A fourth-order Bessel fitting method for the numerical solution of the Schrödinger equation

AbstractA new fourth-order method is developed for the numerical integration of the one-dimensional radial Schrödinger equation. This method integrates Bessel and Neumann functions exactly. It is shown that, for large r, this new formula is much more accurate and rapid than the Bessel fitting method of second order which is developed by Raptis and Cash (1987). The benefit of using this new approach is demonstrated by considering some numerical examples based on the Lenard–Jones potential