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Solutions of all one-dimensional wave equations with time independent potential and separable variables | | Marco Ferraris
; Alessandro D.A.M. Spallicci
; | | Rating: | Visitors: 5/5 (1 visitor) | | Date: |
7 Sep 2003 | | Journal: | Gen.Rel.Grav. 36 (2004) 1955-1963 | | Subject: | General Relativity and Quantum Cosmology; Mathematical Physics; Analysis of PDEs | gr-qc math-ph math.AP math.MP | | Affiliation: | Dip. Matematica, Univ. di Torino, Observatoire de la Cote d’Azur, Nice | | Abstract: | Exact 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 variable separation, have been found. The real valueness of the solutions from computer algebra programs is not always manifest and in this work we provide ready to use solutions. We discussed especially the potential $cosh^{-2}x (m_1 + m_2 sinh x)$. Such potential approximates the Schwarzschild black hole potential for even parity. | | Source: | arXiv, gr-qc/0309038 | | Services: | Forum | Review | PDF | Favorites | |
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