Differences

This shows you the differences between two versions of the page.

--- physics_chemistry:orbitals:y [2017/02/23 09:40] – Maurits W. Haverkort
+++ physics_chemistry:orbitals:y [2026/06/20 15:45] (current) – Maurits W. Haverkort
@@ Line 8: / Line 8: @@
 ###
-The spherical harmonics are defined as
+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:
@@ Line 452: / Line 452: @@
 ====== Different orbital basis sets used ======
-{{indexmenu>.#1}}
+{{indexmenu>.#1|msort}}