2006/11/15 by L. B. Castro, L. B Castro, A. S. de Castro +2 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #hep-th #quant-ph
paper · pdf · doi:10.1209/0295-5075/77/20009
published as Europhys.Lett.77:20009,2007 · 10 pages, 1 figure
arxiv created 2006/11/15 · openalex publication_date 2007/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04
The problem of a fermion subject to a convenient mixing of vector and scalar potentials in a two-dimensional space-time is mapped into a Sturm-Liouville problem. For a specific case which gives rise to an exactly solvable effective modified Pöschl-Teller potential in the Sturm-Liouville problem, bound-state solutions are found. The behaviour of the upper and lower components of the Dirac spinor is discussed in detail and some unusual results are revealed. The Dirac delta potential as a limit of the modified Pöschl-Teller potential is also discussed. The problem is also shown to be mapped into that of massless fermions subject to classical topological scalar and pseudoscalar potentials.