# Stark effect and electric dipole moments

1. May 15, 2010

### pitch-black

One excersise of my current homework for experimental physics (Ba, 4th term) is giving me troubles, because I have no idea where to start.

Excersise:
Stark effect: Calculate the electric dipole moment for the interference of 2s and 2p (m=0) states (hydrogen).

The wave functions are given as:

psi_1 = (2)^(-0.5) * (psi_200 + psi_210)
psi_2 = (2)^(-0.5) * (psi_200 - psi_210)

with:
psi_200 = 0.25*(2*pi)^(-0.5) * a_0^(-3/2) * (2 - (r/a_0)) * exp(-r/2a_0)
psi_210 = 0.25*(2*pi)^(-0.5) * a_0^(-3/2) * (r/a_0) * cos(theta) * exp(-r/2a_0)

I qualitatively know what the Stark effect is about, but I seem to have no clue how to calculate the dipole moment using wave functions.
I already searched the internet and my books about the Stark effect and electric dipole moments, but all I found was nothing but descriptions of the effect itself and equations featuring the electric field.

The only idea I had so far was inserting the wave equation into Schrödinger equation in order to calculate the Hamiltonian, but I didn't really succeed by doing so, because I couldn't do anything with it.

How can I calculate the dipole moment using wave functions?
Is the mathematical description of the Stark effect actually necessary?

Any hints (or book recommendations) would be highly appreciated.