: Proofs of uncertainty principle, Ehrenfest's theorem

Lec 8: Parity and translation

Lec 9: Operator equations of motion

Lec 10: Energy-time uncertainty relation

Lec 11: 1D scattering

Lec 12: Resonant tunneling

Lec 13: Harmonic oscillator

Lec 13b: Oscillator matrix elements

Lec 14: Meissner effect

Lec 15: Aharonov-Bohm effect

Lec 16: Feynman path integral approach

Lec 17: Angular momentum operators

Lec 18: Angular momentum matrices

Lec 19: Angular momentum measurements

Lec 20: Rotations

Lec 21: Angular momentum wavefunctions

Lec 22: The density matrix (includes bonus material)

Lec 23: Addition of angular momenta

**Additional references:**

J. J. Sakurai and J. Napolitano, *Modern Quantum Mechanics* (2nd Edition, Pearson/Addison-
Wesley, 2011).

Leslie E. Ballentine,
Quantum Mechanics:
A Modern Development (World Scientific Publishing Company, 2000). Mathematical approach.

Gordon Baym,
Lectures on Quantum Mechanics (CRC Press, 2018). Informal but very good.

Claude Cohen-Tannoudji, Bernard Diu, Franck Laloe *Quantum Mechanics*, Volumes 1-2
(Wiley, 2005). An encyclopedia of QM.

David J. Griffiths, *Introduction to Quantum Mechanics* (2nd Edition, Pearson/Prentice
Hall, 2005). Standard undergraduate text good for a review of the basics.

Simulations of wave packet dynamics and 1D scattering (try it!)