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The quantum Hamilton–Jacobi formalism in complex space

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Abstract

Quantum mechanics in complex space is introduced using the Hamilton–Jacobi theory. A significant consequence of doing so is that a quantum potential function must be admitted to the complex Hamiltonian to obtain compatibility with the Schrödinger equation. The Hamilton–Jacobi equations are studied in detail on a general Riemannian space with a general metric. Then the metric is restricted to the case of spherical coordinates. The Hamilton–Jacobi system is worked out in several ways for the central force problem and results are found to be completely consistent. The theory is extended to include interaction of matter with an electromagnetic field.

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  1. Department of Mathematics, University of Texas, Edinburg, TX, 78540, USA

    Paul Bracken

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  1. Paul Bracken
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Correspondence to Paul Bracken.

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Bracken, P. The quantum Hamilton–Jacobi formalism in complex space. Quantum Stud.: Math. Found. 7, 389–403 (2020). https://doi.org/10.1007/s40509-020-00224-8

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  • DOI: https://doi.org/10.1007/s40509-020-00224-8

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