Understanding Different Quantum Interactions

[jackferry]

I'm an undergrad physics student trying to wrap my head around basic QM ideas, and the question I had was this: when we talk about the energy levels of an atom and the wavefunction of the electron around that atom, we talk about an electric potential that affects the shape the wavefunction takes. How do the protons in the nucleus interact with the electron in a seemingly non-quantized way, with a potential that is well-defined, instantaneous and continuous throughout space. Shouldn't there be a photon traveling between them and some time for information to be communicated from the nucleus to the electron? Is this just a simplification of how the atom works?

Thanks!

 

[hilbert2]

Shouldn't there be a photon traveling between them and some time for information to be communicated from the nucleus to the electron? Is this just a simplification of how the atom works?

Yes, it is a simplification. If you were to do it without approximations, you'd first have to write the Lagrangian function for the system that consists of Dirac field of the electron, the nucleus, and the bosonic electromagnetic field they both interact with. Then you'd find the bound states of that system, which is not at all a simple calculation.