- #1

xoxomae

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## Homework Statement

An interaction occurs so that an instantaneous force acts on a particle imparting a momentum ## p_{0} = \hbar k_{0}## to the ground state SHO wave function. Find the probability that the system is still in its ground state.

## Homework Equations

##\psi _{0} =\left( \frac{mw}{\hbar\pi} \right )^\frac{1}{4} e^{-mwx^{2}/2\hbar} ##

## The Attempt at a Solution

[/B]

##\Psi(x)=\psi_{0}e^{ik_{0}x}##

This wave function gives a <p> =##\hbar k_{0}##

Im confused whether this is the correct Fourier transform to do.

##c(k)=\frac{1}{2\pi}^{0.5}\int_{-\infty}^{\infty}e^{-ikx}\psi_{0}e^{ik_{0}x}dx##

And then solving for when the wavenumber of the ground state using E0=0.5* hbar * w.

Therefore

##c(k)^2 ## = Probability

Is this correct?