- #1
QuantumKyle
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Homework Statement
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
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?