Wronskian differential formula for confluent supersymmetric quantum mechanics
David Bermudez, David J. Fernandez C., and Nicolas Fernandez-Garcia
TL;DR
This paper introduces a Wronskian differential formula that simplifies the application of confluent second-order SUSY transformations to various potentials, demonstrated on free particles and Lame potentials.
Contribution
It presents a new differential formula involving parametric derivatives, offering a simpler alternative to integral equations in supersymmetric quantum mechanics.
Findings
Simplifies SUSY transformation calculations
Applied to free particle and Lame potential
Demonstrates effectiveness of the differential formula
Abstract
A Wronskian differential formula, useful for applying the confluent second-order SUSY transformations to arbitrary potentials, will be obtained. This expression involves a parametric derivative with respect to the factorization energy which, in many cases, is simpler for calculations than the previously found integral equation. This alternative mechanism shall be applied to the free particle and the single-gap Lame potential.
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