Fourier Transform of a wave function

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Homework Statement



[itex] \psi (x) = Ne^{ \frac{-|x|}{a}+ \frac{ixp_o}{/hbar}}[/itex]

Compute Fourier transform defined by
##\phi (p) = \frac{1}{ \sqrt{2 \pi \hbar}} \int \psi (x) e^{ \frac{-ipx} {\hbar}} dx##

to obtain ## \phi (x) ##

Homework Equations



Fourier transform = ##g(x)= \frac {1}{2 \pi} \int f(p) e^{ipx} dx ##

The Attempt at a Solution



I tried first solving the integral of ##\phi (p)##

and I got this hopeless answer of

## \frac{N(-a- \frac{i \hbar p - i \hbar p_o}{p_o p})} { \sqrt{2 \pi \hbar}}##

When I plugged that into the fourier transform, my final answer wound up being some coefficients times ##e ^ \infty##

This problem has multiple steps and depends on me being able to figure out what the ## \phi (x) ## is


Help. I don't know what I'm doing wrong?
 

Answers and Replies

  • #2
vela
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Show your work.
 
  • #3
rude man
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Why are you bringing up an (incorrect) formula for the Fourier transform when the problem has already defined it for you?

I can't figure out what the exponent of ψ(x) is however. What does " /hbar " mean?

Also, the Fourier integral integrates w/r/t x so phi will not be a function of x. So phi(x) is another mystery.
 

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