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## Homework Statement

I am trying to derive a property of the Fourier Transform of the wave function.

[tex]F[\psi(cx)]=\frac{1}{|c|}\overline{\psi}\left(\frac{p}{c}\right)[/tex]

## Homework Equations

The Fourier transform of [tex]\overline{\psi}(p)[/tex] is defined as

[tex] \overline{\psi}(p)=\frac{1}{\sqrt{2\pi\hbar}}\int_{-\infty}^{\infty}e^{-\frac{i}{\hbar}px}\psi(x)dx[/tex]

and the inverse fourier transform

[tex]\psi(x)=\frac{1}{\sqrt{2\pi\hbar}}\int_{-\infty}^{\infty}e^{\frac{i}{\hbar}px}\overline{\psi}(p)dp[/tex]

## The Attempt at a Solution

I tried changing the integration variable

[tex]u=cx[/tex]

Then

[tex]\psi(u)=\frac{1}{\sqrt{2\pi\hbar}}\int_{-\infty}^{\infty}e^{\frac{i}{\hbar}pu}\overline{\psi}(p)dp[/tex]

But when I took the fourier transform and substituted [tex]u=cx[/tex] I did not manage to get the desired result.