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; (Quantum Information -- due June 15);

Exams

Midterm 1 - 16 April
Midterm 2 - 10 June
Final Exam - 25 June

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 -- 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.