Hydrogen atom quantum monte carlo.

This is the first example in the QMC series.
I wanted to try quantum monte carlo to understand it better, so I thought I would work through from simple atoms to more complicated chemicals.

I don't expect that there will be much interest in this, so I'm not going to write it up extensively.

Background

Quantum mechanics allows us to calculate energy levels of atoms and molecules accurately - which is one of the strongest pieces of experimental support for the theory.

For hydrogen, we have an analytic expression for the ground state energy which gives -0.5 Hartrees as the correct answer, but for the purposes of trying QMC, let's do the following: In more detail, here's what happens in the code:

Here's the trial wavefunction:

Here's the history of energy estimates:

Final energy (correct energy = -0.5, correct parameter = 1):

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