Numerical construction of ''optimal'' nonoscillating amplitude and phase functions

A. Matzkin (1, 2) , M. Lombardi (1)

1 LSP - Laboratoire de Spectrométrie Physique
2 UCL - University College of London [London]

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.

Mots clés: Ordinary and partial differential equations; boundary value problems; Solutions of wave equations: bound states; Calculations and mathematical techniques in atomic and molecular physics

Domaines: Physique Quantique [quant-ph]

A. Matzkin, M. Lombardi. Numerical construction of ''optimal'' nonoscillating amplitude and phase functions. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2002, 66, pp.37702. ⟨10.1103/PHYSREVE.66.037702⟩. ⟨hal-00961319⟩