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

摘要

A revision of the recursive method proposed by S.A. Shakir [Am. J.Phys.\textbf{52}, 845 (1984)] to solve bound eigenvalues of the Schr\"odingerequation is presented. Equations are further simplified and generalized forcomputing wave functions of any given one-dimensional potential, providingaccurate solutions not only for bound states but also for scattering andresonant states, as demonstrated here for a few examples.