Title: A new method for the solution of the Schrödinger equation
Abstract: We approximate the potential in the one-dimensional Schrödinger equation by a step function with a finite number of steps. In each step, the resulting differential equation has constant coefficients and is integrated exactly in terms of circular or hyperbolic functions. The solutions are then matched at the interface of each layer to construct the eigenfunctions in the whole domain. Unique features of the numerical method are: (a) All the eigenfunctions and eigenvalues are obtained with the same absolute accuracy for the same number of steps in the potential;(b) any desired number of eigenvalues and eigenfunctions are obtained in one single pass without any need to supply initial guesses for the eigenvalues; (c) for any fixed number of steps in the potential, we obtain in principle the whole infinite spectrum of eigenvalues and eigenfunctions.
Publication Year: 1970
Publication Date: 1970-04-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 84
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