Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-09-28
Annals Phys. 316 (2005) 414-430
Physics
High Energy Physics
High Energy Physics - Theory
16 pages, 6 figures
Scientific paper
10.1016/j.aop.2004.09.013
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 behaviour 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.
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