Exact solution for a fermion in the background of a scalar inversely linear potential

Details Exact solution for a fermion in the background of a scalar inversely linear potential Exact solution for a fermion in the background of a scalar inversely linear potential

2004-06-07

arxiv.org/abs/hep-th/0406067v1

Phys.Lett. A328 (2004) 289-298

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, 6 figures

Scientific paper

10.1016/j.physleta.2004.06.035

The problem of a fermion subject to a general scalar potential in a two-dimensional world is mapped into a Sturm-Liouville problem for nonzero eigenenergies. The searching for possible bounded solutions is done in the circumstance of power-law potentials. The normalizable zero-eigenmode solutions are also searched. For the specific case of an inversely linear potential, which gives rise to an effective Kratzer potential, exact bounded solutions are found in closed form. The behaviour of the upper and lower components of the Dirac spinor is discussed in detail and some unusual results are revealed.

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