### Abstract

Conditions are established under which the Dirac equation for an electron in an electromagnetic field has an exact semiclassical solution. In other words, the phase is identified with a solution of the corresponding relativistic Hamilton-Jacobi equation and the spinor amplitude has no explicit dependence upon ℏ. The complete set of admissible fields is determined for one-dimensional and stationary three-dimensional systems, while an extensive class is indicated for the general time-dependent problem.

Original language | English (US) |
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Pages (from-to) | 2516-2520 |

Number of pages | 5 |

Journal | Journal of Mathematical Physics |

Volume | 12 |

Issue number | 12 |

DOIs | |

State | Published - 1971 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Percus, J. K., & Petrakopoulos, N. L. (1971). On Clifford numbers, Dirac and relativistic Hamilton-Jacobi equations.

*Journal of Mathematical Physics*,*12*(12), 2516-2520. https://doi.org/10.1063/1.1665566