The retarded potential of a non-homogeneous wave equation: introductory analysis through the Green Functions

A. Téllez-Quiñones, J. C. Valdiviezo-Navarro, A. Salazar-Garibay, A. A. López Caloca

Abstract


The retarded potential, a solution of the non-homogeneous wave equation, is a subject of particular interest in many physics and engineering applications. Examples of such applications may be the problem of solving the wave equation involved in the emission and reception of a signal in a synthetic aperture radar (SAR), scattering and backscattering, and general electrodynamics for media free of magnetic charges.
However, the construction of this potential solution is based on the theory of  distributions, a topic that requires special care and time to be understood with mathematical rigor. Thus, the goal of this study is to provide an introductory analysis, with a medium level of formalism, on the construction of this potential solution and the handling of Green functions represented by sequences of well-behaved approximating
functions.

Keywords


Mathematical methods in physics; mathematics; diffraction theory; backscattering; radar.

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DOI: https://doi.org/10.31349/RevMexFisE.64.26

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Revista Mexicana de Física E

ISSN: 2683-2216 (on line), 1870-3542 (print)

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