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: