Differences

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

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision		Previous revision
physics_chemistry:orbitals:y [2016/10/10 09:40] – external edit 127.0.0.1physics_chemistry:orbitals:y [2026/06/20 15:45] (current) – Maurits W. Haverkort
Line 1: Line 1:
 +{{indexmenu_n>1}}
 ====== Spherical Harmonic (Y) ====== ====== Spherical Harmonic (Y) ======
 ~~NOTOC~~ ~~NOTOC~~
Line 7: 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: 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 451: Line 452:
  
 ====== Different orbital basis sets used ====== ====== Different orbital basis sets used ======
-{{indexmenu>.#1}}+{{indexmenu>.#1|msort}}

You are here: Quanty - a quantum many body script language » Physics, Chemistry and Mathematics » One-particle orbitals » Spherical Harmonic (Y)

Print/export