The eighth order Numerov method

A comparison of the shooting and the matrix diagonalization forms of the fi nite difference method for the Schrodinger equation leads to an order doubl ing principle which produces an eigenvalue estimate of gth order from the t raditional Numerov method. Some specimen calculations are given, and a disc ussion is given of some subtle points concerning the order of approximation of various energy contributions and the effect of varying the choice of th e wavefunction at external points. (C) 1999 Published by Elsevier Science B .V. All rights reserved.