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.