On integral and differential representations of Jordan chains and the confluent supersymmetry algorithm

Abstract

We construct a relationship between integral and differential representation of second-order Jordan chains. Conditions to obtain regular potentials through the confluent supersymmetry algorithm when working with the differential representation are obtained using this relationship. Furthermore, it is used to find normalization constants of wave functions of quantum systems that feature energy-dependent potentials. Additionally, this relationship is used to express certain integrals involving functions that are solution of Schrodinger equations through derivatives.

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• Klein four-group and Darboux duality in conformal mechanics
• Confluent Second-Order Supersymmetric Quantum Mechanics and Spectral Design
• Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials
• Sequences of Exact Analytical Solutions for Plane-Waves in Graded Media
• Supersymmetric Quantum Potentials Analogs of Classical Electrostatic Fields
• Special function models of indecomposable $sl(2)$ representations: The Laguerre Case
• Hidden symmetries and nonlinear (super)algebras