Relativistic quantum dynamics of neutral particle in external electric fields: An approach on effects of spin

TL;DR

This paper investigates the relativistic quantum behavior of a neutral spin-1/2 particle in electric fields, deriving new solutions and analyzing energy levels, including effects like Aharonov-Casher and Landau-like levels, with a focus on spin effects.

Contribution

It introduces a direct derivation of first order differential equations from the Dirac equation for neutral particles in electric fields and explores new solutions and energy spectra considering spin.

Findings

Derived new solutions for the Aharonov-Casher effect.

Obtained energy levels analogous to Landau levels, dependent on spin.

Analyzed the full space including the origin using self-adjoint extensions.

Abstract

The planar quantum dynamics of spin-1/2 neutral particle interacting with electrical fields is considered. A set of first order differential equations are obtained directly from the planar Dirac equation with nonminimum coupling. New solutions of this system, in particular, for the Aharonov-Casher effect, are found and discussed in detail. Pauli equation is also obtained by studying the motion of the particle when it describes a circular path of constant radius. We also analyze the planar dynamics in the full space, including the $r=0$ region. The self-adjoint extension method is used to obtain the energy levels and wave functions of the particle for two particular values for the self-adjoint extension parameter. The energy levels obtained are analogous to the Landau levels and explicitly depend on the spin projection parameter.