Error Estimates for the Solution of the Radial Schrödinger Equation by the Rayleigh—Ritz Finite Element Method

Abstract

Approximate eigenvalues and eigenfunctions are obtained for the radial Schrödinger equation by applying the Rayleigh—Ritz method to a function space consisting of polynomial splines of odd degree. Computable a posteriori error estimates for the eigenfunction error estimates are obtained. The sharpness of these estimates is illustrated for the harmonic oscillator and Woods—Saxon potentials, using both cubic splines and piecewise cubic Hermite polynomials.