How Do Frequencies Cancel Out in the Casimir Effect?

[spock0149]

Hey folk,

I'm not sure if this would be more approproate in the Calculus section because I think the anser probably involves Fourier transforms.


My understanding of the Casimir effect is that only standing waves can form between the two plates, and thus the energy looks something like:

$$\sum_{n=0}^\infty 2\pi \hbar \frac{n}{L}$$

My question is the following:

All other possible frequencies CANCEL via destructive interference. Can anyone explain to me how to show this mathematically??

I've always 'known' this, but want to see it in the math.

Any help appreciated!

Spock

 

[dlgoff]

"All other possible frequencies CANCEL via destructive interference."

I don't think this correct. The other waves\frequencies exit outside of the the volume between the plates. These are the ones causing the force.

Someone correct me if this is not a way of thinking of it.