2004/09/21 by Antonio S. de Castro, Marcelo Hott · 31 citations
Mathematics · Physics and Astronomy · #Bound state #Dirac algebra #Dirac equation #Dirac spinor #Exponential function #Mathematical analysis #Mathematical physics #Mathematics #Morse potential #Noncommutative and Quantum Gravity Theories #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Scalar (mathematics) #Scalar potential #Spinor #Topological Materials and Phenomena #Upper and lower bounds #hep-th #quant-ph
paper · pdf · doi:10.1016/j.physleta.2005.05.039
published in Physics Letters A 342(1-2), 53-59 (Elsevier BV) · 16 pages, 3 figures
arxiv created 2004/09/21 · openalex publication_date 2005/06/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The problem of a fermion subject to a general scalar potential in a two-dimensional world for nonzero eigenenergies is mapped into a Sturm-Liouville problem for the upper component of the Dirac spinor. In the specific circumstance of an exponential potential, we have an effective Morse potential which reveals itself as an essentially relativistic problem. Exact bound solutions are found in closed form for this problem. The behaviour of the upper and lower components of the Dirac spinor is discussed in detail, particularly the existence of zero modes.