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Title: Applying supersymmetry to energy dependent potentials

We investigate the supersymmetry properties of energy dependent potentials in the D=1 dimensional space. We show the main aspects of supersymmetry to be preserved, namely the factorization of the Hamiltonian, the connections between eigenvalues and wave functions of the partner Hamiltonians. Two methods are proposed. The first one requires the extension of the usual rules via the concept of local equivalent potential. In this case, the superpotential becomes depending on the state. The second method, applicable when the potential depends linearly on the energy, is similar to what has been already achieved by means of the Darboux transform. -- Highlights: •Supersymmetry extended to energy dependent potentials. •Generalization of the concept of superpotential. •An alternative method used for linear E-dependence leads to the same results as Darboux transform.
Authors:
 [1] ;  [2] ;  [2]
  1. Faculté de Physique, USTHB Bab Ezzouar, Alger (Algeria)
  2. Groupe de Physique Théorique, Institut de Physique Nucléaire, IN2P3 - CNRS, Université Paris-Sud 11, 91406 Orsay Cedex (France)
Publication Date:
OSTI Identifier:
22224234
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 338; Other Information: Copyright (c) 2013 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:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; EIGENVALUES; ENERGY DEPENDENCE; FACTORIZATION; HAMILTONIANS; POTENTIALS; SUPERSYMMETRY