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Kepler problem in Dirac theory for a particle with position-dependent mass

I. O. Vakarchuk
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Abstract

Exact solution of Dirac equation for a particle whose potential energy and mass are inversely proportional to the distance from the force centre has been found. The bound states exist provided the length scale $a$ which appears in the expression for the mass is smaller than the classical electron radius $e^2/mc^2$. Furthermore, bound states also exist for negative values of $a$ even in the absence of the Coulomb interaction. Quasirelativistic expansion of the energy has been carried out, and a modified expression for the fine structure of energy levels has been obtained. The problem of kinetic energy operator in the Schrödinger equation is discussed for the case of position-dependent mass. In particular, we have found that for highly excited states the mutual ordering of the inverse mass and momentum operator in the non-relativistic theory is not important.

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I. O. Vakarchuk. 2005-02-17. Kepler problem in Dirac theory for a particle with position-dependent mass. https://doi.org/10.1088/0305-4470/38/21/016

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