The hyperbolic step potential: Antibound states, SUSY partners and Wigner time delays

Abstract

We study the scattering produced by a one dimensional hyperbolic step potential, which is exactly solvable and shows an unusual interest because of its asymmetric character. The analytic continuation of the scattering matrix in the momentum representation has a branch cut and an infinite number of simple poles on the negative imaginary axis which are related with the so called anti-bound states. This model does not show resonances. Using the wave functions of the anti-bound states, we obtain supersymmetric (SUSY) partners which are the series of Rosen Morse II potentials. We have computed the Wigner reflection and transmission time delays for the hyperbolic step and such SUSY partners.Our results show that the more bound states a partner Hamiltonian has the smaller is the time delay. We also have evaluated time delays for the hyperbolic step potential in the classical case and have obtained striking similitudes with the quantum case.

27 pages, 8 figures

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Cited by in corpus (7)

• Optical Supersymmetry in the Time Domain
• Magnon dynamics in a Skyrmion-textured domain wall of antiferromagnets
• Classical ladder functions for Rosen-Morse and curved Kepler-Coulomb systems
• Analysis of a one-dimensional Hamiltonian with a singular double well consisting of two nonlocal ${\delta }^{\prime }$ interactions
• Self-interacting quantum particles
• Massive and massless two-dimensional Dirac particles in electric quantum dots
• SUSY partners and $S$-matrix poles of the one dimensional Rosen-Morse II Hamiltonian