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--- documentation:standard_operators:orbital_angular_momuntum:start [2016/10/06 07:56] – created Maurits W. Haverkort
+++ documentation:standard_operators:orbital_angular_momuntum:start [2017/02/23 17:26] (current) – Maurits W. Haverkort
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+{{indexmenu_n>2}}
+====== Orbital angular momentum operators (L) ======
+###
+The angular momentum operators need as a basis set two lists defining the spin up and spin down orbitals. These lists must have length $2l+1$ whereby $l$ is the angular momentum of the shell under consideration. The orbital quantum numbers $m_l=-l$ to $m_l=l$ are assigned to the spin-orbitals in both lists in the same order. The basis:
+<code Quanty Example.Quanty>
+IndexDn = {0,2,4}
+IndexUp = {1,3,5}
+</code>
+thus defines a $p$ shell (due to the 3-fold degeneracy) and spin-orbital $0$ has the quantum numbers $l=1$, $m_l=-1$ and $\sigma=-1/2$. The standard basis used is the basis of complex spherical harmonics for the angular part, as defined in section \ref{Section_Orbital_representations}.
+###
+===== Table of contents =====
+{{indexmenu>.#1}}