The Darboux transformation of the Schrödinger equation with an energy-dependent potential

DOI10.1016/j.physleta.2006.10.016zbMath1197.34173OpenAlexW2017234481MaRDI QIDQ601414

Xian-Min Qian, Yi-Shen Li, Ji Lin

Publication date: 28 October 2010

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2006.10.016

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25)

Related Items (13)

Dirac systems with magnetic field and position-dependent mass: Darboux transformations and equivalence with generalized Dirac oscillators ⋮ Darboux transformations and soliton-like solutions of a new system associated with the negative AKNS system ⋮ Applying supersymmetry to energy dependent potentials ⋮ Darboux transformations for energy-dependent potentials and the Klein-Gordon equation ⋮ Higher-order Darboux transformations and Wronskian representations for Schrödinger equations with quadratically energy-dependent potentials ⋮ Modified Darboux transformations with foreign auxiliary equations ⋮ DARBOUX TRANSFORMATIONS FOR EFFECTIVE MASS SCHRÖDINGER EQUATIONS WITH ENERGY-DEPENDENT POTENTIALS ⋮ Generalized Schrödinger equations with quadratical energy-dependence in the potential: Darboux transformations and application to the Heun class ⋮ Characterization of Darboux transformations for quantum systems with quadratically energy-dependent potentials ⋮ Reconstructions of the dark-energy equation of state and the inflationary potential ⋮ Higher-order Darboux transformations for the massless Dirac equation at zero energy ⋮ Spectral parameter power series for Sturm-Liouville equations with a potential polynomially dependent on the spectral parameter and Zakharov-Shabat systems ⋮ Darboux transformations of the one-dimensional stationary Dirac equation with linear potential and its new solutions

Cites Work

• Factorisation of energy dependent Schrödinger operators: Miura maps and modified systems
• Some Water Wave Equations and Integrability
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