Solution of the Dirac equation by separation of variables in spherical coordinates for a large class of non-central electromagnetic potentials |
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Authors: | AD Alhaidari |
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Institution: | Physics Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia |
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Abstract: | A systematic and intuitive approach for the separation of variables of the three-dimensional Dirac equation in spherical coordinates is presented. Using this approach, we consider coupling of the Dirac spinor to electromagnetic four-vector potential that satisfies the Lorentz gauge. The space components of the potential have angular (non-central) dependence such that the Dirac equation becomes separable in all coordinates. We obtain exact solutions for a class of three-parameter static electromagnetic potential whose time component is the Coulomb potential. The relativistic energy spectrum and corresponding spinor wave functions are obtained. The Aharonov–Bohm and magnetic monopole potentials are included in these solutions. |
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Keywords: | Dirac equation Separation of variables Noncentral potentials Aharonov– Bohm effect Magnetic monopole Energy spectrum |
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