# QMI2020

## Quantum Mechanics I (2020 semester 2)

PGF5001

Prof. Matthew Luzum

TA ("monitor"): Davi Bastos Costa <davi.costa@usp.br>

Mondays, Wednesdays, and Thursdays, 2:00-4:00 pm

Typically, lectures will be Mondays and Thursdays.

Wednesdays will be for discussing the homework problems.

Lecture room: 2024 (212-C)

Virtual lecture room: 293-939-199

Link: https://zoom.us/j/293939199

Password: 500028

Advice for lectures:

Please keep your camera on. It helps for me to know whether to go slower or faster, or to explain something again.

Type questions into the Zoom chat, or raise hand (click "Participants", and then click the button "Raise Hand"). Do this at any time during the lecture.

You can download the lecture notes (see below) before the lecture, so it's easier to follow. However, it is best to also write your own notes during the lecture.

You can discuss the course in the Slack channel or the WhatsApp group.

### Homework

Please send your completed homework as one file to Davi (davi.costa@usp.br) before 23:59 on the due date. Please use your name as the filename. For example: MatthewLuzumHW1.pdf

Update: Please upload your homework to the Moodle page for the course.

You can complete the homework problems on ordinary paper, and then digitize them with a scanner or camera. Please use a scanning app such as Adobe Scan, Tiny

Scanner, Camscanner, or something similar, to produce a single clean document. If you have no camera or no way to digitize a document, please tell me as soon as possible.

Homework 1 (Solutions) -- due August 24;

Homework 2 (Solutions) -- due August 31;

Homework 3 (Solutions) -- due September 10;

Homework 4 (Solutions) -- due September 17;

Homework 5 (Solutions) -- due September 24;

Homework 6 (Solutions) -- due October 8;

Homework 7 (Solutions) -- due October 15 October 16;

Homework 8 (Solutions) -- due October 22 October 23;

Homework 9 (Solutions) -- due October 29 October 30;

Homework 10 (Solutions) -- due November 6;

Homework 11 (Solutions) -- due November 23;

Homework 12 (Solutions) -- due November 30;

### Lectures

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

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

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

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

24 August (Recording) - 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)

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

31 August (Recording) - Time evolution (Littlejohn notes)

3 September (Recording) - Harmonic Oscillator (Littlejohn notes)

7 September - No class (Independência do Brasil)

10 September (Recording) - Path Integrals (Littlejohn notes)

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

17 September (Recording) - Some topics in 1D wave mechanics

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

24 September - No class

28 September - Exam 1 (Lectures 1-10, Homework 1-5)

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

5 October (Recording) - Rotations in spin-1/2 systems (Sakurai Ch 3, Littlejohn notes)

8 October (Recording part 1, Recording part 2) - Representations, matrix elements, irreducible subspaces (Sakurai Ch 3, LIttlejohn notes)

12 October - No class (Nossa Senhora Aparecida)

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

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

22 October (Recording) - Coulomb potential, Hydrogen atom, (Sakurai Ch. 3.7 and 4.1), addition of angular momentum (Littlejohn notes, Sakurai Ch. 3)

26 October (Recording) - Clebsch-Gordon Coefficients, tensor operators, irreducible tensor operators, spherical tensor operators (Sakurai Ch. 3.11, Littlejohn notes)

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

2 November - No class (Finados)

5 November - No class

9 November - No class

12 November - Exam 2 (Lectures 11-18, Homework 6-10)

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

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

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

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

3 December - Final Exam (All topics from the semester)

### Exams

Midterm 1 - 28 September (Lectures 1-10, Homework 1-5)

Midterm 2 - 12 November (Lectures 11-18, Homework 6-10)

Final Exam - 3 December (All topics from the semester)

### 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%, depending on assignment of a monitor for the course) 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