B-spline expansion bases for excited states and discretized scattering states

High-order B-splines provide effective basis functions for constructing solutions to the Schroedinger equation. For high-lying levels of the Morse potential, septic splines yield an accuracy comparable to harmonic oscillators. They can also approximate hydrogenic wavefunctions; typically one-third of the N eigenvalues of an N x N matrix are more accurate than 0.01%. Matrix eigenvectors can also represent scattering states. The approximation is uniformly valid spatially when basis functions terminate sharply