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Simplifying expectation values

  1. Jun 20, 2009 #1
    Just a quick question.
    I finished an expectation value sum and noticed that the given solution had me stumped.
    Ive attached a quick picture of the simplifying process which was given as the solution.

    The only thing i don't understand is how to get the value iCm/(pi*hbar)^1/2.
    I don't know how it simplifies to that as i get another answer. You'll have to have a look at the attached picture to see what i mean.
    Any help would be appreciated.
    Thanks.
     

    Attached Files:

  2. jcsd
  3. Jun 20, 2009 #2

    CompuChip

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    The first factor underlined in red comes from the two factors of
    [tex]\left( \frac{\sqrt{C m}}{\pi \hbar} \right)^{1/4}[/tex]
    on the top line, which are - IIRC - from the normalisation of your wave function.
    The second factor in red comes from the [itex]-i\hbar[/itex] in front of the d/dx, combined with the [itex]2 \left( \sqrt{C m}/(2 \hbar) \right) [/itex] which comes down from the exponential when you apply the d/dx.

    In the third red underlined term, I suspect that instead of C m there should be (C m)^(3/4). Because if you let k = sqrt(C m) you have a sqrt(k) multiplied by k, which gives k^(3/2), i.e. ((C m)^(1/2))^(3/2) = (C m)^(3/4).
     
  4. Jun 20, 2009 #3
    Thanks CompuChip

    That was my thought exactly. I could not see how there was not a (C m)^(3/4) term. At least i was on the ball there. I suppose that the solution which was given (the working i showed in the pic) is just wrong then?
     
  5. Jun 20, 2009 #4

    Avodyne

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    The mistake is at the beginning. The 1/4 should be 1/2 for correct normalization.
     
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