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Energy-levels crossing and radial Dirac equation: Supersymmetry and quasi-parity spectral signatures

Omar Mustafa
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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.

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Omar Mustafa. 2007-08-20. Energy-levels crossing and radial Dirac equation: Supersymmetry and quasi-parity spectral signatures. https://doi.org/10.1007/s10773-007-9564-2

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