Quantum Mechanics I (2020 semester 2)
PGF5001
Prof. Matthew Luzum
TA ("monitor"): Davi Bastos Costa <davi.costa@usp.br>
Mondays, Wednesdays, and Thursdays, 2:004:00 pm Typically, lectures will be Mondays and Thursdays. Wednesdays will be for discussing the homework problems.
Lecture room: 2024 (212C) Virtual lecture room: 293939199 Password: 500028
Advice for lectures:  Please keep your camera on. It helps for me to know whether to go slower or faster, or to explain something again.
 Type questions into the Zoom chat, or raise hand (click "Participants", and then click the button "Raise Hand"). Do this at any time during the lecture.
 You can download the lecture notes (see below) before the lecture, so it's easier to follow. However, it is best to also write your own notes during the lecture.
HomeworkPlease send your completed homework as one file to Davi (davi.costa@usp.br) before 23:59 on the due date. Please use your name as the filename. For example: MatthewLuzumHW1.pdf
You can complete the homework problems on ordinary paper, and then digitize them with a scanner or camera. Please use a scanning app such as Adobe Scan, Tiny Scanner, Camscanner, or something similar, to produce a single clean document. If you have no camera or no way to digitize a document, please tell me as soon as possible. Lectures
Lectures are scheduled for Mondays, Wednesdays, and Thursdays, 2:004:00 pm. Normally, Wednesdays will be used for problem solving sessions.  17 August (Recording)  Structure of Quantum Mechanics: postulates, Hilbert space (Shankar ch. 1. Other references: Sakurai ch. 1, Weinberg ch 3, Littlejohn lecture notes, Jaffe lecture notes)
 20 August (Recording)  Structure of QM: Operators; commutators, outer product, resolutions of the identity, Hermitian antiHermitian and Unitary operators, spectra (Shankar Ch. 1, Littlejohn lecture notes)
 20 August (See above)  Structure of QM: Normalizable and nonnormalizable states, measurement, uncertainty principle (Sakurai Ch. 1, Littlejohn lecture notes)
 24 August (Recording)  Application of postulates to a physical system  SternGerlach experiment; Mixed states and the density operator (Littlejohn SternGerlach , Littlejohn density operator, Sakurai Ch. 1)
 27 August (Recording)  Spatial degrees of freedom  configuration space wavefunctions, spatial translations, momentum space (LIttlejohn notes)
 31 August (Recording)  Time evolution (Littlejohn notes)
 3 September (Recording)  Harmonic Oscillator (Littlejohn notes)
 7 September  No class (Independência do Brasil)
 10 September (Recording)  Path Integrals (Littlejohn notes)
 14 September (Recording)  Path Integrals II  stationary phase approximation, classical limit (Littlejohn notes)
 17 September (Recording)  Some topics in 1D wave mechanics
 21 September (Recording)  Particle in an electromagnetic field, gauge invariance, AharonovBohm effect (Sakurai Ch 2.7)
 24 September  No class
 28 September  Exam 1 (Lectures 110, Homework 15)
 1 October (Recording)  Rotations/angular momentum (Sakurai Ch 3, Littlejohn classical rotations, Littlejohn spin1/2 rotations)
 5 October (Recording)  Rotations in spin1/2 systems (Sakurai Ch 3, Littlejohn notes)
 8 October (Recording part 1, Recording part 2)  Representations, matrix elements, irreducible subspaces (Sakurai Ch 3, LIttlejohn notes)
 12 October  No class (Nossa Senhora Aparecida)
 15 October (Recording)  Orbital angular momentum and spherical harmonics (Sakurai Ch 3, Littlejohn notes)
 19 October (Recording)  Central potentials (Littlejohn notes, Sakurai Ch. 3)
 22 October (Recording)  Coulomb potential, Hydrogen atom, (Sakurai Ch. 3.7 and 4.1), addition of angular momentum (Littlejohn notes, Sakurai Ch. 3)
 26 October (Recording)  ClebschGordon Coefficients, tensor operators, irreducible tensor operators, spherical tensor operators (Sakurai Ch. 3.11, Littlejohn notes)
 29 October (Recording)  products of spherical tensor operators, WignerEckart theorem (Sakurai Ch. 3.11, Littlejohn notes)
 2 November  No class (Finados)
 5 November  No class
 9 November  products of spherical tensor operators, WignerEckart theorem (Sakurai Ch. 3.11, Littlejohn notes)
 12 November  Exam 2 (Lectures 1118, Homework 610)
 16 November  timeindependent perturbation theory; nondegenerate (Sakurai Ch. 5)
 19 November  degenerate timeindependent perturbation theory, variational method (Sakurai Ch. 5)
 23 November  timedependent perturbation theory, Dyson series (Littlejohn notes, Sakurai Ch 5)
 26 November  fine structure of the hydrogen atom (LIttlejohn notes)
 3 December  Final Exam (All topics from the semester)
Exams Midterm 1  28 September (Lectures 110, Homework 15)
 Midterm 2  12 November (Lectures 1118, Homework 610)
 Final Exam  3 December (All topics from the semester)
Suggested textbooks
Main text  J.J. Sakurai, "Modern Quantum Mechanics"
Other texts  Shankar, Principles of Quantum Mechanics.
 Weinberg, Lectures on Quantum Mechanics
Evaluation
Grades will be based on homework (10%, depending on assignment of a monitor for the course) and the best 2 out of 3 exams (45% each).
The two midterm exams will cover ~50% of the material, and the final exam will review the entire semester. The lowest score of the three exams will be dropped, and the remaining 2 scores will determine 90% of your final grade.
ProgramTentative list of topics:  General structure of quantum mechanics
 Examples
 Angular momentum / spin
 Approximation methods

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