Abstract
A numerical recipe for the construction of nonoscillating amplitude and phase functions for potentials with a single minimum is given. We give different examples illustrating the recipe, showing the usefulness of the procedure for the construction of basis functions in bound-state scattering processes, such as those described by quantum defect theory. The resulting amplitude and accumulated phase functions are coined as "optimal" nonoscillating (as a function of the space and energy variables) because they are the counterpart for the quantum problem of the classical action for the analog semiclassical problem.
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