Lecture Notes

Below are lecture notes for courses I have taken and/or TA’d. Please send me an email if you spot any errors!

Graduate Statistical Mechanics (PHYS 516)

  • Files: PDF - TeX Source (GitHub)
  • Description: Notes taken (live) from UBC’s PHYS 516. The course is a topics course in statistical mechanics.
  • Topics Covered: Fundamentals of statistical mechanics, Phase transitions and critical exponents, \(D = 1,2,3\) Ising models, mean field theory, quantum field theory, universality, renormalization, and elementary conformal field theory.
  • Pre-requisites: Undergraduate statistical mechanics, thermodynamics, and quantum mechanics.

Graduate Quantum Field Theory I (PHYS 526)

  • Files: PDF - TeX Source (GitHub)
  • Description: Notes taken (live) from UBC’s PHYS 526. The course is a first course in graduate quantum field theory, and uses Gordon Semenoff’s Quantum Field Theory: A Physicist’s Introduction as the primary textbook.
  • Topics Covered: Many-particle systems, Second Quantization, Symmetries and Noether’s theorem, Space-time symmetries, Scalar/Tensor/Vector fields, Emergent relativistic QFT, Dirac equation and Dirac QFT, Photons, Quantum Electrodynamics, Functional methods, Perturbation theory, Feynman diagrams, Renormalization of QED.
  • Pre-requisites: (Advanced) undergraduate courses in quantum mechanics, special relativity, calculus, differential equations and linear algebra.

Graduate Condensed Matter Physics I (PHYS 502)

  • Files: PDF - TeX Source (GitHub)
  • Description: Notes taken (live) from UBC’s PHYS 502. The course is a first course in graduate condensed matter theory, and uses Aschroft & Mermin’s Solid State Physics as the primary textbook.
  • Topics Covered: Solids as interacting quantum many-body systems, Second quantization for fermions and bosons, Electrons in solids, Boson systems, Electrons in periodic potentials, Semiclassical theory of conduction in metals, Electron-phonon interactions, Elements of superconductivity.
  • Pre-requisites: Undergraduate courses in solid-state physics, quantum mechanics, and statistical mechanics.

Graduate Quantum Mechanics I (PHYS 500)

  • Files: PDF - TeX Source (GitHub)
  • Description: Notes taken (live) from UBC’s PHYS 500. The course is a first course in graduate quantum mechanics, and does not follow a set textbook in particular (though primarily references Goswami’s Quantum Mechanics and Griffith’s Introduction to Quantum Mechanics).
  • Topics Covered: Angular momentum and spin, Electromagnetic interactions, Gauge invariance, Addition of angular momentum, Time-independent perturbation theory, Fine and hyperfine structure of Hydrogen, WKB approximation, Time-dependent perturbation theory, Spontaneous Emission, Electric transitions, Selection rules, Adiabatic approximation, Berry phase, Aharonov-Bohm Effect, Scattering and resonance scattering.
  • Pre-requisites: One or two courses in undergraduate quantum mechanics.

Quantum Mechanics II (PHYS 402)

  • Files: (Work In Progress) TeX Source (GitHub)
  • Description: Notes written for students of UBC’s PHYS 402. The course is an advanced undergraduate course in quantum mechanics, covering portions of the first six chapters in Sakurai’s Modern Quantum Mechanics as well as some additional topics.
  • Topics Covered: Fundamental concepts/formalism, Quantum dynamics, Quantum information and foundations, Symmetries, Angular momentum, Approximation methods.
  • Pre-requisites: A first course in quantum mechanics (covering the first four chapters of Griffith’s Introduction to Quantum Mechanics). However, the theory is developed from the ground up, and formally one only needs linear algebra and some experience with differential equations.

Real Analysis I/II (MATH 320/321)

  • Files: PDF - TeX Source (GitHub)
  • Description: Notes taken from UBC’s MATH 320/321. The courses go through the standard undergraduate analysis sequence, covering the first nine chapters of Rudin’s Principles of Mathematical Analysis.
  • Topics Covered: The real and complex numbers, cardinality, basic topology, sequences and series, continuity, differentiation, the Riemann-Stieltjes integral, Sequences and series of functions, Power series, Special functions, Fourier series, Multi-variable functions.
  • Pre-requisites: Familiarity with mathematical proofs. Some calculus background is also helpful.

Classical Mechanics II (PHYS 306)

  • Files: PDF - TeX Source (GitHub)
  • Description: Notes taken (live) from UBC’s PHYS 306. The course is a second course in undergraduate classical mechanics, covering chapters 6-7, 9-14, and 16 of Taylor’s Classical Mechanics.
  • Topics Covered: Calculus of variations, Lagrangian mechanics, Mechanics in non-inertial frames, Rigid-body rotational mechanics, Coupled oscillators and normal modes, Nonlinear mechanics and chaos, Hamiltonian mechanics, Collision theory, Continuum mechanics.
  • Pre-requisites: A first course in mechanics (covering at least the first five chapters of Taylor’s Classical Mechanics).
  • Remark: These notes were a first attempt at taking live typeset notes, and are therefore the least elegant, by some margin.

Thermodynamics I (SCIE 001)

  • Files: PDF - TeX Source (GitHub)
  • Description: A pseudo-textbook co-written with Justin Lawrence to act as a resource for the thermodynamics unit of UBC’s SCIE 001 (first-year honours science).
  • Topics Covered: The laws of thermodynamics, Microscopic definition of temperature, Degrees of freedom, Ideal gases, Thermodynamic processes, Heat engines, Entropy.
  • Pre-requisites: Basic mechanics, derivative and integral calculus.
  • Remark: Includes practice problems and solutions.