The intrinsically relativistic problem of neutral fermions subject to kink-like potentials (∼tanhγx) is investigated and the exact bound-state solutions are found. Apart from the lonely hump solutions for E=±mc2, the problem is mapped into the exactly solvable Sturm-Liouville problem with a modified Pöschl-Teller potential. An apparent paradox concerning the uncertainty principle is solved by resorting to the concepts of effective mass and effective Compton wavelength. © 2005 Elsevier B.V. All rights reserved.
De Castro, A. S., & Hott, M. (2006). Trapping neutral fermions with kink-like potentials. Physics Letters, Section A: General, Atomic and Solid State Physics, 351(6), 379–383. https://doi.org/10.1016/j.physleta.2005.11.033