Energy-Levels Crossing and Radial Dirac Equation: Supersymmetry and Quasi-Parity Spectral Signatures

2007/03/31 by Omar Mustafa · 1 citation
Physics and Astronomy · #Dirac (video compression format) #Dirac equation #Electromagnetic field #Position (finance) #Property (philosophy) #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Quantum field theory #Spectral signature #Supersymmetry #Topological Materials and Phenomena #quant-ph

paper · pdf · doi:10.1007/s10773-007-9564-2

published as Int. J. Theor. Phys. 47, 1300 (2008) · 15 pages, no figures

arxiv created 2007/08/20 · openalex publication_date 2007/10/03 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The (3+1)-dimensional Dirac equation with position dependent mass in 4-vector electromagnetic fields is considered. Using two over-simplified examples (the Dirac-Coulomb and Dirac-oscillator fields), we report energy-levels crossing as a spectral property or as an effect of the hidden supersymmetric quantum mechanical language and/or quasi-parity signatures. Under different settings of the related interactions' way-of-coupling into Dirac equation, it is observed that the two ultimate/effective descendents, Dirac-Coulomb and Dirac-oscillator, exhibit different conditions on the energy-levels crossings.

Citations

• Quasi-exact solvability of Dirac equation with Lorentz scalar potential
• Deformed algebras, position-dependent effective masses and curved spaces: an exactly solvable Coulomb problem
• Supersymmetry and Quantum Mechanics
• First-order intertwining operators and position-dependent mass Schrödinger equations in d dimensions

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• The crypto-Hermitian smeared-coordinate representation of wave functions