New modified Runge-Kutta-Nystroem methods for the numerical integration of the Schrodinger equation

摘要

In this work we construct new Runge-Kutta-Nystrom methods especially designed to integrate exactly the test equation y" = - w~2y. We modify two existing methods: the Runge-Kutta-Nystrom methods of fifth and sixth order. We apply the new methods to the computation of the eigenvalues of the Schroedinger equation with different potentials such as the harmonic oscillator, the doubly anharmonic oscillator and the exponential potential.