Stark Effect using first order variation theory.

[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?

 

[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>

 

[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 =(