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