Extended WKB method, resonances and supersymmetric radial barriers

TL;DR

This paper develops a semiclassical approach to calculate low energy resonances in radial barriers, constructs supersymmetric partner potentials, and explores their potential in studying transient quantum phenomena like Moshinsky's diffraction in time.

Contribution

It introduces an extended WKB method for resonances, and constructs supersymmetric partner potentials for radial barriers, enabling new insights into transient quantum effects.

Findings

Accurate calculation of resonance energies and widths.

Construction of supersymmetric partner potentials.

Potential applications in transient quantum phenomena.

Abstract

Semiclassical approximations are implemented in the calculation of position and width of low energy resonances for radial barriers. The numerical integrations are delimited by t/T<<8, with t the period of a classical particle in the barrier trap and T the resonance lifetime. These energies are used in the construction of `haired' short range potentials as the supersymmetric partners of a given radial barrier. The new potentials could be useful in the study of the transient phenomena which give rise to the Moshinsky's diffraction in time.