On the new translational shape invariant potentials

Abstract

Recently, several authors have found new translational shape invariant potentials not present in classic classifications like that of Infeld and Hull. For example, Quesne on the one hand and Bougie, Gangopadhyaya and Mallow on the other have provided examples of them, consisting on deformations of the classical ones. We analyze the basic properties of the new examples and observe a compatibility equation which has to be satisfied by them. We study particular cases of such equation and give more examples of new translational shape invariant potentials.

9 pages, uses iopart10.clo, version 2

References in corpus (4)

• Infinitely many shape invariant potentials and new orthogonal polynomials
• Group theoretical approach to the intertwined Hamiltonians
• Generation of a Complete Set of Supersymmetric Shape Invariant Potentials from an Euler Equation
• Method for Generating Additive Shape Invariant Potentials from an Euler Equation

Cited by in corpus (14)

• Extended Krein-Adler theorem for the translationally shape invariant potentials
• Multistep DBT and regular rational extensions of the isotonic oscillator
• Rationally-extended radial oscillators and Laguerre exceptional orthogonal polynomials in kth-order SUSYQM
• New rational extensions of solvable potentials with finite bound state spectrum
• Extensions of solvable potentials with finitely many discrete eigenstates
• Inter-relations between additive shape invariant superpotentials
• Exceptional orthogonal polynomials and new exactly solvable potentials in quantum mechanics
• Shape Invariant Rational Extensions And Potentials Related to Exceptional Polynomials
• A short note on "Group theoretic approach to rationally extended shape invariant potentials" [Annals of Physics 359, 46 (2015)]
• Symmetries and the compatibility condition for the new translational shape invariant potentials
• Supersymmetric Quantum Mechanics, Engineered Hierarchies of Integrable Potentials, and the Generalised Laguerre Polynomials
• Generalized coherent states of exceptional Scarf-I potential: Their spatio-temporal and statistical properties
• Quantum Hamilton-Jacobi Quantization and Shape Invariance
• Infinite families of shape invariant potentials with n parameters subject to translation