Quantum Mechanics: Hydrogen atom in an Electric field

[ArjSiv]

So, we have an external electric field $E_{ex}$ being subjected to a hydrogen atom and thus adding the following term to the perturbation:

$H^{'} = -e\vec{E_{ex}} \cdot r$.

The first question asks to find the correction to the energy treating it as a perturbation, and hints to use the external field being in the Z direction. So... I have absolutely no idea how to approach this problem other than having $H^{'} = -eE_{ex} * z$, but I have no idea where to go from here.

This problem can't be that difficult, I'm just stumped as to where to go from here.

By the way, this problem is from Griffiths 1st ed, Problem 6.31

Thanks in advance!

 

[inha]

Are you somehow stuck with the integration when you try to calculate the expectation value of z? Your choice of perturbation is correct.