Quantum Mechanics II (2021)

Quantum Mechanics II (2021 semester 1)

Lectures:  Mondays, Thursdays 14:00-16:00

Discussion:  Wednesdays 14:00-1600

Classroom:  2019 (207-C)

T.A. ("Monitor"):   Felipe Manoel de Sousa Freitas

felipefreitas@usp.br

Prof. Matthew Luzum

Office:  3093

Online lecture information

It is recommended to 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 848879.

Homework

• Homework 1;  Solutions;   (identical particles -- due April  4); 

• Homework 2;  Solutions;   (Symmetries 1 -- due April 11); 

• Homework 3;  Solutions;   (Symmetries 2 -- due April 18); 

• Homework 4;  Solutions;   (Scattering 1 -- due May 12); 

• Homework 5;  Solutions;   (Scattering 2 -- due May 26);  

• Homework 6;  Solutions;   (Density operator -- due June 20);

Exams

• Midterm 1 - 22 April

• Midterm 2 - 7 June

• Final Exam - 8 July

Lectures

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

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

• 1 April (Recording) -- Identical particles:  Helium atom, periodic table, nuclear shell model (Sakurai 6.4, Shankar 13.4)

• 5 April (Recording) --  Symmetries:  Continuous symmetries + conservation laws, groups, parity (Sakurai 4, Shankar 11)

• 6 April (Recording) -- Symmetries:  Parity (Sakurai 4, Shankar 11)

• 12 April (Recording) --  Symmetries: Time reversal (Sakurai 4, Shankar 11)

• 15 April (Recording Part 1 and Part 2)  --  Symmetries: Lattice translation (Sakurai 4)

• 19 April --  No class

• 22 April  -- Midterm Exam 1 (Symmetries, identical particles)

• 26 April (Recording) -- Scattering:  Introduction, cross sections, 2-body kinematics

• 29 April (Recording) -- Scattering: Green's function methods -- Lippmann-Schwinger equation (Sakurai 7.1)

• 3 May (Recording) -- Scattering: Born approximation, Optical Theorem (Sakurai 7.2-7.3)

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

• 10 May (Recording) --  Scattering: Partial waves -- Hard Sphere  (Sakurai 7.6-7.7)

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

• 17 May -- No class

• 20 May (Recording) --  Scattering: Symmetry considerations (Sakurai 7.10), Coulomb scattering (Weinberg 7.9)

• 24 May (Recording) --  Scattering: Eikonal approximation (Shajesh notes), General Scattering Theory - S-matrix and Dyson Formula (Weinberg)

• 27 May (Recording) -- Scattering:  General Scattering -- S-matrix, Born, Fermi's golden rule, optical theorem (Weinberg)

• 31 May --  No class

• 3 June -- Corpus Christi (no class)

• 7 June -- Midterm Exam 2 (Scattering)

• 10 June (Recording) -- Quantum entanglement;  Density matrix, Shannon entropy, von Neumann entropy (Horodecki)

• 14 June (Recording) -- Quantum entanglement;  entanglement, entanglement entropy, EPR, Bell's inequalities (Horodecki)

• 17 June -- No class

• 21 June (Recording) -- Anderson localization; (Domínguez-Adame and Malyshev; Bruns, Haenel,  and Tom ,   numerical solution code)

• 24 June --  No class

• 28 June --  No class

• 1 July -- No class

• 5 July --  No class

• 8 July -- Final Exam (symmetries, identical particles, scattering, entanglement, Anderson localization)

Lecture Notes

• Full lecture notes: Identical Particles, Symmetries, Scattering, Entanglement, Anderson localization

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 (send me suggestions if you have a preference)

List of possible topics:

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.