Trapping neutral fermions with kink-like potentials

Abstract

The intrinsically relativistic problem of neutral fermions subject to kink-like potentials ( ∼ tanh γ x ) is investigated and the exact bound-state solutions are found. Apart from the lonely hump solutions for E = ± m c 2 , 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.