Hi! I’m William, an undergraduate from Toronto, Canada studying physics at Cambridge.
I started Quantumplations in my freshman year to prepare for Cambridge’s Tripos exams. Over time however, Quantumplations has evolved to become my weapon for achieving rapid, deep understanding of anything that piques my curiosity: quantum electrodynamics, reinforcement learning, Riemannian geometry, etc.
I like to explain ideas by posing explicit Problems followed by their Solutions as I find this approach helps to isolate key concepts for greater emphasis.
Feel free to reach out at: wdd24@cam.ac.uk
Posts
- Where Do Observables Come From? (April 18, 2024)
- Legendre Transforms as Derivative Symmetrizers (April 24, 2024)
- Wave Impedance (April 28, 2024)
- Linear Elastostatics & Elastodynamics (May 4, 2024)
- Noether’s Theorem in Classical Particle Mechanics (May 6, 2024)
- Free Klein-Gordon QFT & Propagators (May 9, 2024)
- The Subtleties of Angular Momentum (May 13, 2024)
- Nonrelativistic vs. Relativistic Propagators (May 14, 2024)
- Rotation of Rigid Bodies (May 16, 2024)
- Lippman-Schwinger Equation (May 19, 2024)
- Free, Dispersionless Waves (May 26, 2024)
- Michaelis-Menten Enzyme Kinetics (May 27, 2024)
- Vorticity as Twice Angular Velocity (May 28, 2024)
- Electrostatic & Magnetostatic Dipoles (May 28, 2024)
- The Doppler Ellipse (May 28, 2024)
- Chaos & Nonlinear Dynamics (May 28, 2024)
- Advanced Python (May 28, 2024)
- Recurrent Neural Networks (May 29, 2024)
- Reciprocal Lattices (May 31, 2024)
- Electric Dipole Moment as Center of Charge (June 4, 2024)
- Part 1A Chemistry Overview (June 5, 2024)
- Canonical Quantization (June 11, 2024)
- The Quantum Theory of Angular Momentum (June 18, 2024)
- Born-Oppenheimer Approximation (June 20, 2024)
- High-Power Rocketry (June 27, 2024)
- Classification of \(SU(2)\) Representations (July 7, 2024)
- Convolution vs. Cross-Correlation (July 12, 2024)
- Antenna Theory (July 18, 2024)
- A Curious Nonlinear Dynamical System (August 4, 2024)
- Gross, Fine & Hyperfine Structures of Hydrogenic Atoms (August 17, 2024)
- What is Pontryagin Duality? (August 19, 2024)
- A Quick Proof of Schur’s Lemma (“Fundamental Theorem of Representation Theory”) (August 21, 2024)
- Discrete Symmetries in Quantum Mechanics (August 25, 2024)
- The Stern-Gerlach Experiment (August 28, 2024)
- Intuition For the Density Operator (August 29, 2024)
- An Unintuitive Result on 1D Scattering (September 4, 2024)
- Tinkering (September 5, 2024)
- Classical vs. Quantum Rutherford Scattering (September 5, 2024)
- Virial Theorem (September 6, 2024)
- Tight-Binding Electrons (September 6, 2024)
- Equilibrium Ensembles (September 8, 2024)
- Classical Ideal Gases (September 11, 2024)
- Relativistic Electrodynamics (September 12, 2024)
- Motivating the Wigner-Eckart Theorem (September 14, 2024)
- Perturbation Theory and the Stark Effect (September 15, 2024)
- Fermi’s Golden Rule (September 16, 2024)
- Nearly Free Electrons (September 18, 2024)
- The Scattering Operator \(S\) (September 20, 2024)
- Van der Waals Equation of State (September 23, 2024)
- Planckian Statistics (September 24, 2024)
- Debye Model of Insulators (September 25, 2024)
- Driven, Damped Harmonic Oscillators (September 26, 2024)
- Bloch’s Theorem (September 27, 2024)
- Landau Levels (September 27, 2024)
- The Aharanov-Bohm Phase & Dirac Quantization (September 29, 2024)
- Answering ChatGPT’s \(z\)-Transform Questions (September 30, 2024)
- Coupled Harmonic Oscillators & Normal Modes (October 1, 2024)
- Classical Computation Theory (October 1, 2024)
- Qubits, Quantum Logic Gates, Approximate Universality, \(\textbf{BQP}\) (October 3, 2024)
- The Deutsch-Jozsa Algorithm (October 6, 2024)
- Band Structure, Fermi Seas & Graphene (October 17, 2024)
- Insights on Thermodynamics (October 18, 2024)
- Variational Method & \(1\)D Band Structure (October 19, 2024)
- Electronics (October 25, 2024)
- Electromagnetism in Materials (November 5, 2024)
- Rabi Oscillations & Optical Bloch Equations (November 13, 2024)
- Bose-Einstein Condensation (November 16, 2024)
- Ideal Fermi Gases (November 23, 2024)
- Oversaturated Absorption Imaging of Atomic Clouds (November 29, 2024)
- Beer-Lambert Law & Radiative Broadening (December 6, 2024)
- Experimental Optics (December 6, 2024)
- Turbulence (December 14, 2024)
- Phases of the Classical Ising Model (December 15, 2024)
- Classical Optics (December 19, 2024)
- AC Stark Effect & Optical Dipole Traps (December 20, 2024)
- Classical Field Theory (December 20, 2024)
- Weak Wave Turbulence (WWT) (December 21, 2024)
- Biology Basics (January 3, 2025)
- Spectral Line Shape Broadening Mechanisms (January 4, 2025)
- Amplitude-Splitting Interferometry (January 9, 2025)
- Laser Cooling & Trapping of Atoms (January 11, 2025)
- The IR Spectrum of \(\text{C}_{60}\) (February 1, 2025)
- Toric Code (February 15, 2025)
- Weakly Coupled Quantum Field Theories (February 22, 2025)
- The Dirac Equation (March 3, 2025)
- Landau-Ginzburg Theory (March 26, 2025)
- Gaussians & Feynman Diagrams (April 17, 2025)
- Resolvents and Perturbation Theory (April 30, 2025)
- Algorithms & Data Structures (May 6, 2025)
- Frequentist Estimation (May 11, 2025)
- Manifesto on Learning (May 19, 2025)
- Sturm-Liouville Theory & Green’s Functions (May 24, 2025)
- Semiconductors (May 26, 2025)
- Method of Images (June 6, 2025)
- The Hall Effect (June 10, 2025)
- Basic Kinetic Theory (June 12, 2025)
- Supervised Machine Learning: Regression & Classification (June 12, 2025)
- Fermi Liquid Theory (June 20, 2025)
- Identical Quantum Particles & Second Quantization (June 23, 2025)
- Many-Body Green’s Functions (June 28, 2025)
- Advanced Learning Algorithms (July 15, 2025)
- Unsupervised Learning, Recommenders, Reinforcement Learning (August 8, 2025)
- Linear Response Theory (August 12, 2025)
- Classical Hydrodynamics (Part 1) (August 19, 2025)
- Quantum Mechanics on Phase Space (September 4, 2025)
- Hartree-Fock Method (September 10, 2025)
- SVD, Pseudoinverse, and PCA (September 23, 2025)
- Information Theory & Inference (October 4, 2025)
- Numerical Computation (October 30, 2025)
- Support Vector Machines (November 8, 2025)
- Differential Geometry (November 15, 2025)
- Monte Carlo Methods (November 21, 2025)
- JAX Fundamentals (Part \(1\)) (December 7, 2025)
- Tokenization & Transformers (December 31, 2025)
- PyTorch Fundamentals (Part \(1\)) (January 25, 2026)
- PyTorch Fundamentals (Part \(2\)) (January 27, 2026)
- Density Functional Theory (January 28, 2026)
- Reinforcement Learning (Part \(1\)) (February 1, 2026)
- Pseudo-Riemannian Geometry (February 13, 2026)
- Hamilton’s Optics-Mechanics Analogy (February 19, 2026)
- Convolutional Neural Networks (March 1, 2026)
- Renormalization Group (March 1, 2026)
- Graph Neural Networks (March 4, 2026)
- Autoencoders (March 26, 2026)
- Information Geometry (March 27, 2026)
- Diffusion & Flow-Matching Models (April 12, 2026)
- Physics-Informed Neural Networks (May 5, 2026)
- Magnetism (May 16, 2026)
- Polymers (May 21, 2026)
- Schwarzschild Metric, Orbits & Black Holes (May 24, 2026)
- Screening (June 4, 2026)
- Graphics Processing Units (GPUs) (June 16, 2026)
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