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

Marco Ferraris; Alessandro D. A. M. Spallicci

doi:10.1023/B:GERG.0000036053.75204.a2

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

广义相对论与量子宇宙学 2009-11-10 v2 数学物理偏微分方程分析 math.MP

作者: Marco Ferraris , Alessandro D. A. M. Spallicci

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摘要

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.

引用

@article{arxiv.gr-qc/0309038,
  title  = {Solutions of all one-dimensional wave equations with time independent potential and separable variables},
  author = {Marco Ferraris and Alessandro D. A. M. Spallicci},
  journal= {arXiv preprint arXiv:gr-qc/0309038},
  year   = {2009}
}

备注

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

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

摘要

引用

备注

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