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--- physics_chemistry:orbitals:y [2026/06/20 15:44] – Maurits W. Haverkort
+++ physics_chemistry:orbitals:y [2026/06/20 15:45] (current) – Maurits W. Haverkort
@@ Line 8: / Line 8: @@
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-The complex spherical harmonics are defined as the simulatneous eigenstates of $L^2$ and $L_z$
+The complex spherical harmonics are defined as the simultaneous eigenstates of $L^2$ and $L_z$ and given by
 $$
-Y_l^{(m)} = \frac{\sqrt{2 l+1}}{2 \sqrt{\pi }} \sqrt{\frac{(l-m)!}{(l+m)!}} e^{i m \phi } P_l^{(m)}(\cos (\theta )),
+Y_l^{(m)}(\theta,\phi) = \frac{\sqrt{2 l+1}}{2 \sqrt{\pi }} \sqrt{\frac{(l-m)!}{(l+m)!}} e^{i m \phi } P_l^{(m)}(\cos (\theta )),
 $$
 with $l$ the angular momentum and $m$ the z projection of the angular momentum, $-l \leq m\leq l$. $P_l^{(m)}$ are the associated Legendre polynomials. For positive $m$ these are defined in terms of the unassociated Legendre polynomials as: