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


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 MalyshevBruns, 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.


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HW1.pdf
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Matt Luzum,
Mar 18, 2021, 6:30 AM
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Apr 5, 2021, 2:34 AM
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HW2.pdf
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Mar 18, 2021, 6:31 AM
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Matt Luzum,
Apr 15, 2021, 8:12 AM
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HW3.pdf
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Apr 19, 2021, 4:17 PM
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HW4.pdf
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Mar 18, 2021, 6:31 AM
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Matt Luzum,
May 16, 2021, 5:17 AM
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HW5.pdf
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Mar 18, 2021, 6:33 AM
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Matt Luzum,
May 27, 2021, 10:49 AM
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HW6.pdf
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Jun 9, 2021, 9:37 AM
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Matt Luzum,
Jun 19, 2021, 6:28 AM
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Notes.pdf
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Matt Luzum,
Jun 21, 2021, 6:41 AM