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.