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Title: Potentials of the Heun class: The triconfluent case

We study special classes of potentials for which the one-dimensional (or radial) Schrödinger equation can be reduced to a triconfluent Heun equation by a suitable coordinate transformation together with an additional transformation of the wave function. In particular, we analyze the behaviour of those subclasses of the potential arising when the ordinary differential equation governing the coordinate transformation admits explicit analytic solutions in terms of the radial variable. Furthermore, we obtain formulae for solutions of the eigenvalue problem of the associated radial Schrödinger operator. Last but not least, using methods of supersymmetric quantum mechanics we relate the considered potentials to a new class of exactly solvable ones.
Authors:
;  [1] ;  [2]
  1. Department of Mathematics, University of the West Indies, Kingston 6 (Jamaica)
  2. Departamento de Fisica, Universidad de los Andes, Cra. 1E No. 18A-10, Bogota (Colombia)
Publication Date:
OSTI Identifier:
22403142
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 5; Other Information: (c) 2015 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; DIFFERENTIAL EQUATIONS; EIGENVALUES; EXACT SOLUTIONS; QUANTUM MECHANICS; SUPERSYMMETRY; WAVE FUNCTIONS