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We tested our program using one string of beads to model one particle, the
electron in a hydrogen atom.
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Hydrogen is tricky, though: computers are stupid and will crash the electron into the nucleus since the Coulomb potential goes to negative infinity at the nucleus.
Instead of the Coulomb potential, we use the Yukawa potential, developed by Muser and Berne for this use in 1997. As you can see, it is just like the Coulomb potential until you get close to the origin, and then it drops off less steeply and goes to some finite value.
It turns out that the Yukawa potential is a very accurate way to model the Coulomb potential, which governs both hydrogen and positronium behavior.