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Transmission coefficient for one-dimensional potential barriers using continued fractions

1980; Institute of Physics; Volume: 13; Issue: 4 Linguagem: Inglês

10.1088/0305-4470/13/4/011

1361-6447

J. P. Vigneron, Ph. Lambin,

Scientific Research and Discoveries

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.