The multidimensional Darboux transformation

DOI10.1016/S0393-0440(97)00044-2zbMath0951.37042arXivhep-th/9612100OpenAlexW3099219667MaRDI QIDQ1299235

Niky Kamran, Artemio González-López

Publication date: 2 January 2001

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9612100

zbMATH Keywords

supersymmetric quantum mechanicsDarboux transformationquasi-exact solvabilityMoutard transformation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Supersymmetry and quantum mechanics (81Q60) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (9)

SEPARATION OF COUPLED SYSTEMS OF SCHRODINGER EQUATIONS BY DARBOUX TRANSFORMATIONS ⋮ Darboux transformations for energy-dependent potentials and the Klein-Gordon equation ⋮ Precanonical quantization of Yang-Mills fields and the functional Schrödinger representation ⋮ Matrix Calogero-Sutherland Hamiltonians and the multi-dimensional Darboux transformation ⋮ Multidimensional integrable Schrödinger operators with matrix potential ⋮ Darboux transformations for Schrödinger equations in two variables ⋮ Two-dimensional magnetic Schrödinger equations, Darboux transformations and solutions of associated auxiliary equations ⋮ Darboux transformations for (1+2)-dimensional Fokker-Planck equations with constant diffusion matrix ⋮ Multidimensional quasi-exactly solvable potentials with two known eigenstates

Cites Work

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• Dynamical breaking of supersymmetry
• Supersymmetry and Morse theory
• New quasi-exactly solvable Hamiltonians in two dimensions
• Laplace transformation in higher dimensions
• Inverse scattering on the line
• On some geometry associated with a generalised Toda lattice
• Real Lie algebras of differential operators and quasi-exactly solvable potentials
• The Factorization Method
• ASSOCIATED STURM-LIOUVILLE SYSTEMS

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