I know that the average momentum <p> is defined as m[itex]\frac{d}{dt}<x>[/itex]. But why is this also equal to :(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int[/itex]ψ*[itex]\frac{h}{(2\pi)i}[/itex][itex]\frac{\partial ψ}{\partial x}[/itex]dx ?

the integral goes from negative inf to inf, * indicates conjugate,ψ the wavefunction.

Also, why is it in general that for any average value <q> there is an operator [q] such that

<q> = [itex]\int[/itex]ψ*[q] ψ dx ?

I cannot find simple explanation anywhere and my book just skips the derivation..

Also, how come for the potential energy operator [U(x)]:

[U(x)] = U([x]) = U(x) ??

I understand that [x] = x, so U([x]) must equal U(x), but I dont understand the jump from [U(x)] to U([x])..

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# Prrof of momentum operator

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