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Title: Solutions to position-dependent mass quantum mechanics for a new class of hyperbolic potentials

We analytically solve the position-dependent mass (PDM) 1D Schrödinger equation for a new class of hyperbolic potentials V{sub q}{sup p}(x)=−V{sub 0}(sinh{sup p}x/cosh{sup q}x), p=−2,0,⋯q [see C. A. Downing, J. Math. Phys. 54, 072101 (2013)] among several hyperbolic single- and double-wells. For a solitonic mass distribution, m(x)=m{sub 0} sech{sup 2}(x), we obtain exact analytic solutions to the resulting differential equations. For several members of the class, the quantum mechanical problems map into confluent Heun differential equations. The PDM Poschl-Teller potential is considered and exactly solved as a particular case.
Authors:
 [1] ;  [2] ;  [3]
  1. Physics Department, State University Vale do Acaraú, Av. da Universidade 850, 62040-370 Sobral-CE (Brazil)
  2. (UECE), Av. Paranjana 1700, 60740-903 Fortaleza-CE (Brazil)
  3. Grupo de Física Teórica, State University of Ceara (UECE), Av. Paranjana 1700, 60740-903 Fortaleza-CE (Brazil)
Publication Date:
OSTI Identifier:
22217738
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; EXACT SOLUTIONS; MASS DISTRIBUTION; POTENTIALS; QUANTUM MECHANICS; SCHROEDINGER EQUATION