Wronskian representation of second-order Darboux transformations for Schrödinger equations with quadratically energy-dependent potentials
- 22 August 2019
- journal article
- research article
- Published by IOP Publishing in Physica Scripta
- Vol. 95 (1), 015001
- https://doi.org/10.1088/1402-4896/ab3ddf
Abstract
We construct a Wronskian representation of second-order Darboux transformations for Schrodinger-type equations that feature quadratically energy-dependent potentials. Besides generalizing the conventional Darboux transformation of second order, our results can be adapted to generate zero-energy solutions to the massless Dirac equation in two dimensions.Keywords
This publication has 21 references indexed in Scilit:
- Integrable dispersive chains and energy dependent Schrödinger operatorJournal of Physics A: Mathematical and Theoretical, 2014
- Applying supersymmetry to energy dependent potentialsAnnals of Physics, 2013
- The Darboux transformation of the Schrödinger equation with an energy-dependent potentialPhysics Letters A, 2007
- Darboux Transformations in Integrable SystemsPublished by Springer Science and Business Media LLC ,2005
- Wave Equations with Energy-Dependent PotentialsCzechoslovak Journal of Physics, 2004
- Darboux transformation, factorization, and supersymmetry in one-dimensional quantum mechanicsTheoretical and Mathematical Physics, 1995
- Supersymmetry and quantum mechanicsPhysics Reports, 1995
- Darboux Transformations and SolitonsPublished by Springer Science and Business Media LLC ,1991
- Inverse scattering problems in absorbing mediaJournal of Mathematical Physics, 1976
- Nonlinear evolution equations associated with ‘enegry-dependent Schrödinger potentials’Letters in Mathematical Physics, 1976