Bounded solutions of neutral fermions with a screened Coulomb potential

Details Bounded solutions of neutral fermions with a screened Coulomb potential Bounded solutions of neutral fermions with a screened Coulomb potential

2005-05-03

arxiv.org/abs/hep-th/0505025v1

Annals Phys. 320 (2005) 56-70

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, 7 figures

Scientific paper

10.1016/j.aop.2005.05.003

The intrinsically relativistic problem of a fermion subject to a pseudoscalar screened Coulomb plus a uniform background potential in two-dimensional space-time is mapped into a Sturm-Liouville. This mapping gives rise to an effective Morse-like potential and exact bounded solutions are found. It is shown that the uniform background potential determinates the number of bound-state solutions. The behaviour of the eigenenergies as well as of the upper and lower components of the Dirac spinor corresponding to bounded solutions is discussed in detail and some unusual results are revealed. An apparent paradox concerning the uncertainty principle is solved by recurring to the concepts of effective mass and effective Compton wavelength.

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