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Can I assume this is a travelling wave?

  1. Feb 27, 2012 #1
    Hello,

    I was solving the time dependent schrodinger equation in a time-independent potential such that E<V and I got the following solution:

    ψ = exp(-[itex]\sqrt{k}[/itex]x - (iE/[itex]\bar{h}[/itex])t)

    where k > 0 and k = (2m/[itex]\bar{h}[/itex][itex]^{2}[/itex])(V-E)

    I was wondering if this was a left travelling wave i.e. whether I could write it as:
    ψ = exp(-i ([itex]\sqrt{-k}[/itex]x + (E/[itex]\bar{h}[/itex])t) )

    Would this be correct?
     
  2. jcsd
  3. Feb 28, 2012 #2
    No. Because you know that k is positive (and real), thus the simplest form is [itex]-\sqrt{k}[/itex], it means that as [itex]|x|[/itex] increases, the wave-function is exponentially damped.
     
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