## Change-of-variable

I want to find the expectation value $$\langle x^2 \rangle$$ in some problem. To do this I make a change-of-variable,

$$\xi = \sqrt{\frac{m\omega}{\hslash}}x,$$

and compute the expectation value $$\langle \xi^2 \rangle$$ like this:

$$\langle \xi^2 \rangle = \int\xi^2\vert\psi(\xi)\vert^2d\xi.$$

Finally I change back to x:

$$\langle \xi^2 \rangle = \langle \frac{m\omega}{\hslash}x^2 \rangle = \frac{m\omega}{\hslash}\langle x^2 \rangle \Rightarrow \langle x^2 \rangle = \frac{\hslash}{m\omega}\langle \xi^2 \rangle.$$

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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 Quote by broegger $$\langle \xi^2 \rangle = \int\xi^2\vert\psi(\xi)\vert^2d\xi.$$
Be carefull that your psi is still correctly normalized when expressed in xi !

cheers,
Patrick.
 Yep, that's it :D Thank you very much! How do you spot these things right away?

Recognitions:
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## Change-of-variable

 Quote by broegger Yep, that's it :D Thank you very much! How do you spot these things right away?
Because I'm an expert

An expert is someone who has made all possible and imaginable errors in a very small domain

cheers,
Patrick.
 I see I'm on the right track, then...

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