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Hydrogen Atom and Equivalent Form of the Lévy-Leblond Equation |
| Muhammad Adeel Ajaib1,2** |
1Department of Physics, California Polytechnic State University, San Luis Obispo 93401, USA
2Department of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar
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| Cite this article: |
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Muhammad Adeel Ajaib 2017 Chin. Phys. Lett. 34 050301 |
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Abstract We discuss the equivalent form of the Lévy-Leblond equation 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, propose a Hamiltonian for the equation in (3+1) dimensions, and solve it for a Coulomb potential. The quantized energy levels for the hydrogen atom are obtained, and the result is consistent with the non-relativistic quantum mechanics.
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Received: 25 January 2017
Published: 29 April 2017
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| PACS: |
03.65.-w
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(Quantum mechanics)
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03.65.Ta
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(Foundations of quantum mechanics; measurement theory)
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03.65.Ge
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(Solutions of wave equations: bound states)
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| [1] | Lévy-Leblond J M 1967 Commun. Math. Phys. 6 286 | | [2] | Ajaib M A 2015 Found. Phys. 45 1586 | | [3] | Ajaib M A 2016 Int. J. Quantum Found. 2 109 | | [4] | Sobhani H and Hassanabadi H 2016 arXiv:1605.09158 | | [5] | Sakurai J J and Napolitano J J 2014 Modern Quantum Mechanics 2nd edn (New York: Pearson Higher) | | [6] | Sakurai J J 1967 Advanced Quantum Mechanics (New York: Addison-Wesley) | | [7] | Greiner W 2000 Relativistic Quantum Mechanics (Berlin: Springer-Verlag) |
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