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Exact solutions to the Dirac equation for a Coulomb potential in $D+1$ dimensions

Xiao-Yan Gu·Zhong-Qi Ma·Shi-Hai Dong
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Abstract

The Dirac equation is generalized to $D+1$ space-time.The conserved angular momentum operators and their quantum numbers are discussed. The eigenfunctions of the total angular momenta are calculated for both odd $D$ and even $D$ cases. The radial equations for a spherically symmetric system are derived. The exact solutions for the system with a Coulomb potential are obtained analytically. The energy levels and the corresponding fine structure are also presented.

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Xiao-Yan Gu, Zhong-Qi Ma, Shi-Hai Dong. 2002-09-10. Exact solutions to the Dirac equation for a Coulomb potential in $D+1$ dimensions. https://doi.org/10.1142/s0218301302000879

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