### 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) |
---|---|

Pages (from-to) | 2516-2520 |

Number of pages | 5 |

Journal | Journal of Mathematical Physics |

Volume | 12 |

Issue number | 12 |

State | Published - 1971 |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*12*(12), 2516-2520.

**On Clifford numbers, Dirac and relativistic Hamilton-Jacobi equations.** / Percus, Jerome; Petrakopoulos, Nikitas L.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 12, no. 12, pp. 2516-2520.

}

TY - JOUR

T1 - On Clifford numbers, Dirac and relativistic Hamilton-Jacobi equations

AU - Percus, Jerome

AU - Petrakopoulos, Nikitas L.

PY - 1971

Y1 - 1971

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=36849098640&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36849098640&partnerID=8YFLogxK

M3 - Article

VL - 12

SP - 2516

EP - 2520

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 12

ER -