Higher Order Finite Element Solution of the One-Dimensional Schrodinger Equation

Abstract

The one-dimensional Schrodinger equation has been examined by means of the confined system defined on a finite interval. The eigenvalues of the resulting bounded problem subject to the Dirichlet boundary conditions are calculated accurately to 20 significant figures using higher order shape functions in the usual isoparametric finite element method. Numerical results are given for an arbitrary polynomial potential of degree M. (C) 1999 John Wiley & Sons, Inc.