(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to show that < n l m | z | n l m > = 0 for all states | n l m>

2. Relevent Equations:

L^2 = Lx^2 + Ly^2 + Lz ^2

Lx = yp(z) - zp(y)

Ly = zp(x) - xp(z)

Lz = xp(y) - yp(x)

L+/- = Lx +/- iLy

3. The attempt at a solution

I really don't know where to begin because z is not an eigenfuntion of | n l m> (and if it was this equation would not be 0 anyways). My intuition tells me that I need to somehow represent z as a function of the operators L^2, Lz, and maybe L+/-. But I can't seem to isolate z. Maybe I'm looking at this problem the wrong way. Is there some fundamental theorem that would show that this equation is true?

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# Homework Help: Z-operator acting on an angular momentum quantum state

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