Dirac Equation with vector and scalar potentials via Supersymmetry in Quantum Mechanics

In this work, a spin \(\frac 12\) relativistic particle described by a generalized potential containing both the Coulomb potential and a Lorentz scalar potential in Dirac equation is investigated in terms of the generalized ladder operators from supersymmetry in quantum mechanics. This formalism is...

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Bibliographic Details
Published inarXiv.org
Main Authors Rodrigues, E S, de Lima, A F, de Lima Rodrigues, R
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.01.2013
Subjects
Coulomb potential
Dirac equation
Eigenvalues
Eigenvectors
Particle spin
Quantum mechanics
Quantum physics
Quantum theory
Relativism
Relativistic effects
Relativistic particles
Supersymmetry
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Summary:In this work, a spin \(\frac 12\) relativistic particle described by a generalized potential containing both the Coulomb potential and a Lorentz scalar potential in Dirac equation is investigated in terms of the generalized ladder operators from supersymmetry in quantum mechanics. This formalism is applied for the generalized Dirac-Coulomb problem, which is an exactly solvable potential in relativistic quantum mechanics. We obtain the energy eigenvalues and calculate explicitly the energy eigenfunctions for the ground state and the first excited state.
ISSN:2331-8422