General recursive solution for one dimensional quantum potentials: a simple tool for applied physics

2006/05/15 by Sérgio L. Morelhão, Morelhão, Sérgio L., André V. Perrotta +1
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0605115

Final version to appear in the Brazilian Magazine of Physics Teaching (http://www.sbfisica.org.br/noticias/publicacoes.shtml)

arxiv created 2007/05/15 · arxiv updated 2009/12/01

Abstract

A revision of the recursive method proposed by S.A. Shakir [Am. J.Phys. 52, 845 (1984)] to solve bound eigenvalues of the Schrödinger equation is presented. Equations are further simplified and generalized for computing wave functions of any given one-dimensional potential, providing accurate solutions not only for bound states but also for scattering and resonant states, as demonstrated here for a few examples.

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