- #1

arenaninja

- 26

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## Homework Statement

Given [tex]\Psi(x,0)=\frac{A}{x^{2}+a^{2}}, (-\inf<x<\inf)[/tex]

a) determine A

c) find the momentum space wave function [tex]\Phi(p,0)[/tex], and check that it is normalized

## Homework Equations

At t=0, we can find the momentum space wave function by the formula [tex]\Phi(p,0)=\frac{1}{\sqrt(2\pi\hbar)}\int_{-\inf}^{inf} e^{-\frac{ipx}{\hbar}}\Psi(x,0)dx[/tex]

## The Attempt at a Solution

I found that [tex]A=\sqrt(\frac{2a^{3}}{\pi})[/tex].

To find the momentum wave function, I haev

[tex]\Phi(p,0)=\frac{A}{\sqrt(2\pi\hbar)}\int_{-inf}^{inf} \frac{e^{-\frac{ipx}{\hbar}}}{x^{2}+a^{2}}dx[/tex]

but frankly I have never seen an integral of this kind and have no clue on how to proceed. I've looked at my old calculus book, some tables of integrals and wolframalpha but they're yielding nothing. Am I missing something?