Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials

Abstract

The existence of a novel enlarged shape invariance property valid for some rational extensions of shape-invariant conventional potentials, first pointed out in the case of the Morse potential, is confirmed by deriving all rational extensions of the Rosen-Morse II and Eckart potentials that can be obtained in first-order supersymmetric quantum mechanics. Such extensions are shown to belong to three different types, the first two strictly isospectral to some starting conventional potential with different parameters and the third with an extra bound state below the spectrum of the latter. In the isospectral cases, the partner of the rational extensions resulting from the deletion of their ground state can be obtained by translating both the potential parameter $A$ (as in the conventional case) and the degree $m$ of the polynomial arising in the denominator. It therefore belongs to the same family of extensions, which turns out to be closed.

References in corpus (5)

• Infinitely many shape invariant potentials and new orthogonal polynomials
• Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics
• Solvable rational extensions of the isotonic oscillator
• Isospectral Potentials from Modified Factorization
• Global Solutions of Certain Second-Order Differential Equations with a High Degree of Apparent Singularity

Cited by in corpus (9)

• Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : II
• Exactness of SWKB for Shape Invariant Potentials
• Ladder operators for solvable potentials connected with exceptional orthogonal polynomials
• Breakup of SUSY Quantum Mechanics in the Limit-Circle Region of the Reflective Kratzer Oscillator
• Heun-Polynomial Representation of Regular-at-Infinity Solutions for the Basic SUSY Ladder of Hyperbolic Pöschl-Teller Potentials Starting from the Reflectionless Symmetric Potential Well
• Exactly Solvable Quantum Mechanics
• Casoratian Identities for the Discrete Orthogonal Polynomials in Discrete Quantum Mechanics with Real Shifts
• Hidden symmetries and nonlinear (super)algebras
• Ladder operators and coherent states for the Rosen-Morse system and its rational extensions