So I was reading Jackson's discussion on Image charge method of a grounding sphere.
He first assumed an image charge q inside Sphere with radius a, so the potential for real change and image charge is .
The by set potential equal to 0 at x=a, he solved q' and y'
Then he can get potential...
@Jilang @DrClaude Thank you for help! I mislead by the integral sign to think it gained by doing some rearrangement inside the integral. Everything become clear if I do integral by part and use the fact that momentum operator is hermitian. Thanks a lot!
Thank you advance for help!
So the problem is find <x> in P space.
The solution's logic is use formula: The submit with Then one will get the integral
by noticing that , one can replace xeipx/ħ in the integral
so that
and then after solving the integral one can find the expectation value...