Abstract
The properties of coordinate systems that admit separation of the Laplacian and Hamilton–Jacobi operators have been thoroughly explored so that the nature of solutions in separable form of Laplace’s equation, the wave equation, Schrödinger’s equation and the Hamilton–Jacobi equation are well understood. The corresponding problems for the Dirac operator in flat spacetime have been less completely examined and this paper contains studies intended to produce a more systematic account of possible solutions of Dirac’s equation. Because the Dirac operator differs from the Laplacian in being a first-degree differential operator and in having matrix coefficients, it is not possible to discuss possible solutions in as general a way and the separable solutions are far less rich than for equations with the Laplacian. In particular, the forms of the potentials for which separable solutions are possible are not for the most part of physical interest. Although the discussion is confined to coordinates in flat space–time, some of the procedures are derived from those developed to solve Dirac’s equation in coordinates with a Kerr metric.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
