Accurate numerical method for the solutions of the Schrödinger equation and the radial integrals based on the CIP method Original Research Article

A new accurate numerical method based on the constrained interpolation profile (CIP) method to solve the Schrödinger wave equation for bound and free states in central fields and to calculate radial integrals is presented. The radial wave equation is integrated on an arbitrary grid system by the adaptive stepsize controlled Runge–Kutta method controlling the truncation errors within a prescribed accuracy. For the continuum orbitals in the highly oscillating region, the non-linear radial wave equation in the phase-amplitude representation is used. In the evaluation of the derivatives of the radial wave function, the potential energy is approximated by the CIP method. In addition, the radial integrals encountered in the computation of various atomic process are accomplished with the CIP method using the values and their analytical derivatives at the grids. This numerical procedure can be extended in a straightforward way to solve the Dirac wave equation.