# Quantum Mechanics I 2017

## Quantum Mechanics I (2017 semester 2)

Prof. Matthew Luzum

Sala 202, Ala II

Monitor: Daniel Teixeira

Sala 329, Ala Central

### Homework

Homework 1 -- due August 14; Solutions

Homework 2 -- due August 21; Solutions

Homework 3 -- due August 28; Solutions

Homework 4 -- due September 11; Solutions

Homework 5 -- due September 18; Solutions

Homework 6 -- due October 2; Solutions

Homework 7 -- due October 9; Solutions

Homework 8 -- due October 16; Solutions

Homework 9 -- due October 23; Solutions

Homework 10 -- due October 30; Solutions

Homework 11 -- due November 13; Solutions

Homework 12 -- due November 20; Solutions

### Lectures

Lectures are scheduled for Mondays, Wednesdays, and Thursdays, 2:00-4:00 pm. Normally, Wednesdays will be used for problem solving sessions.

7 August - Structure of Quantum Mechanics: postulates, Hilbert space (Shankar ch. 1. Other references: Sakurai ch. 1, Weinberg ch 3, Littlejohn lecture notes, Jaffe lecture notes)

10 August - Structure of QM: Operators; commutators, outer product, resolutions of the identity, Hermitian anti-Hermitian and Unitary operators, spectra (Shankar Ch. 1, Littlejohn lecture notes)

14 August - Structure of QM: Normalizable and non-normalizable states, measurement, uncertainty principle (Sakurai Ch. 1, Littlejohn lecture notes)

17 August - Application of postulates to a physical system -- Stern-Gerlach experiment; Mixed states and the density operator (Littlejohn Stern-Gerlach , Littlejohn density operator, Sakurai Ch. 1)

23 August - Spatial degrees of freedom -- configuration space wavefunctions, spatial translations, momentum space (LIttlejohn notes)

24 August - Time evolution (Littlejohn notes)

28 August - Harmonic Oscillator (Littlejohn notes)

31 August - Path Integrals (Littlejohn notes)

11 September - Path Integrals II -- stationary phase approximation, classical limit (Littlejohn notes)

14 September - Particle in an electromagnetic field, gauge invariance, Aharonov-Bohm effect (Sakurai Ch 2.7)

25 September - Rotations/angular momentum (Sakurai Ch 3, Littlejohn classical rotations, Littlejohn spin-1/2 rotations)

28 September - Rotations in spin-1/2 systems (Sakurai Ch 3, Littlejohn notes)

2 October - Representations, matrix elements, irreducible subspaces (Sakurai Ch 3, LIttlejohn notes)

5 October - Orbital angular momentum and spherical harmonics (Sakurai Ch 3, Littlejohn notes)

9 October - Central potentials (Littlejohn notes, Sakurai Ch. 3)

16 October - Coulomb potential, Hydrogen atom (Sakurai Ch. 3.7 and 4.1)

18 October - Addition of angular momenta (Littlejohn notes, Sakurai Ch. 3)

23 October - tensor operators, irreducible tensor operators, spherical tensor operators (Sakurai Ch. 3.11, Littlejohn notes)

26 October - products of spherical tensor operators, Wigner-Eckart theorem (Sakurai Ch. 3.11, Littlejohn notes)

6 November - time-independent perturbation theory; nondegenerate (Sakurai Ch. 5)

9 November - degenerate time-independent perturbation theory, variational method (Sakurai Ch. 5)

13 November - time-dependent perturbation theory, Dyson series (Littlejohn notes, Sakurai Ch 5)

16 November - fine structure of the hydrogen atom (LIttlejohn notes)

### Exams

Midterm 1 - 21 September

Midterm 2 - 1 November

Final Exam - 23 November

### Suggested textbooks

Main text

J.J. Sakurai, "Modern Quantum Mechanics"

Other texts

Shankar, Principles of Quantum Mechanics.

Weinberg, Lectures on Quantum Mechanics

### Evaluation

Grades will be based on homework (10%) and the best 2 out of 3 exams (45% each).

The two midterm exams will cover ~50% of the material, and the final exam will review the entire semester. The lowest score of the three exams will be dropped, and the remaining 2 scores will determine 90% of your final grade.

### Program

Tentative list of topics:

General structure of quantum mechanics

Examples

Angular momentum / spin

Approximation methods