Solutions of all one-dimensional wave equations with time independent potential and separable variables
نویسنده
چکیده
Solutions, in terms of special functions, of all wave equations uxx − utt = 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 (m1 + m2 sinh x) cosh −2 x. Such potential approximates the Schwarzschild black hole potential for even parity and its use for determining black holes quasi-normal modes is hinted to. PACS: 02.30Jr 04.70Bw
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