On Clifford numbers, Dirac and relativistic Hamilton-Jacobi equations

Jerome K. Percus; Nikitas L. Petrakopoulos

doi:10.1063/1.1665566

On Clifford numbers, Dirac and relativistic Hamilton-Jacobi equations

Jerome K. Percus, Nikitas L. Petrakopoulos

Mathematics

Research output: Contribution to journal › Article › peer-review

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
DOIs	https://doi.org/10.1063/1.1665566
State	Published - 1971

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.1665566

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title = "On Clifford numbers, Dirac and relativistic Hamilton-Jacobi equations",

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.",

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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.

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On Clifford numbers, Dirac and relativistic Hamilton-Jacobi equations

Abstract

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