Relativistic confinement of neutral fermions with a trigonometric tangent potential

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 ($\sim \mathrm{tan} γx$) 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.