Relativistic confinement of neutral fermions with a trigonometric tangent potential

The problem of neutral fermions subject to a pseudoscalar potential is investigated. Apart from the solutions for E = ±mc², the problem is mapped into the Sturm-Liouville equation. The case of a singular trigonometric tangent potential (~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.