# Quantum Mechanics II (2020)

## Quantum Mechanics II (2020 semester 1)

Lectures: Mondays, Thursdays 14:00-16:00 (Online)

Discussion: Wednesdays 14:00-1600. (Cancelled until further notice)

Classroom: 2019 (207-C)

Prof. Matthew Luzum

Office: 3093

### Online lecture information

You must 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 078807.

### Homework

Homework 1; Solutions; (identical particles -- due March 23);

Homework 2; Solutions; (Symmetries 1 -- due March 30);

Homework 3; Solutions; (Symmetries 2 -- due April 13);

Homework 4; Solutions; (Scattering 1 -- due May 11);

Homework 5; Solutions; (Scattering 2 -- due May 25);

Homework 6; Solutions; (Quantum Information -- due June 15);

### Exams

Midterm 1 - 16 April

Midterm 2 - 10 June 15 June

Final Exam - 25 June 2 July

### Lectures

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

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

16 March -- Identical particles: Helium atom, periodic table, nuclear shell model (Sakurai 6.4, Shankar 13.4)

19 March -- No Lecture

23 March (Online) -- Symmetries: Continuous symmetries + conservation laws, groups, parity (Sakurai 4, Shankar 11)

26 March (Download Recording, View Recording on Youtube with automatically generated subtitles) -- Symmetries: Parity (Sakurai 4, Shankar 11)

30 March -- (Youtube recording) Symmetries: Time reversal (Sakurai 4, Shankar 11)

2 April -- (Youtube recording) Symmetries: Time reversal, Lattice translation (Sakurai 4, Shankar 11)

Semana santa -- no lectures

13 April -- (No recording) Scattering: Introduction, cross sections, 2-body kinematics

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

23 April -- (Youtube recording) Scattering: Green's function methods -- Lippmann-Schwinger equation (Sakurai 7.1)

27 April -- (Youtube recording) Scattering: Born approximation, Optical Theorem (Sakurai 7.2-7.3)

30 April -- (Youtube recording) Scattering: Partial waves & phase shifts (Shankar 19.5, Sakurai 7.6)

4 May -- (Youtube recording) Scattering: Partial waves -- Hard Sphere (Sakurai 7.6-7.7)

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

11 May -- (Youtube recording) Scattering: Symmetry considerations (Sakurai 7.10), Coulomb scattering (Weinberg 7.9)

14 May -- (Youtube recording) Scattering: Eikonal approximation (Shajesh notes), General Scattering Theory - S-matrix and Dyson Formula (Weinberg)

18 May -- Cancelled

21 May -- (Youtube recording) Scattering: General Scattering -- S-matrix, Born, Fermi's golden rule, optical theorem (Weinberg)

25 May -- (Recording) Quantum information theory: Classical information theory, Shannon entropy, joint entropy, mutual information, source coding theorem, density matrix (Grazioso, Nielsen & Chuang)

28 May -- (Recording) QIT: density matrix, quantum measurement, discerning (non-)orthogonal states (Grazioso, Nielsen & Chuang)

1 June -- (Recording) QIT: quantum complementarity, Holevo theorem, no-cloning theorem; applications -- black hole information paradox (Grazioso, Nielsen & Chuang)

4 June -- (Recording) QIT: applications -- quantum cryptography (Nielsen & Chuang, Mertz, Stumpf)

### Lecture Notes

Sections 1-3: Identical Particles, Symmetries, Scattering

### 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 (depending on time)

List of possible topics (struck topics were covered in QMI, semester 2 of 2019):

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.