# Fourier Transform of a wave function

1. Sep 8, 2013

### d3nat

1. The problem statement, all variables and given/known data

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

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

to obtain $\phi (x)$
2. Relevant equations

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

3. 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?

2. Sep 8, 2013

### vela

Staff Emeritus

3. Sep 9, 2013

### rude man

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.