Factorization of Sturm–Liouville operators: solvable potentials and underlying algebraic structure

Hounkonnou, Mahouton Norbert; Sodoga, Komi; Azatassou, E S

doi:10.1088/0305-4470/38/2/007

Cited by 22 publications

(14 citation statements)

References 28 publications

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“…which correspond to a problem with a position dependent mass; this is a particular example or factorization of Sturm-Liouville operators [59]. In this case we should look for two operators A and A + of the following form…”

Section: Schrödinger Factorization Formalismmentioning

confidence: 99%

A quantum exactly solvable non-linear oscillator with quasi-harmonic behaviour

2007

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The quantum version of a non-linear oscillator, previouly analyzed at the classical level, is studied. This is a problem of quantization of a system with position-dependent mass of the form m = (1 + λx 2 ) −1 and with a λ-dependent nonpolynomial rational potential. This λ-dependent system can be considered as a deformation of the harmonic oscillator in the sense that for λ → 0 all the characteristics of the linear oscillator are recovered. Firstly, the λ-dependent Schrödinger equation is exactly solved as a Sturm-Liouville problem and the λ-dependent eigenenergies and eigenfunctions are obtained for both λ > 0 and λ < 0. The λ-dependent wave functions appear as related with a family of orthogonal polynomials that can be considered as λ-deformations of the standard Hermite polynomials. In the second part, the λ-dependent Schrödinger equation is solved by using the Schrödinger factorization method, the theory of intertwined Hamiltonians and the property of shape invariance as an approach. Finally, the new family of orthogonal polynomials is studied. We prove the existence of a λ-dependent Rodrigues formula, a generating function and λ-dependent recursion relations between polynomials of different orders.

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Section: Schrödinger Factorization Formalismmentioning

confidence: 99%

A quantum exactly solvable non-linear oscillator with quasi-harmonic behaviour

2007

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“…Despite the complications introduced by the generalizations, it is possible to find a first order formalism that is compatible with the equations that minimizes the action and govern the non-canonical system. Nevertheless, the generalized nature of the models makes a Sturm-Liouville eigenvalue equation [10] arise in the study of the linear stability, instead of the Schrödinger-like one as in the standard scenario. A possible manner to overcome this difficulty is to make a change of variables to transform this equation into a Schrödinger-like one.…”

Section: Introductionmentioning

confidence: 99%

Stability of kinklike structures in generalized models

2020

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We study the stability of topological structures in generalized models with a single real scalar field. We show that it is driven by a Sturm-Liouville equation and investigate the conditions that lead to the existence of explicit supersymmetric operators that factorize the stability equation and allow us to construct partner potentials. In this context, we discuss the property of shape invariance as a possible manner to calculate the discrete states and their respective eigenvalues.

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“…In this section, we introduce the SUSY QM factorization method [19] (and references therein), give the integrability condition, known as shape invariance condition, and define the associated generalized coherent states. Let H = L 2 (]a, b[, dx) be the Hilbert space with the inner product defined by :…”

Section: Introductionmentioning

confidence: 99%