E1 Transitions: Finding the Minimal Emission Direction in a Hydrogen Atom

[MathematicalPhysicist]

Homework Statement

A hydrogen atom is in state (|210>+|211>)/sqrt(2) relative to some fixed coordinate system. Assume only E1 transitions contribute. To which direction in space the rate of emission will be minimal?

Homework Equations

The rate of emission is proportional to
$$|<F|X|I> \cdot \epsilon|^2$$
where F is the final state and I is initial state.
F=(|210>-|211>)/sqrt(2)
I=(|210>+|211>)/sqrt(2)
epsilon is polarization vector.

The Attempt at a Solution

I don't know how to find epsilon here, the TA said that <F|X|I> should be complex valued but if I am not mistaken it equals 0.5(<210|X|210>-<211|X|211>), and this is real valued.

 

[Physics Monkey]

Hi MathematicalPhysicist,

Your formula for the expectation value isn't quite right. You should be able to check, either by symmetry arguments or by direct evaluation, that the diagonal terms you've written are zero. It may be useful to look again at the off diagonal terms.

Hope this helps.