A new approach to the numerical solution of boundary value problems for differential equations which originated in recent papers by Greengard and Rokhlin, is improved and adapted to the numerical solution of the radial Schrödinger equation. The approach is based on the conversion of the differential equation into an integral equation together with the application of a spectral type Clenshaw-Curtis quadrature.
The Integral Equation Method (IEM) is then extended to handle systems of coupled Schrödinger equations with both positive and negative channel energies. Through numerical examples, the IEM is shown to be superior to commonly used finite difference methods.
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