I have been trying to solve this problem
Therefore, the integral to be solved is
which gets simplified using spherical polar coordinates into
However, I have seen that the expectation value for the potential energy should be
Obtained using the same integral that I used, but using this expression for the wavefunction
which, from my understanding, should be the same expression but not in atomic units.
I am not familiar with conversions using atomic units, Bohr radius, Hartree, and so on. So I am not sure if what I have done is correct or if there's something missing.
For part c), using the virial theorem, the expectation value of the kinetic energy is
[T] = [E] - [V] = -0.5 - [V]
I am also confused by the Hamiltonian and the Laplacian which I did not use in my solution, am I missing something?
If I am not being clear please let me know and I will try to explain myself better. Thanks very much to whoever is willing to help me understand this problem better!