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arXiv:quant-ph/0510003 · International Journal of Modern Physics A

THE PEREMPTORY INFLUENCE OF A UNIFORM BACKGROUND FOR TRAPPING NEUTRAL FERMIONS WITH AN INVERSELY LINEAR POTENTIAL

ANTONIO S. DE CASTRO

Published Apr 30, 2006• 8 citations
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Abstract

The problem of neutral fermions subject to an inversely linear potential is revisited. It is shown that an infinite set of bound-state solutions can be found on the condition that the fermion is embedded in an additional uniform background potential. An apparent paradox concerning the uncertainty principle is solved by introducing the concept of effective Compton wavelength.

DOI
10.1142/s0217751x0602903x

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The problem of neutral fermions subject to an inversely linear potential is revisited. It is shown that an infinite set of bound-state solutions can be found on the condition that the fermion is embedded in an additional uniform background potential. An apparent paradox concerning the uncertainty principle is solved by introducing the concept of effective Compton wavelength.
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The transmission of fermions of mass mmm and energy EEE through an electrostatic potential barrier of rectangular shape (i.e., supporting an infinite electric field), of height U>E+mc2U>E+m{c}^{2}U>E+mc2---due to the many-body nature of the Dirac equation evidentiated by the Klein paradox---has been widely studied. Here we exploit the analytical solution, given by Sauter for the linearly rising potential step, to show that the tunneling rate through a more realistic trapezoidal barrier is exponentially depressed, as soon as the length of the regions supporting a finite electric field exceeds the Compton wavelength of the particle---the latter circumstance being hardly escapable in most realistic cases.
Abstract We investigate the spectral properties of coupled noninteracting trapped fermions in a spin-dependent harmonic trapping potential. It is shown that for certain specific parameter conditions, there exist an infinite number of the exact energies and wave functions of the bound states. Two different types of the exact energies have been identified, and they are associated with the level-crossings and avoided level-crossings, respectively. In addition, the effect of the energy bias on the energy spectrum is also discussed. In particular, it is found that under suitably chosen parameter conditions, the exact wave functions of the bound states provide an analytical demonstration of the existence of the spin segregation.