# Fourier Transform of a wave function

## Homework Statement

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

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) ##

## 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?

vela
Staff Emeritus
Homework Helper