hyperbolic step potential: Anti-bound states, SUSY partners and Wigner time delays

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Gadella M., KURU Ş., Negro J.

ANNALS OF PHYSICS, cilt.379, ss.86-101, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 379
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1016/j.aop.2017.02.013
  • Dergi Adı: ANNALS OF PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.86-101
  • Anahtar Kelimeler: Scattering matrix, Factorization, Anti-bound state, Wigner time delay
  • Ankara Üniversitesi Adresli: Evet

Özet

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. (C) 2017 Elsevier Inc. All rights reserved.