Fourier Transform of a wave function

  • Thread starter d3nat
  • Start date
  • #1
102
0

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
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,873
1,447
Show your work.
 
  • #3
rude man
Homework Helper
Insights Author
Gold Member
7,864
792
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.
 

Related Threads on Fourier Transform of a wave function

  • Last Post
Replies
2
Views
2K
Replies
2
Views
2K
Replies
2
Views
643
Replies
4
Views
2K
Replies
6
Views
16K
Replies
2
Views
831
Replies
2
Views
13K
  • Last Post
2
Replies
44
Views
6K
Replies
1
Views
1K
Replies
10
Views
3K
Top