American Journal of Physics

Double-group theory on the half-shell and the two-level system. I. Rotation and half-integral spin states

William G. Harter, Narciso dos Santos

Published Mar 1, 1978• 15 citations

Abstract

A geometrical construction by Hamilton is used to simplify the quantum mechanics of half-integral spin. A slide rule is described which can be used to (a) compute products of half-integral or integral spin rotation operators, (b) convert between the Euler-angle and ’’axis-angle’’ rotation operator parameters, and (c) calculate the time evolution of a spin-1/2 state for a constant Hamiltonian operator. A type of nomogram is developed which suggests ways to simplify the ’’double-group’’ theory of half-integral spin in molecular point symmetry, as well as the ’’ordinary’’ group theory for integral spin systems. Cubic and icosahedral symmetry group characters are derived for half-integral spin operators.

DOI: 10.1119/1.11134

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