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

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.