Relativistic confinement of neutral fermions with a trigonometric tangent potential

TL;DR

This paper presents an exact solution for neutral fermions confined by a relativistic trigonometric tangent potential, demonstrating true confinement without particle-antiparticle creation, advancing understanding of relativistic quantum confinement.

Contribution

It provides an exact analytical solution for neutral fermions under a singular trigonometric tangent potential, showing true relativistic confinement without pair production.

Findings

Exact solutions for the tangent potential case.

Potential achieves true relativistic confinement.

Fermions localized in arbitrarily small regions.

Abstract

The problem of neutral fermions subject to a pseudoscalar potential is investigated. Apart from the solutions for $E=\pm mc^{2}$, the problem is mapped into the Sturm-Liouville equation. The case of a singular trigonometric tangent potential ($\sim \mathrm{tan} \gamma x$) is exactly solved and the complete set of solutions is discussed in some detail. It is revealed that this intrinsically relativistic and true confining potential is able to localize fermions into a region of space arbitrarily small without the menace of particle-antiparticle production.