This is not a homework question, just a question I have developed to get a better conceptual understanding of the results of the Schrödinger equation.

If I had a 3D spherical container or radius R, containing 2 particles of opposite charge, say a proton and an electron, what does the solution to the resulting Schrödinger equation look like?

How does the solution compare to the solution of the Schrödinger equation for a simple hydrogen atom? What happens as R approaches infinity?