On 15-component theory of a charged spin-1 particle with polarizability in Coulomb and Dirac monopole fields

TL;DR

This paper develops a 15-component quantum model for a charged spin-1 particle with polarizability in Coulomb and monopole fields, revealing conditions where polarizability effects are hidden and analyzing bound states and energy spectra.

Contribution

It introduces a generalized 15-component equation for a charged spin-1 particle with polarizability and analyzes its solutions in Coulomb and monopole fields, identifying states where polarizability is not observable.

Findings

Existence of states where polarizability does not manifest

Derivation of a 2nd order differential equation for j=0 states with 1/r^4 potential

Identification of bound states and energy spectra in Coulomb and monopole fields

Abstract

The problem of a spin 1 charged particle with electromagnetic polarizability, obeying a generalized 15-component quantum mechanical equation, is investigated in presence of the external Coulomb potential. With the use of the Wigner's functions techniques, separation of variables in the spherical tetrad basis is done and the 15-component radial system is given. It is shown that there exists a class of quantum states for which the additional characteristics, polarizability, does not manifest itself anyhow; at this the energy spectrum of the system coincides with the known spectrum of the scalar particle. For j=0 states, a 2-order differential equation is derived, it contains an additional potential term 1/r^{4}. In analogous approach wave functions the generalized particle are examined in presence of external Dirac monopole field. It is shown that there exists one special state with minimal conserved quantum number j_{min}. It this solution, first, the polarizability does not exhibits itself. Analysis of the usual vector particle in external Coulomb potential is given. It is shown that at j=0 some bound states will arise. The corresponding energy spectrum is found.