(a) All spherical harmonics for l = 3 have odd parity. Show that this is true in the cases where m=0 and m=±2. (b) State which l = 3 spherical harmonics correspond to zero probability density along the z-axis. Justify your answer.
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If you haven't already done so, do parts $(a)$ and (b) of Problem $8.33$, and then do part $(c)$, but for the five spherical harmonics with $l=2$.
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