Hi, I’m William! Welcome to What a Time to be Alive!
Here, you’ll find a soup of notes on subjects ranging from quantum electrodynamics to reinforcement learning to Riemannian geometry, etc. basically wherever my Cambridge degree curiosity happens to take me.
I like learning/retaining/explaining concepts by distilling their key subconcepts into explicit (Problem, Solution) pairs as I find this approach gets fairly close to the Kolmogorov complexity of an idea.
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)
- Reinforcement Learning (Part \(2\)) (July 6, 2026)
- Machine Learning Interatomic Potentials (July 15, 2026)
- Relativistic Astrophysics & Cosmology (Experimental) (August 28, 2026)
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