I'm thinking about trying to do a numerical simulation of some very simple QM problems.
How much space do I need? To simulate the Hilbert space?
I'd like to eventually simulate the absorption or emission of a photon by a hydrogen atom. So at least three particles (two fermions, one boson). Let's generalize that to three particles with arbitrary spin, so I can look at three photons or three electrons if I want to.
In order to do a numerical simulation I need to replace the continuous spacetime with a rectangular grid or lattice. I'd like to eventually get more precision, but let's start with just ten cells per dimension to begin with. So including time, I need ten thousand cells in a four dimensional lattice. `
How many cells do I need to simulate the Hilbert space? and what goes in each cell?
If I put restrictions on the shape of the wavefunction, does that help?