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Letter: Solutions of All One-Dimensional Wave Equations with Time Independent Potential and Separable Variables

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Abstract

Solutions, in terms of special functions, of all wave equations u xx − u tt = V(x) u(t,x), characterised by eight inequivalent time independent potentials and by variables separation, have been found. The real valueness and the properties of the solutions produced by computer algebra programs are not always manifest and in this work we provide ready to use solutions. We discuss especially the potential (m 1 + m 2 sinh x)cosh−2x. Such potential approximates the Schwarzschild black hole potential and its use for determining black holes quasi-normal modes is hinted to.

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Authors and Affiliations

  1. Dip. Matematica, Univ. di Torino, Italy

    Marco Ferraris

  2. Dép, d'Astrophysique Relativiste, ARTEMIS UMR 6162 CNRS, Observatoire de la Côte d'Azur, Nice, France

    Alessandro D. A. M. Spallicci

Authors
  1. Marco Ferraris
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  2. Alessandro D. A. M. Spallicci
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Ferraris, M., Spallicci, A.D.A.M. Letter: Solutions of All One-Dimensional Wave Equations with Time Independent Potential and Separable Variables. General Relativity and Gravitation 36, 1955–1963 (2004). https://doi.org/10.1023/B:GERG.0000036053.75204.a2

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  • DOI: https://doi.org/10.1023/B:GERG.0000036053.75204.a2

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