Bounded solutions of fermions in the background of mixed vector-scalar inversely linear potentials

Journal Article · Fri Apr 01 00:00:00 EST 2005 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2004.09.013· OSTI ID:20690141

Castro, Antonio S. de . ^[1]

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1. UNESP, Campus de Guaratingueta, Departamento de Fisica e Quimica, Caixa Postal 205, 12516-410 Guaratingueta SP (Brazil)

The problem of a fermion subject to a general mixing of vector and scalar potentials in a two-dimensional world is mapped into a Sturm-Liouville problem. Isolated bounded solutions are also searched. For the specific case of an inversely linear potential, which gives rise to an effective Kratzer potential in the Sturm-Liouville problem, exact bounded solutions are found in closed form. The case of a pure scalar potential with their isolated zero-energy solutions, already analyzed in a previous work, is obtained as a particular case. The behavior of the upper and lower components of the Dirac spinor is discussed in detail and some unusual results are revealed. The nonrelativistic limit of our results adds a new support to the conclusion that even-parity solutions to the nonrelativistic one-dimensional hydrogen atom do not exist.

• OSTI ID: 20690141
• Journal Information: Annals of Physics (New York), Vol. 316, Issue 2; Other Information: DOI: 10.1016/j.aop.2004.09.013; PII: S0003-4916(04)00187-3; Copyright (c) 2004 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EXACT SOLUTIONS
FERMIONS
HYDROGEN
ONE-DIMENSIONAL CALCULATIONS
PARITY
POTENTIALS
SCALARS
TWO-DIMENSIONAL CALCULATIONS
VECTORS