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Title: Shape invariant potentials in higher dimensions

In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended to arrive at a large class of new shape invariant potentials in arbitrary dimensions. A reformulation of the shape invariance property and possible generalizations are proposed. These may lead to an important extension of the shape invariance property to Hamiltonians that are related to standard potential problems via space time transformations, which are found useful in path integral formulation of quantum mechanics.
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [5]
  1. Department of Physics, Osmania University, Hyderabad (India)
  2. School of Physics, University of Hyderabad, Hyderabad, 500046 (India)
  3. (Declared as deemed-to-be University u/s 3 of the UGC Act 1956), Dontanapally, Hyderabad, 501203 (India)
  4. Department of Physics, Shiv Nadar University, Village Chithera, Tehsil Dadri, Gautam Budh Nagar, UP, 203207 (India)
  5. (India)
Publication Date:
OSTI Identifier:
22451197
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 359; Other Information: Copyright (c) 2015 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; EXACT SOLUTIONS; HAMILTONIANS; MANY-DIMENSIONAL CALCULATIONS; PATH INTEGRALS; POLYNOMIALS; POTENTIALS; QUANTUM MECHANICS; SPACE-TIME