Abstract
The recently developed method of segments applicable to problems of one-dimension in Quantum Mechanics, is extended to the exact limit of infinitesimal segmentation. The resulting infinite sequence of multiple integrals for the elements of the 2 × 2 product matrix of central importance to this method, is exactly evaluated for the case of polynomial 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.
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