A new efficient method for calculation of energy eigenvalues and eigenstates of the one-dimensional Schrödinger equation

Abstract

A method for the numerical solution of the one-dimensional Schrödinger equation based on a matrix formulation of Numerov’s method is described. Some matrix theory leading to an efficient algorithm for the slicing of the spectrum of the related eigenproblem for a pair of tridiagonal matrices is developed. Finally the application of defect correction to the discretization gives a method of order of accuracy eight. Results of example calculations are presented.