Two electrons each occupy a orbital ( ) of a transition-metal ion
PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Quantum Mechanics · Symmetry, angular momentum and spin
Invariance, Ch Representations of Lie algebras: spin, products and SU(3)
Problem
Two electrons each occupy a d orbital (l=2) of a transition-metal ion, and their orbital angular momenta combine (spin is ignored). Model this as the tensor product 2⊗2 of su(2) representations. Using the Clebsch-Gordan series, decompose 2⊗2 into irreducible representations of total orbital angular momentum L, and check that the dimensions sum to 25.