This Prob is from Shankar, 17.2.3(adsbygoogle = window.adsbygoogle || []).push({});

"we assumed that the proton is a point charge e. If the proton is a uniformly dense charge distribution of radius R, the interaction is modified as

V(r)= -2(e)^2/(2R) + (er)^2/(2(R)^3) r<R

= -e^2/r r>R

Calculate 1st Order shift in the ground-state energy of H, due to this modification

Assume Exp[-R/a0]~1. (Correct answer is E(1)=2(eR)^2/(5(a0)^3))"

I try ro make perturbated Hamiltonian term to use |nlm>

H=T+V=T-e^2/r+e^2/r+V=H0+H`

H` is V+e^2/r (this H` gives zero when r>R)

and calculate 1st order purtubation. but it doesn't give correct answer

I think the method I used is something wrong.(because calculation has no error)

Please show me the way~

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# Homework Help: Volume Effect of the Proton in Hydrogen Atom

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