So I have already calculated correctly that the expectation of the interaction potential for hydrogenic atoms is(adsbygoogle = window.adsbygoogle || []).push({});

<nlm|V(r)|nlm>=-(uZ^2e^4)/((hbar^2)*n^2)

Note that u= mass,and V(r)=-Ze^2/r

I now have to calculate <nlm|T|nlm> where T is the kinetic energy operator, and

T=p^2/(2u) + L^2/(2ur^2)

Note that p is the radial momentum operator and L is the angular momentum operator

I know hbar^2l(l+1)=L^2 and I know (pretty sure) that <1/r^2>=e^2/(2n^3hbar^2).

However, I am unsure how to find the expectation value of the p^2/(2u) term, and don't see how <T> is going to equal <V> which the book hints at being true since <T> and <V> are said to satisfy the Virial Theorem.

Help anyone?

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# Showing that the Virial Theorem holds

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