I want to find the expectation value [tex]\langle x^2 \rangle[/tex] in some problem. To do this I make a change-of-variable,(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\xi = \sqrt{\frac{m\omega}{\hslash}}x,[/tex]

and compute the expectation value [tex]\langle \xi^2 \rangle[/tex] like this:

[tex]\langle \xi^2 \rangle = \int\xi^2\vert\psi(\xi)\vert^2d\xi.[/tex]

Finally I change back tox:

[tex]\langle \xi^2 \rangle = \langle \frac{m\omega}{\hslash}x^2 \rangle = \frac{m\omega}{\hslash}\langle x^2 \rangle \Rightarrow \langle x^2 \rangle = \frac{\hslash}{m\omega}\langle \xi^2 \rangle.[/tex]

I really can't see what is wrong here, but something is! I've tried it 10 times and I keep getting the wrong result.

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# I want to find the expectation value [tex]\langle x^2 \rangle[/tex] in

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