| 摘 要： | 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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