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  3. please only do part quotdquot only part quotdquot equation 129...

Question: please only do part quotdquot only part quotdquot equation 129...

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3. (10 marks) Consider the hydrogen ground-state wave function (rexp(-r/a) (a) Prove that ψ1s(r) satisfies the eigenvalue equation h2 h2 (b) Calculate the standard deviation (c) The virial theorem relates the mean values of kinetic and potential energies T) and (V) to the total energy E. For the Coulomb problem it reads Prove this relation for the hydrogen ground state. (d) Calculate the momentum space wave function of the hydrogen ground state Hint: use Eq 1.29) of the lecture notes and the 0h-order spherical Bessel function a(z) = sinz/r. You can do this question using atomic units L=0 M=-L

PLEASE ONLY DO PART "d". ONLY PART "D". Equation 1.29 is given with the question. Please write clearly and show all steps. Thank you.

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