System of hydrogen atoms in an electric field

[Reid]

Using the first order perturbation theory I will determine the probability of finding some atoms in a certain state. The electric field is directed along the z-axis. But i don't understand how this is done.

Should I convert the hydrogen atoms state equations into cartesian coordinates or should I keep the spherical ones and just convert the electric field? Or is that necessary?

Should I only regard the magnitude of the electric field or is the direction relevant?

I am confused. :S

 

[javierR]

You're perturbing with an interaction of the form E\cdot \mu, where \mu=e*r is the dipole moment for the electron relative to the origin of the Hydrogen atom (e is the charge of the electron and r is the vector pointing to the electron). With the electric field E in the +z direction, the dot product gives |E||r|cos\theta, where theta is the angle in spherical coordinates with respect to the z-axis, and |r| is the radial distance r in spherical coordinates.