Wronskian differential formula for k-confluent SUSY QM

Abstract

The confluent SUSY QM usually involves a second-order SUSY transformation where the two factorization energies converge to a single value. In order to achieve it, one generally needs to solve an indefinite integral, which limits the actual systems to which it can be applied. Nevertheless, not so long ago, an alternative method to achieve this transformation was developed through a Wronskian differential formula [Phys Lett. A 3756 (2012) 692]. In the present work, we consider the k-confluent SUSY transformation, where k factorization energies merge into a single value, and we develop a generalized Wronskian differential formula for this case. Furthermore, we explicitly work out general formulas for the third- and fourth-order cases and we present as examples the free particle and the single-gap Lamé potentials.

Final version. 19 pages, 6 figures, 39 references

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Cited by in corpus (8)

• Trends in supersymmetric quantum mechanics
• Confluent Crum-Darboux transformations in Dirac Hamiltonians with $PT$-symmetric Bragg gratings
• Bilayer graphene in magnetic fields generated by supersymmetry
• Recursive Representation of Wronskians in Confluent Supersymmetric Quantum Mechanics
• Klein four-group and Darboux duality in conformal mechanics
• Confluent Second-Order Supersymmetric Quantum Mechanics and Spectral Design
• Supersymmetric Quantum Potentials Analogs of Classical Electrostatic Fields
• Exactly-solvable quantum systems in terms of Lambert-W functions