Quantum Mechanics II (2017 semester 1)

Prof. Matthew Luzum


Homework


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 (GraziosoNielsen & Chuang)
  • 12 June -- QIT: density matrix, quantum measurement, discerning (non-)orthogonal states (GraziosoNielsen & Chuang)
  • 14 June -- QIT:  quantum complementarity, Holevo theorem, no-cloning theorem (GraziosoNielsen & Chuang)
  • 19 June -- QIT:  applications -- black hole information paradox (Grazioso)
  • 22 June -- QIT: applications -- quantum cryptography (Nielsen & Chuang, Mertz,   Stumpf)

Lecture Notes


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 approximationVariational methodsTime-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
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Ch1.pdf
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