Transmission coefficient for one-dimensional potential barriers using continued fractions

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Abstract
An explicit formula is given for evaluating the transmission coefficient of one-dimensional potential barriers corresponding to localised forces. The method is based on a simple discretisation of the Schrodinger equation leading to a three-term recursion relation. A continued fraction is then introduced in a quite natural way. Examples are provided to shed some light on the efficiency of the procedure, as compared to semiclassical approximations.

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