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I'm brand new to Mathmematica, so please be nice. I don't understand where I'm going wrong. I just need to use the method of inverse fourier transform on this wavefunction to get the momentum-space wavefunction.

The original wavefunction:

enter image description here

The output, which doesn't seem right

enter image description here

The code:

InverseFourierTransform[(m*w/(Pi*\[HBar]))^(1/4) E^(-m*w*x^2/(2*\[HBar])) E^(-I*w*t/2), x, t]
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    $\begingroup$ 'Pi' versus 'pi' and'E' versus 'e' and 'I' versus 'i'. All built-in names start with a capital. $\endgroup$
    – Bob Hanlon
    Oct 5, 2016 at 2:15
  • $\begingroup$ Ok I fixed that but it still gives me the same output as the image above. $\endgroup$
    – whatwhatwhat
    Oct 5, 2016 at 2:17
  • $\begingroup$ Then enter code in code blocks vice images so people can can work with it and correct/edit your question. $\endgroup$
    – Bob Hanlon
    Oct 5, 2016 at 2:19
  • $\begingroup$ @BobHanlon Done. Good idea, I don't know why I didn't do that initially. I normally do that on SO. $\endgroup$
    – whatwhatwhat
    Oct 5, 2016 at 2:21
  • $\begingroup$ Why are the transform and original variables both present in your wavefunction? $\endgroup$
    – J. M.'s eventual burnout ♦
    Oct 5, 2016 at 2:32

1 Answer 1

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J.M.' s comment related to both w and t appearing in the expression to be transformed. Assuming that the t in E^(-I*w*t/2) was actually meant to be an x then

InverseFourierTransform[(m*w/(Pi*ℏ))^(1/4) E^(-m*w*
     x^2/(2*ℏ)) E^(-I*w*x/2), w, t]

(*  (((m/ℏ)^(1/4)*
           (-((x*(m*x + I*ℏ))/ℏ))^
             (1/4) - (-(m/ℏ))^(1/4)*
           ((x*(m*x + I*ℏ))/ℏ)^(1/4))*
      ℏ*Gamma[1/4]*
      (Abs[t]*Cos[(5/4)*ArcTan[
                 (2*t*ℏ)/(m*x^2 + 
                      I*x*ℏ)]] - 
         I*t*Sin[(5/4)*ArcTan[
                 (2*ℏ*Abs[t])/(m*x^2 + 
                      I*x*ℏ)]]))/
   (2*2^(1/4)*Pi^(3/4)*x*
      (m*x + I*ℏ)*
      ((x^2*((-I)*m*x + ℏ)^2)/ℏ^2)^
        (1/4)*(1 + (4*t^2*ℏ^2)/
             (x^2*(m*x + I*ℏ)^2))^(5/8)*
      Abs[t])  *)

Assumptions on any of the parameters might simplify this.

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