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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. Keywords: one-dimensional quantum potentials, numerical solutions, computationaldoi:10.1590/s1806-11172007000300004 fatcat:g5ppkewhqfa7zbg3zdjkjpwk5m