Quantum Monte Carlo

This is my attempt to model various atoms and molecules in javascript. It starts simple and works up.

Hydrogen atom

This is really simple. Just pick random positions in 3-D space, and evaluate the wavefunction and the hamiltonian. Average over lots of positions, and that gives you an estimate for the energy of the atom. The wavefunction has parameters, and we do a gradient descent to find the parameters that give the lowest energy.

Hydrogen molecule

This is still quite simple. We have two nuclei now and two electrons. The thing which makes this easy is that we can assume that one electron is spin up and the other is spin down. That allows us to ignore spin and exchange symmetries (although the wavefunctions we search for should be symmetric with respect to swapping the two electrons).

Other Articles:

How SpaceX land first stage boosters

The algorithms that SpaceX (probably) use to control their first stage boosters. Several animations.

Generating Plant-like Structures Using Neural Networks

How to simulate fractal ice crystal growth in Python

This presents python code to draw snowflakes, simulating a diffusion process with Fourier transforms.

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