How to Calculate Expectation Values in Spherical Coordinates?

[M. next]

Hey,

can you explain how to find expectation value in spherical coordinates?
and give me a numeric example?

to make this clearer, if we considered potential wells..
how can this question be included in such an exercise?


thanks loads, answer as much as you can.. whatever comes to mind

 

[jfy4]

Without further information, all I can say is you find expecation values pretty much the same way you usually do. For example:
$$\langle A \rangle = \int_{\sigma} \Psi^{*}\hat{A}\Psi$$
however you will want $\Psi$ to be in spherical coordinates. In other words, you want your solution to Schrodinger's equation to reflect the symmetry of the problem (which I imagine is spherical). For instance if you are working in 3D:
$$\langle A \rangle = \int_{\text{Volume}} \psi^{*}(r,\theta,\phi)\hat{A}\psi(r,\theta,\phi)$$
will give you the expectation value of $A$.