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Title: Non-polynomial extensions of solvable potentials à la Abraham-Moses

Abraham-Moses transformations, besides Darboux transformations, are well-known procedures to generate extensions of solvable potentials in one-dimensional quantum mechanics. Here we present the explicit forms of infinitely many seed solutions for adding eigenstates at arbitrary real energy through the Abraham-Moses transformations for typical solvable potentials, e.g., the radial oscillator, the Darboux-Pöschl-Teller, and some others. These seed solutions are simple generalisations of the virtual state wavefunctions, which are obtained from the eigenfunctions by discrete symmetries of the potentials. The virtual state wavefunctions have been an essential ingredient for constructing multi-indexed Laguerre and Jacobi polynomials through multiple Darboux-Crum transformations. In contrast to the Darboux transformations, the virtual state wavefunctions generate non-polynomial extensions of solvable potentials through the Abraham-Moses transformations.
Authors:
 [1] ;  [1] ;  [2]
  1. Department of Physics, Shinshu University, Matsumoto 390-8621 (Japan)
  2. (China)
Publication Date:
OSTI Identifier:
22217887
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 10; 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; EIGENFUNCTIONS; EIGENSTATES; EIGENVALUES; MATHEMATICAL SOLUTIONS; MATRICES; OSCILLATORS; POLYNOMIALS; POTENTIALS; QUANTUM MECHANICS; SEEDS; SILICON OXIDES; STOCHASTIC PROCESSES; SYMMETRY; TRANSFORMATIONS; VIRTUAL STATES; WAVE FUNCTIONS