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

  1. Sep 23, 2009 #1

    jaketodd

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    Gold Member

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

    Thanks!
     
    Last edited: Sep 23, 2009
  2. jcsd
  3. Sep 23, 2009 #2

    alxm

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    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:
    https://www.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.
     
  4. Sep 23, 2009 #3

    jaketodd

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    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
     
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