Solution of Schroedinger's one-dimensional equation in finite range potentials

The recently developed method of segments applicable to problems of onedimension in Quantum Mechanics, is extended to the exact limit of infinitesimal segmentation. The resulting infinite sequence of multiple integrals for the elements of the 2x2 product matrix of central importance to this method, is exactly evaluated for the case of polynominal potentials, yielding as a bi-product, accurate segment approximations to more general potential shapes. Numerical examples are given to show the computational power in practical application involving finite range potentials. (orig.)