Computational Physics Notes

Worked physics derivations with visuals and code.

Negative temperature part 3: the Ising Model

Intermediate
statistical mechanics
Monte Carlo
simulation

Introducing and solving the 2-D Ising Model using a Metropolis Monte Carlo simulation.

Sep 18, 2026
Kyle Arean-Raines

Negative temperature part 2: an exact solution to the spin lattice

Intermediate
statistical mechanics

Extending the discussion from part 1 and coming up with an analytical solution for entropy as a function of energy. This demonstrates temperature going negative quantitatively.

Aug 23, 2026
Kyle Arean-Raines

Negative temperature: going below absolute zero

Intro
temperature
thermodynamics
statistical mechanics

A description and simulation of a grid of magnets in a magnetic field, used to illustrate the concept of temperature going below 0 Kelvin.

Aug 13, 2026
Kyle Arean-Raines

Odds that you’re the one

Intermediate
probability
combinatorics
reality TV

Using derangements and the “Are You The One” matching game to work out the odds of getting every couple right.

Jul 24, 2026
Kyle Arean-Raines

Doppler cooling: using lasers to cool atoms

Intermediate
lasers
doppler effect
atomic physics

A description and simulation of cooling atoms with lasers.

Jul 19, 2026
Kyle Arean-Raines

The double slit experiment, part 2: the math

Advanced
quantum mechanics
Schrödinger equation
Gaussian integrals
python

Solving the Schrödinger equation for a Gaussian wave packet incident on two Gaussian-aperture slits, deriving a closed-form interference pattern via complex Gaussian integrals, and checking the predicted fringe spacing numerically.

Jul 16, 2026
Kyle Arean-Raines

The double slit experiment, part 1: the background

Intro
quantum mechanics
wave-particle duality
interference

A conceptual walkthrough of diffraction and interference in the classical wave picture, the quantum double-slit thought experiment with single photons, and Feynman’s neutron-scattering-crystal analogy for which-path information.

Jul 10, 2026
Kyle Arean-Raines
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