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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 ???.

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