Trapping neutral fermions with kink-like potentials

TL;DR

This paper investigates the relativistic quantum behavior of neutral fermions in kink-like potentials, providing exact solutions and resolving paradoxes related to the uncertainty principle through effective mass concepts.

Contribution

It introduces exact bound-state solutions for neutral fermions in kink-like potentials and maps the problem to a solvable Pöschl-Teller potential, addressing fundamental quantum paradoxes.

Findings

Exact bound-state solutions for neutral fermions in kink-like potentials.

Mapping of the problem to a solvable Pöschl-Teller potential.

Resolution of the uncertainty principle paradox using effective mass.

Abstract

The intrinsically relativistic problem of neutral fermions subject to kink--like potentials ($\sim \mathrm{tanh} \gamma x$) is investigated and the exact bound-state solutions are found. Apart from the lonely hump solutions for $E=\pm mc^{2}$, the problem is mapped into the exactly solvable Surm-Liouville problem with a modified P\"{o}schl-Teller potential. An apparent paradox concerning the uncertainty principle is solved by resorting to the concepts of effective mass and effective Compton wavelength.