# Quantum Mechanics II (2017)

## Quantum Mechanics II (2017 semester 1)

Prof. Matthew Luzum

### Homework

Homework 1 (identical particles -- due March 27); Solutions

Homework 2 (Symmetries 1 -- due April 3); Solutions

Homework 3 (Symmetries 2 -- due April 17); Solutions

Homework 4 (Scattering 1 -- due May 15); Solutions

Homework 5 (Scattering 2 -- due May 29; Solutions

### Exams

Midterm 1 - 24 April

Midterm 2 - 5 June

Final Exam - 26 June

### Lectures

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

16 March -- Identical particles: 2 electron system, more than 2 particles, anyons (Sakurai Ch 6, Shankar Ch 10)

20 March -- Identical particles: Young tableaux, (Sakurai Ch 6.5)

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

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

30 March -- Symmetries: Parity (Sakurai 4, Shankar 11)

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

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

17 April -- Symmetries: Lattice Translation (Sakurai 4.3)

27 April -- Scattering: Introduction, cross sections, 2-body kinematics

3 May -- Scattering: Green's function methods -- Lippmann-Schwinger equation (Sakurai 7.1)

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

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

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

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

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

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

29 May -- Scattering: General Scattering -- S-matrix, Born, Fermi's golden rule, optical theorem

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

12 June -- QIT: density matrix, quantum measurement, discerning (non-)orthogonal states (Grazioso, Nielsen & Chuang)

14 June -- QIT: quantum complementarity, Holevo theorem, no-cloning theorem (Grazioso, Nielsen & Chuang)

19 June -- QIT: applications -- black hole information paradox (Grazioso)

22 June -- 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

Grades will be based on homework (10%) and the best 2 out of 3 exams (45% 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 2016):

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.

Suggestions from students:

Anderson localization

Berry Phase/Aharonov-Bohm effect

Interpretations of Quantum Mechanics

S-matrix Theory

Basic of quantum computation

Entanglement

Bell's inequality

Quantum Hall Effect