Solvable rational extensions of the isotonic oscillator

Journal Article · Mon Aug 15 04:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2011.03.001· OSTI ID:21583324

Grandati, Yves ^[1]

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1. Institut de Physique, Equipe BioPhyStat, ICPMB, IF CNRS 2843, Universite Paul Verlaine-Metz, 1 Bd Arago, 57078 Metz, Cedex 3 (France)

Highlights: > We obtain in a new way the solvable rational extensions of the isotonic oscillator. > The method is systematic without resorting to any ansatz. > We use a generalization of the SUSY quantum partnership to excited states. > They are regularized by specific discrete symmetries of the potential. > The proof of the shape invariance of the extensions is direct. - Abstract: Combining recent results on rational solutions of the Riccati-Schroedinger equations for shape invariant potentials to the finite difference Baecklund algorithm and specific symmetries of the isotonic potential, we show that it is possible to generate the three infinite sets (L1, L2 and L3 families) of regular rational solvable extensions of this potential in a very direct and transparent way.

• OSTI ID: 21583324
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 8 Vol. 326; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
BAECKLUND TRANSFORMATION
DIFFERENTIAL EQUATIONS
ELECTRONIC EQUIPMENT
ENERGY LEVELS
EQUATIONS
EQUIPMENT
EXACT SOLUTIONS
EXCITED STATES
MATHEMATICAL LOGIC
MATHEMATICAL SOLUTIONS
MECHANICS
OSCILLATORS
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIALS
QUANTUM MECHANICS
SCHROEDINGER EQUATION
SUPERSYMMETRY
SYMMETRY
TRANSFORMATIONS
WAVE EQUATIONS