Recent content by hexidecimel10

You need to remember to use the product rule when taking derivatives.

Right so just for an example pretend you had m=5. When summing over n you would keep the n=4 term and the n=6 term because these would be the only two non-zero integrals.

You are on the right track. You will not have two different expressions depending on your n and m values because you sum over the m values. So you will only have two integrals that are not zero but you will sum and square them giving you one second order energy shift.

You know that before the force is applied there is no radiation. You also know that the acceleration is in the opposite direction of the velocity. The cross product of any two col-linear vectors is 0 so you can drop the cross product term.