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

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Abstract
High‐order B‐splines provide effective basis functions for constructing solutions to the Schrödinger 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×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.