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I just finished learning how to solve the Schrodinger equation for the H atom and a few things trouble me.

1) The relative particle, CoM particle treatment: From what I understand, we are solving this for the case where the nucleus is taken to have mass m1+m2 and the electron has mass m1m2/(m1+m2), where m1 is the actual mass of the nucleus and m2 the actual mass of the electron. Am I correct in saying this? And isn't this going to cause an error?

2) Ignoring the nucleus: The wavefunction for the nucleus turns out to be a plane wave. Well, what I don't understand is why we ignore it. Shouldn't we add on that plane wave wavefunction at the end and multiply it to the solution of the wavefunction we get for the electron?

3) Suppose I could not make the first assumption. Let's say I had a system where m1 and m2 were comparable. Then what? How should I proceed?

Thank you for your help.