In fall 2015, as part of my UofT M.Eng (course based engineering master’s), I took Graduate Quantum Mechanics (PHY1520H) and have PDF notes for that course available *(redacted: 358 pages, full version: 434 pages)*. This course was taught by Prof. Arun Paramekanti.

This was a fun course, and I enjoyed the chance to revisit the subject. I’ve taken three QM courses (not including QFT), and each time through I’ve learned a bit more. This was the best round of my match against QM, and I think I came out ahead in points this time.

Feel free to contact me for the complete version (i.e. including my problem set solutions) of these notes, provided you are not asking because you are taking or planning to take this course.

My notes from my the undergrad QM courses that I took as a non-degree student are also available (unredacted) :

- Quantum Physics I (PHY356H1F), taught by Prof. Vatche Deyirmenjian, fall 2010.
- Quantum Physics II (PHY456H1F), taught 2011 by Prof. John E. Sipe, fall 2011.

Contents for Grad QM notes:

- 1 Fundamental concepts
- 1.1 Classical mechanics
- 1.2 Quantum mechanics
- 1.3 Transformation from a position to momentum basis
- 1.4 Matrix interpretation
- 1.5 Time evolution
- 1.6 Review: Basic concepts
- 1.7 Average of an observable
- 1.8 Left observables
- 1.9 Pure states vs. mixed states
- 1.10 Entropy when density operator has zero eigenvalues
- 1.11 Problems
- 2 Quantum Dynamics
- 2.1 Classical Harmonic Oscillator
- 2.2 Quantum Harmonic Oscillator
- 2.3 Coherent states
- 2.4 Coherent state time evolution
- 2.5 Expectation with respect to coherent states
- 2.6 Coherent state uncertainty
- 2.7 Quantum Field theory
- 2.8 Charged particle in a magnetic field
- 2.9 Gauge invariance
- 2.10 Diagonalizating the Quantum Harmonic Oscillator
- 2.11 Constant magnetic solenoid field
- 2.12 Lagrangian for magnetic portion of Lorentz force
- 2.13 Problems
- 3 Dirac equation in 1D
- 3.1 Construction of the Dirac equation
- 3.2 Plane wave solution
- 3.3 Dirac sea and pair creation
- 3.4 Zitterbewegung
- 3.5 Probability and current density
- 3.6 Potential step
- 3.7 Dirac scattering off a potential step
- 3.8 Problems
- 4 Symmetries in quantum mechanics
- 4.1 Symmetry in classical mechanics
- 4.2 Symmetry in quantum mechanics
- 4.3 Translations
- 4.4 Rotations
- 4.5 Time-reversal
- 4.6 Problems
- 5 Theory of angular momentum
- 5.1 Angular momentum
- 5.2 Schwinger’s Harmonic oscillator representation of angular momentum operators.
- 5.3 Representations
- 5.4 Spherical harmonics
- 5.5 Addition of angular momentum
- 5.6 Addition of angular momenta (cont.)
- 5.7 Clebsch-Gordan
- 5.8 Problems
- 6 Approximation methods
- 6.1 Approximation methods
- 6.2 Variational methods
- 6.3 Variational method
- 6.4 Perturbation theory (outline)
- 6.5 Simplest perturbation example.
- 6.6 General non-degenerate perturbation
- 6.7 Stark effect
- 6.8 van der Walls potential
- 6.9 Problems
- A Useful formulas and review
- B Odds and ends
- B.1 Schwartz inequality in bra-ket notation
- B.2 An observation about the geometry of Pauli x,y matrices
- B.3 Operator matrix element
- B.4 Generalized Gaussian integrals
- B.5 A curious proof of the Baker-Campbell-Hausdorff formula
- B.6 Position operator in momentum space representation
- B.7 Expansion of the squared angular momentum operator
- C Julia notebooks
- D Mathematica notebooks
- Bibliography