Generalized angular momentum is defined by the relation:

, and

In non-orthonormal coordinates:

from this, you can derive the orbital angular momentum spectrum.

Define ,

This means: , ,

still commutes with everything.

CSCO is and

are related.

Similarly, ,

It must be that:

s.t.

Similarly, for a minimal j,

is an integer because if it is not, the ladder operators will yield contradictions.

and

m must be an integer because otherwise is multivalued.

source psfile jl@crush.caltech.edu index angular_momentum_coupling orbital_angular_momentum representation