Solutions of all one-dimensional wave equations with time independent potential and separable variables

Details Solutions of all one-dimensional wave equations with time independent potential and separable variables Solutions of all one-dimensional wave equations with time independent potential and separable variables

2003-09-07

arxiv.org/abs/gr-qc/0309038v2

Gen.Rel.Grav. 36 (2004) 1955-1963

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, 1 figure. Accepted by Gen. Rel. Grav. J.

Scientific paper

10.1023/B:GERG.0000036053.75204.

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.

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