Numerov numerical method applied to the Schr\"odinger equation

Abstract

In this paper it is shown how to solve numerically eigenvalue problems associated to second order linear ordinary differential equations, containing also terms which depend on the variable. A didactic presentation of the Numerov Method is given and, in the sequel, it is applied to two quantum non-relativistic problems with well known analytical solutions: the simple harmonic oscillator and the hydrogen atom. The numerical results are compared to those obtained analytically.