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arXiv:hep-th/0412160 · Modern Physics Letters A

PSEUDO-HERMITIAN INTERACTION BETWEEN AN OSCILLATOR AND A SPIN-1/2 PARTICLE IN THE EXTERNAL MAGNETIC FIELD

Bhabani Prasad Mandal

Published Mar 21, 2005• 41 citations
arXivHTMLPDF

Abstract

We consider a spin-1/2 particle in the external magnetic field which couples to a harmonic oscillator through some pseudo-hermitian interaction. We find that the energy eigenvalues for this system are real even though the interaction is not PT-invariant.
DOI
10.1142/s0217732305016488

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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.
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