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

1. Sep 23, 2009

### jaketodd

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

Thanks!

Last edited: Sep 23, 2009
2. Sep 23, 2009

### alxm

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

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:
$$\psi(x,t) = \int^{+\infty}_{-\infty}a(k)e^{ikx-\omega_kt}dk$$
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.

3. Sep 23, 2009

### 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