Valence-band of cubic semiconductors: Clifford algebra approach II

Application of Clifford algebra in the analysis of valence-band spin properties in semiconductors is considered. In the first part (Dargys A 2009 Phys. Scr. 80 065701), for this purpose the isomorphism between multivectors and their matrix representations was used to transform the problem to Clifford algebra. Here equivalence rules are established between the spinors of Hilbert space and basis elements of the five-dimensional Clifford algebra Cl4, 1. Then, the rules are applied to the total angular momentum components and the two-band hole Hamiltonian. The resulting biquaternionic Schrodinger equation for hole spin is solved as an example.