2004/09/28 by Antonio S. de Castro · 1 citation
Mathematics · Physics and Astronomy · #Bounded function #Dirac equation #Fermion #Limit (mathematics) #Mixing (physics) #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Scalar (mathematics) #Scalar potential #Spectral Theory in Mathematical Physics #Spinor #hep-th #quant-ph
paper · pdf · doi:10.1016/j.aop.2004.09.013
published as Annals Phys. 316 (2005) 414-430 · 16 pages, 6 figures
arxiv created 2004/09/28 · openalex publication_date 2005/02/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.