- #1

z2394

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## Homework Statement

I want to show that <n',l',m'|[itex]\hat{z}[/itex]|n,l,m> = 0 unless m=m', using the form of the spherical harmonics.

## Homework Equations

Equations for spherical harmonics

## The Attempt at a Solution

Not sure how to begin here since there aren't any simple eigenvalues for [itex]\hat{z}[/itex]|n,l,m>. I have a feeling that it may have something to do with normalization of the spherical harmonics (because they have Legendre polynomials that are P(cosΘ) = P(z) and would also give you a exp(imø)*exp(im'ø) term), but I have no idea how this could actually give you something for [itex]\hat{z}[/itex]as an operator, or something you could actually use to figure out [itex]\hat{z}[/itex]|n,l,m>.

Any help at all would be appreciated!