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Title: Scattering amplitudes for multi-indexed extensions of solvable potentials

New solvable one-dimensional quantum mechanical scattering problems are presented. They are obtained from known solvable potentials by multiple Darboux transformations in terms of virtual and pseudo virtual wavefunctions. The same method applied to confining potentials, e.g.  Pöschl–Teller and the radial oscillator potentials, has generated the multi-indexed Jacobi and Laguerre polynomials. Simple multi-indexed formulas are derived for the transmission and reflection amplitudes of several solvable potentials. -- Highlights: •Scattering amplitudes calculated for infinitely many new solvable potentials. •New scattering potentials obtained by deforming six known solvable potentials. •Multiple Darboux transformations in terms of (pseudo) virtual states employed. •Scattering amplitudes checked to obey the shape invariance relation. •Errors in scattering amplitudes of some undeformed potentials in the literature corrected.
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. Department of Physics, Tamkang University, Tamsui 251, Taiwan, ROC (China)
  2. Department of Electrophysics, National Chiao-Tung University, Hsinchu, Taiwan, ROC (China)
  3. Center for Theoretical Sciences, National Taiwan University, Taipei, Taiwan, ROC (China)
  4. (Japan)
Publication Date:
OSTI Identifier:
22314791
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 343; Journal Issue: Complete; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; LAGUERRE POLYNOMIALS; ONE-DIMENSIONAL CALCULATIONS; OSCILLATORS; POTENTIALS; QUANTUM MECHANICS; REFLECTION; SCATTERING; SCATTERING AMPLITUDES; TRANSFORMATIONS; VIRTUAL STATES