Stark Effect using first order variation theory.

1. Jul 6, 2008

scorpion990

EDIT: Sorry... I have to use perturbation theory. My mistake.

Hey... I have a quick question. I have to calculate the approximate change in energy via variation theory when the 'error' Hamiltonian for the Stark effect is defined as: $$|\vec{E}|cos\theta\bullet eR$$

If I'm not mistaken, the change in energy of the 1s orbital of a hydrogen atom will be:

<E>=k$$\int r^3e^{-2r/a}dr \int sin\theta cos\theta d\theta \int d\varphi$$

However, the middle integral becomes 0 when the limits of 0 and pi are plugged in. This doesn't seem right. Am I doing anything incorrectly?

2. Jul 6, 2008

per.sundqvist

The perturbation couples 1s with 2p state. It would not perturb the 1s only (In this case your integral is correct). Besides your volume element in r should be r^2 and not r^3.

H_stark=<1s|z|2p>

3. Jul 7, 2008

scorpion990

One "r" comes from the definition of the perturbed Hamiltonian. The other two come from the jacobian in spherical coordinates.

I'm not really sure what I have to do now, though. I'm not familiar with your notation. Sorry =(