Coulombic interaction between the proton and electron of a hydrogen atom

[Demon117]

In the position representation, its true that we can use operators to represent the coulombic interaction between the proton and electron of a Hydrogen atom. I've never actually given any thought as to what the elements of such an operator would be (in matrix form of course). I know these elements would have to do with the principle, angular momentum, and magnetic quantum numbers but I cannot seem to come up with something. Is there anyone out there that is familiar with this notion who could tell me what that would be and why?

 

[Chopin]

I'm confused--are you just asking about the behavior of an electron in a Coulomb potential? If so, that's a pretty standard problem, and the equation can be found in just about any QM book. The quantum numbers you mention arise from the multiplicity of the solutions to that equation.

 

[Bob S]

I am confused also. There are three common models for the hydrogen atom:

1) Solution to the non-relativistic Schroedinger equation
2) Solution to the relativistic Schroedinger equation.
3) Solution to the relativistic Dirac equation (with spin-orbit coupling)

The energy levels for the first model is degenerate in the magnetic moment (no fine structure).

Why don't you show us what you expect to see.

Bob S