Relativistic effects in one-dimensional hydrogen atom |
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Authors: | K A Sveshnikov D I Khomovskii |
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Institution: | 1. Faculty of Physics and Institute for Theoretical Problems of Microphysics, Moscow State University, Moscow, 119899, Russia
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Abstract: | The dependence of stationary levels of a Dirac particle in the regularized Coulomb potential V ??(z) = ?q/(|z| + ??) on the cutoff parameter ?? is studied. It is shown that, in 1 + 1 D, the energy spectrum of a Dirac particle in such a potential reveals some specific features which nonanalytically depend on the coupling constant q and are essentially relativistic in nature. These properties turn out to be most important for ?? ? 1, explicitly demonstrating the existence of a physically reasonable energy spectrum for an arbitrarily small ?? > 0 and, at the same time, the absence of regular limit ?? ?? 0 (hence, the absence of a well-defined spectral problem for the Dirac equation without regularization for arbitrary q in 1 + 1 D). |
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