Abstract
We construct confluent supersymmetric partners of quantum systems that emerge from the spheroidal equation. Properties of the systems and of their transformed counterparts are discussed.
Highlights
The supersymmetry (SUSY) formalism is a method for generating solvable models in quantum mechanics
Based on the Darboux transformation [1,2,3], it converts a known quantum system into a transformed counterpart, the so-called SUSY partner. As this formalism is compatible with basically any exactly-solvable quantum model governed by the Schrödinger equation and many systems described by the Dirac equation, a large amount of applications can be found in the literature
The formalism of SUSY can be split into two different versions, commonly referred to as standard and confluent algorithm, respectively
Summary
The supersymmetry (SUSY) formalism is a method for generating solvable models in quantum mechanics. Based on the Darboux transformation [1,2,3], it converts a known quantum system into a transformed counterpart, the so-called SUSY partner As this formalism is compatible with basically any exactly-solvable quantum model governed by the Schrödinger equation and many systems described by the Dirac equation, a large amount of applications can be found in the literature. Recent works on the confluent algorithm include its application to the inverted oscillator [7] and to the Dirac equation for pseudoscalar potentials [8]. All digits of numerical values stated throughout this work are significant
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