Hydrogen atom (perturbation theory)

Apr 2017
1
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For the simplest situation of hydrogen atom (no relativistic, spin-orbit interaction) we have a situation where proton is creating electric field equal to a point charge e. Then electron is affected by that potential fi0(r)
and hydrogen atom hamiltonian radial part is H0 (see the attachment).
The question is how to include corrections based on the proton limited geometry (charged ball) rp=0.88*10^-15 m. Charge is spread equally in the proton (see the attachment for the potential, where r<=R).
How to calculate electron ground state energy first order correction based on perturbation theory?

Edit: Solved.
 

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