Wronskian formula for confluent second-order supersymmetric quantum mechanics

Abstract

The confluent second-order supersymmetric quantum mechanics, with factorization energies ǫ 1 , ǫ 2 tending to a single ǫ-value, is studied. We show that the Wronskian formula remains valid if generalized eigenfunctions are taken as seed solutions. The confluent algorithm is used to generate SUSY partners of the Coulomb potential.

Wronskian differential formula for confluent supersymmetric quantum mechanics

“…1). It is known that a non-singular SUSY transformation for the free particle that adds a single new level to this system will always lead to a Pöschl-Teller potential, a one-soliton KdV potential [4,5,23,24], and this is the case for the k-confluent transformation, so our result agrees with the previous ones. Nevertheless, it does not have to be this way for all potentials, in fact, the outcome for the single-gap Lamé potential in the next Section points out to a different direction.…”

“…In this work we deal with a specific case of higher-order SUSY transformations, the confluent case, in which several factorization energies converge to the same value [3][4][5]. Taking such limit appropriately, this transformation leads to more flexibility for spectral design compared to the usual real case.…”

Confluent Supersymmetric Partners of Quantum Systems Emerging from the Spheroidal Equation

“…For further details, particularly on spectral design, we refer the reader to [11,22,23] and references therein. We start out by considering an initial equation that has the general form…”

The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials

“…In contrast to the previous example, this time we will start out from a boundary-value problem for the Schrödinger equation (14), and generate the Dirac SUSY partners arising from the confluent algorithm. Let us consider the following problem…”