# Quantum Mechanics II (2021)

## Quantum Mechanics II (2021 semester 1)

Lectures: Mondays, Thursdays 14:00-16:00

Discussion: Wednesdays 14:00-1600

Classroom: 2019 (207-C)

T.A. ("Monitor"): Felipe Manoel de Sousa Freitas

felipefreitas@usp.br

Prof. Matthew Luzum

Office: 3093

### Online lecture information

It is recommended to first download the software from https://zoom.us/download .

Then, at the time of the lecture, click this link: https://zoom.us/j/561958509

Or, open the Zoom app and click "Join" (or "ingressar") and paste the code 561958509.

The password for the Zoom meeting is 848879.

### Homework

Homework 1; Solutions; (identical particles -- due April 4);

Homework 2; Solutions; (Symmetries 1 -- due April 11);

Homework 3; Solutions; (Symmetries 2 -- due April 18);

Homework 4; Solutions; (Scattering 1 -- due May 12);

Homework 5; Solutions; (Scattering 2 -- due May 26);

Homework 6; Solutions; (Density operator -- due June 20);

### Exams

Midterm 1 - 22 April

Midterm 2 - 7 June

Final Exam - 8 July

### Lectures

25 March (Recording) -- Identical particles: Multiparticle states, evolution of multiparticle states, permutation symmetry, indistinguishable particles, 2 electron system (Sakurai Ch 6, Shankar Ch 10)

29 March (Recording) -- Identical particles: more than 2 particles, anyons, Young tableaux (Sakurai Ch 6, Shankar Ch 10)

1 April (Recording) -- Identical particles: Helium atom, periodic table, nuclear shell model (Sakurai 6.4, Shankar 13.4)

5 April (Recording) -- Symmetries: Continuous symmetries + conservation laws, groups, parity (Sakurai 4, Shankar 11)

6 April (Recording) -- Symmetries: Parity (Sakurai 4, Shankar 11)

12 April (Recording) -- Symmetries: Time reversal (Sakurai 4, Shankar 11)

15 April (Recording Part 1 and Part 2) -- Symmetries: Lattice translation (Sakurai 4)

19 April -- No class

22 April -- Midterm Exam 1 (Symmetries, identical particles)

26 April (Recording) -- Scattering: Introduction, cross sections, 2-body kinematics

29 April (Recording) -- Scattering: Green's function methods -- Lippmann-Schwinger equation (Sakurai 7.1)

3 May (Recording) -- Scattering: Born approximation, Optical Theorem (Sakurai 7.2-7.3)

6 May (Recording) -- Scattering: Partial waves & phase shifts (Shankar 19.5, Sakurai 7.6)

10 May (Recording) -- Scattering: Partial waves -- Hard Sphere (Sakurai 7.6-7.7)

13 May (Recording) -- Scattering: Partial waves -- Finite spherical well / barrier, Resonance scattering, scattering of identical particles (Sakurai 7.7-7.9)

17 May -- No class

20 May (Recording) -- Scattering: Symmetry considerations (Sakurai 7.10), Coulomb scattering (Weinberg 7.9)

24 May (Recording) -- Scattering: Eikonal approximation (Shajesh notes), General Scattering Theory - S-matrix and Dyson Formula (Weinberg)

27 May (Recording) -- Scattering: General Scattering -- S-matrix, Born, Fermi's golden rule, optical theorem (Weinberg)

31 May -- No class

3 June -- Corpus Christi (no class)

7 June -- Midterm Exam 2 (Scattering)

10 June (Recording) -- Quantum entanglement; Density matrix, Shannon entropy, von Neumann entropy (Horodecki)

14 June (Recording) -- Quantum entanglement; entanglement, entanglement entropy, EPR, Bell's inequalities (Horodecki)

17 June -- No class

21 June (Recording) -- Anderson localization; (Domínguez-Adame and Malyshev; Bruns, Haenel, and Tom , numerical solution code)

24 June -- No class

28 June -- No class

1 July -- No class

5 July -- No class

8 July -- Final Exam (symmetries, identical particles, scattering, entanglement, Anderson localization)

### Lecture Notes

Full lecture notes: Identical Particles, Symmetries, Scattering, Entanglement, Anderson localization

### Suggested textbooks

Main text

J.J. Sakurai, "Modern Quantum Mechanics", (chapter numbers refer to Revised edition, not second edition)

Other texts

Shankar, Principles of Quantum Mechanics.

Weinberg, Lectures on Quantum Mechanics

### Evaluation

The final grade will be an average of the best 2 out of 3 exams (50% each).

### Program

Tentative list of topics:

Identical particles

Symmetries and conservation laws

Scattering theory

Other topics (send me suggestions if you have a preference)

List of possible topics:

WKB approximation, Variational methods, Time-dependent perturbation theory, Identical particles, Scattering theory, S-matrix, Eikonal approximation, Interaction radiation/matter, Canonical formalism, Path integrals, Symmetries and conservation laws, Particles in e/m fields, Entanglement, Interpretations of Quantum Mechanics, Basics of quantum computation,

Bell's inequality, Berry phase, Anderson localization.