2014/03/31 by J. A. Sánchez-Monroy, J. A. Sanchez-Monroy, C. J. Quimbay
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Dirac (video compression format) #Dirac algebra #Dirac equation #Dirac fermion #Dirac sea #Dirac spinor #Factorization #Fermion #Klein–Gordon equation #Mathematical physics #Meson #Nonlinear system #Physics #Pseudoscalar #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Scalar (mathematics) #Topological Materials and Phenomena #Two-body Dirac equations #quant-ph
paper · pdf · doi:10.1016/j.aop.2014.07.015
published as Annals of Physics 350 (2014) 69-83 · 24 pages, 4 references added, types corrected
openalex publication_date 2014/07/14 · arxiv created 2014/09/30 · arxiv updated 2014/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equation in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the factorization method can be applied. We show that the presence of electric potentials in the Dirac equation leads to a two Klein-Gordon equations including an energy-dependent potential. We then generalize the factorization method for the case of energy-dependent Hamiltonians. Additionally, the shape invariance is generalized for a specific class of energy-dependent Hamiltonians. We also present a condition for the absence of the Klein's paradox (stability of the Dirac sea), showing how Dirac particles in low dimensions can be confined for a wide family of potentials.