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 ml=−l to ml=l are assigned to the spin-orbitals in both lists in the same order. The basis:
- Example.Quanty
IndexDn = {0,2,4} IndexUp = {1,3,5}
thus defines a p shell (due to the 3-fold degeneracy) and spin-orbital 0 has the quantum numbers l=1, ml=−1 and σ=−1/2. The standard basis used is the basis of complex spherical harmonics for the angular part, as defined in section ???.