A new propagation method for the radial Schrödinger equation

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Abstract
A new method of propagating the radial Schrödinger equation, based upon a Taylor series expansion of the wavefunction and partial re-summation of the infinite series, is extended to piece-wise quadratic potentials. The Light-Walker R-matrix method of solving close-coupled equations is implemented in such a manner as to take advantage of the rapid convergence properties of the new propagators and is applied to the well-known problem of an atom colliding with a harmonic oscillator. The results indicate that reasonable accuracy can be obtained; furthermore, they are monotonically converging to the proper answer, unlike some other implementations.