What are the equation(s) that determine free electron wave amplitude?

jaketodd

I'm not talking about the wavefunction but instead, the physical free electron wave.

Thanks!

alxm

If you don't mean the wave function, what do you mean by 'physical free electron wave'?

If you mean the 'electron waves' you were talking about in your previous thread:
http://physicsforums.com/showthread.php?t=324515

Then, all the answers there are talking about the wave function. (specifically, a plane-wave approximation to the wave function) But a plane-wave is not actually a proper wave function. It's not square-integrable and so it can't be normalized. That also means that it doesn't have a meaningful amplitude (in absolute terms).

If you want a real wave function (that's normalizable), you need a wave packet:
[tex]\psi(x,t) = \int^{+\infty}_{-\infty}a(k)e^{ikx-\omega_kt}dk[/tex]
Where a(k) is some function describing the overall shape of the packet.

In which case you'll get the true amplitudes from applying the nomalization condition.

jaketodd

I used this page to convert the latex to an image i can actually see: http://www.equationsheet.com/textoimage.php

and I don't know what all the variables and/or constants are, please fill me in if you'd be so kind