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
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