and these are essentially the commutators the orbital and spin angular momentum operators satisfy. Therefore, A and B form operator algebras analogous to angular momentum; same ladder operators, z -projections, etc., independently of each other as each of their components mutually commute. By the analogy to the spin quantum number, we can introduce positive integers or half integers, a, b, with corresponding sets of values m = a, a − 1,... − a + 1, − a and n = b, b − 1,... − b + 1, − b. The matrices satisfying the above commutation relations are the same as for spins a and b have components given by multiplying Kronecker delta values with angular momentum matrix elements: