New rational extensions of solvable potentials with finite bound state spectrum
arXiv:1203.4149 · doi:10.1016/j.physleta.2012.09.037
Abstract
Using the disconjugacy properties of the Schrödinger equation, it is possible to develop a new type of generalized SUSY QM partnership which allows to generate new solvable rational extensions for translationally shape invariant potentials having a finite bound state spectrum. For this we prolong the dispersion relation relating the energy to the quantum number out of the physical domain until a disconjugacy sector. The prolonged excited states Riccati-Schrödinger (RS) functions are used to build Darboux-Bäcklund transforms which give regular isospectral extensions of the initial potential. We give the spectra of these extensions in terms of new orthogonal polynomials and study their shape invariance properties.
References in corpus (14)
- Infinitely many shape invariant potentials and new orthogonal polynomials
- Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
- Exactly Solvable Quantum Mechanics and Infinite Families of Multi-indexed Orthogonal Polynomials
- Two-step Darboux transformations and exceptional Laguerre polynomials
- Solvable rational extensions of the isotonic oscillator
- Exceptional orthogonal polynomials and the Darboux transformation
- Higher-order SUSY, exactly solvable potentials, and exceptional orthogonal polynomials
- Group theoretical approach to the intertwined Hamiltonians
- Multistep DBT and regular rational extensions of the isotonic oscillator
- Solvable rational extensions of the Morse and Kepler-Coulomb potentials
- Revisiting (quasi-)exactly solvable rational extensions of the Morse potential
- Rationally-extended radial oscillators and Laguerre exceptional orthogonal polynomials in kth-order SUSYQM
- On the new translational shape invariant potentials
- The theory of disconjugacy for a second order linear differential equation
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- Generalized coherent states of exceptional Scarf-I potential: Their spatio-temporal and statistical properties
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- Deformed Shape Invariant Superpotentials in Quantum Mechanics and Expansions in Powers of
- Infinite families of shape invariant potentials with n parameters subject to translation