Calculating the expectation of a quantity using wavefunctions

[spaghetti3451]

I am reading the fine structure article from Wikipedia at http://en.wikipedia.org/wiki/Fine_structure.

Under the heading 'Kinetic energy relativistic correction', we have the following:

For the hydrogen atom, V = e²/r. This implies that the expectation of V = -e²/a₀n².

Now, I know that you use the unperturbed wavefunction ψ⁰ to find the expectation of V, but I am not sure of the exact form of ψ⁰. Any help on this will be greatly appreciated.

 

[spaghetti3451]

I need the form as I want to calculate the expectation myself. Is there a general formula for the wavefunction?

 

[dextercioby]

Usually the expectation value is computed with the ground state wavefunction. You can find the n=1, l=0, m=0 wavefunction in any book on QM.