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A New Method for Approximate Solution of One-Dimensional Schrödinger Equations

S. Travlos
J. Boeyens
Journal / Anthology

Theoretica Chimica Acta
Year: 1994
Volume: 87
Page range: 453-464

A general method for approximate solution of one-dimensional Schrödinger equations with a wide range of square-integrable potentials is described. The potential is expanded in terms of either Jacobi or Bessel functions of argument exp(-r). This allows the Schrödinger equation to be solved by the Frobenius method. In the absence of super-computing power the input requirement of a large number of significant figures was handled by an algebraic computing package, for illustrative purposes. A sum of Gaussian wells and a Morse potential are treated as examples. Key words: Bound-state -- Scattering solutions -- Schrödinger equation -- Frobenius method

*Science > Physics > Quantum Physics