Comparison of matrix methods applied to the radial Schrödinger eigenvalue equation: The Morse potential

Abstract

This paper demonstrates the application of matrix methods based on finite differences and on variational (Rayleigh‐Ritz‐Galerkin) procedures to solution of the radial Schrödinger equation for bound states of the Morse potential. It demonstrates sources of numerical inaccuracy: truncation, termination, tolerance, and quadrature. Cubic splines, harmonic oscillators, floating Gaussians, and sines are used as basis functions.