The Darboux and Abraham-Moses transformations of the one-dimensional periodic Schrodinger equation and inverse problems

DOI10.1088/0266-5611/5/6/019zbMath0725.34101OpenAlexW2020434116MaRDI QIDQ5203406

Publication date: 1989

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0266-5611/5/6/019

zbMATH Keywords

inverse problems spectral data bound states one-dimensional periodic Schrödinger equation Darboux and Abraham-Moses transformations modified Milne equation

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Inverse problems involving ordinary differential equations (34A55)

Related Items (9)

Minimal realizations of supersymmetry for matrix Hamiltonians ⋮ Exactly solvable associated Lamé potentials and supersymmetric transformations ⋮ Equivalence of integral differential methods of generating accurately solvable potentials of the steady Schrödinger equation ⋮ Factorization of nonlinear supersymmetry in one-dimensional quantum mechanics. III: precise classification of irreducible intertwining operators ⋮ Scattering amplitudes for multi-indexed extensions of solvable potentials ⋮ Non-polynomial extensions of solvable potentials à la Abraham-Moses ⋮ New supersymmetric partners for the associated Lamé potentials ⋮ Exactly solvable potentials with finitely many discrete eigenvalues of arbitrary choice ⋮ Polynomial supersymmetry for matrix Hamiltonians

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