Consider the ground state of the hydrogen atom. Estimate the correction [tex]\frac{\Delta E}{E_1s} [/tex] caused by the finite size of the nucleus. Assume that it is a unifromly charged shell with radius b and the potential inside is given by [tex]\frac{-e^2}{4\pi \epsilon b}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

Calculate the first order energy eorrection to the ground state and expand in [tex]\frac{b}{a_0}[/tex]. Keep the leading term and observe [tex]\frac{\Delta E}{E_1s}[/tex] for b = 10^-15m.

Ok, I need help in constructing the interaction W (or H'). Once I get that, I would then calculate the expectation value of it by sandwiching it between [tex]\psi_1s[/tex]. Is this correct and how would I construct the interaction?

Here is what I have so far

H0 = (p^2)/2m - e^2/r and H = H0 for r > r0

H = (p^2)/2m -e^2/(4pi epsilon b) = H0 + H' for r < r0

Then I would solve for H' and use the perturbation equation. Is this correct ?

James

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# Perturbation of hydrogen energy due to nucleus

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