Confinement of spin-0 and spin-1/2 particles in a mixed vector-scalar coupling with unequal shapes for the potentials

TL;DR

This paper investigates the confinement of spin-0 and spin-1/2 particles using Klein-Gordon and Dirac equations with mixed vector-scalar potentials, revealing differences in localization and providing exact solutions for specific potential functions.

Contribution

It introduces a general condition for isospectral Klein-Gordon and Dirac problems with squared trigonometric potentials and analyzes particle localization.

Findings

Spin-0 particles are better localized than spin-1/2 particles under the same potentials.

Bound states are found for particles and antiparticles.

Eigenvalues and eigenfunctions are explicitly discussed.

Abstract

The Klein-Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, $V_{v}=V_{s} + \mathrm{const.}$ These isospectral problems are solved in a case of squared trigonometric potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfuntions are discussed in some detail. It is revealed that a spin-0 particle is better localized than a spin-1/2 particle when they have the same mass and are subject to the same potentials.