2012
DOI: 10.1016/j.aop.2012.07.004
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Multistep DBT and regular rational extensions of the isotonic oscillator

Abstract: In some recent articles we developed a new systematic approach to generate solvable rational extensions of primary translationally shape invariant potentials. In this generalized SUSY QM partnership, the DBT are built on the excited states Riccati-Schrödinger (RS) functions regularized via specific discrete symmetries of the considered potential. In the present paper, we prove that this scheme can be extended in a multistep formulation. Applying this scheme to the isotonic oscillator, we obtain new towers of r… Show more

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Cited by 59 publications
(80 citation statements)
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References 52 publications
(115 reference statements)
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“…32 We have first confirmed that g (α) μ (z) cannot have any pole at the origin and is a polynomial with non-zero constant term, a property that was conjectured in Ref. 31.…”
Section: -12mentioning
confidence: 65%
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“…32 We have first confirmed that g (α) μ (z) cannot have any pole at the origin and is a polynomial with non-zero constant term, a property that was conjectured in Ref. 31.…”
Section: -12mentioning
confidence: 65%
“…32, the Wronskian (3.8) has no node on the positive half-line, which ensures the regularity of the rationally extended potential V (2) (x) on this domain. The bound-state wavefunctions of the latter are then given by 31…”
Section: Laguerre Eop and Reducible Kth Order Susyqmmentioning
confidence: 99%
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