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One-Dimensional Gaussian Wave Packet

  1. Feb 7, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider a one-dimensional wave packet with [itex]\phi[/itex](p) = A [itex]\Theta[/itex] ((h/2[itex]\pi[/itex]) / d -|p-p0|)

    Determine the constant A and find the spatial wave function ψ(x). Ignore temporal evolution.

    2. Relevant equations



    3. The attempt at a solution
    Honestly this is a little embarrassing, but the only thing I really need to know is what [itex]\Theta[/itex] is. Is it a constant, or shorthand for e^? If I know that, I should be good. I can't find any info in my notes.
     
    Last edited: Feb 7, 2012
  2. jcsd
  3. Feb 7, 2012 #2

    vela

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    I'm not familiar with that notation at all. A Gaussian has the form
    $$e^{-\frac{(p-p_0)^2}{2\sigma^2}}$$where p0 is the average and σ is the characteristic width.
     
  4. Feb 7, 2012 #3
    Never before have I seen that notation...
    Usually the capital phi or psi are linear combinations of the little phi/psi's...
     
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