Abstract
The exact solutions of quantum systems in real three-dimensional space play an important role in physics. As mentioned above, a number of works have been contributed to the Schrödinger equation case. On the contrary, the studies of the Dirac equation in higher dimensions are less than those of the Schrödinger equation case except for the works in usual three-, two- and one-dimensional space. In this Chapter, we shall generalize the Dirac equation to (D+1) space-time and discuss the conserved angular momentum operators and their quantum numbers. Also, we will calculate the eigenfunctions of the total angular momentums for both odd (2N+1) and even 2N cases with the technique of group theory and present the radial equations. As an illustration, the hydrogen-like atoms are discussed by the series method.
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Dong, SH. (2011). Dirac Equation in Higher Dimensions. In: Wave Equations in Higher Dimensions. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1917-0_4
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DOI: https://doi.org/10.1007/978-94-007-1917-0_4
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