A note on the eigenvalues of S.π for spin-1 in a constant magnetic field
J. Jayaraman, M Antonius, B de Oliveira
Exploiting the intimate connection of the problem of a charged spin-1 particle in a homogeneous magnetic field to that of a harmonic oscillator, it is demonstrated that the eigenvalues of the matrix operator S. pi for spin-1 and for a constant magnetic field are governed by a Hermitian matrix defined on the space of the particle number n and spin and are thus constrained to be real for any intensity of the external magnetic field H, thereby contradicting a recent affirmation of Weaver (1978) that for n=0, complex eigenvalues are present for sufficiently intense magnetic fields. The errors in Weaver's analysis which have led to complex eigenvalues as well as to an excessive number of eigenvalues compared with that demanded by the spin degrees of freedom are pointed out.
Journal of Physics A Mathematical and General•Oct 21, 1985•1 citation