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arXiv · 1607.06729

The Hydrogen Atom and the Equivalent Form of Levy-Leblond Equation

Muhammad Adeel Ajaib
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Abstract

We discuss the equivalent form of Levy-Leblond equation [1, 2] such that the nilpotent matrices are two dimensional. We show that this equation can be obtained in the non-relativistic limit of the (2+1) dimensional Dirac equation. Furthermore, we analyze the case with four dimensional matrices and propose a Hamiltonian for the equation in (3+1) dimensions and solve it for a Coulomb potential. We show that the quantized energy levels for the hydrogen atom are obtained and the result is consistent with non-relativistic quantum mechanics.

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Muhammad Adeel Ajaib. 2017-03-26. The Hydrogen Atom and the Equivalent Form of Levy-Leblond Equation. https://doi.org/10.1088/0256-307x%2F34%2F5%2F050301

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