Bounded solutions of fermions in the background of mixed vector-scalar Pöschl-Teller-like potentialsL. B. Castro, A. S. de Castro and M. B. Hott
UNESP, Campus de Guaratinguetá, Departamento de Física e Química - 12516-410 Guaratinguetá SP, Brazil
received 28 July 2006; accepted in final form 21 November 2006; published January 2007
published online 23 January 2007
The problem of a fermion subject to a convenient mixing of vector and scalar potentials in a two-dimensional space-time is mapped into a Sturm-Liouville problem. For a specific case which gives rise to an exactly solvable effective modified Pöschl-Teller potential in the Sturm-Liouville problem, bound-state solutions are found. The behaviour of the upper and lower components of the Dirac spinor is discussed in detail and some unusual results are revealed. The Dirac delta potential as a limit of the modified Pöschl-Teller potential is also discussed. The problem is also shown to be mapped into that of massless fermions subject to classical topological scalar and pseudoscalar potentials.
03.65.Ge - Solutions of wave equations: bound states .
03.65.Pm - Relativistic wave equations .
© Europhysics Letters Association 2007