Spectral/quadrature duality: Picard-Vessiot theory and finite-gap potentials

zbMath1248.81032arXiv1011.1642MaRDI QIDQ2895563

Yurii V. Brezhnev

Publication date: 3 July 2012

Full work available at URL: https://arxiv.org/abs/1011.1642

zbMATH Keywords

Schrödinger equationquadraturesfinite-gap potentialstheta-functionsPicard-Vessiot theoryAbelian integralsLiouvillian extensions

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Exactly and quasi-solvable systems arising in quantum theory (81U15) Subvarieties of abelian varieties (14K12) Differential algebra (12H05)

Related Items (9)

Nonlinear supersymmetry in the quantum Calogero model ⋮ Differential Galois theory and Darboux transformations for integrable systems ⋮ Factorization of KdV Schrödinger operators using differential subresultants ⋮ Integrability of the one dimensional Schrödinger equation ⋮ Picard-Vessiot theory and integrability ⋮ An exactly solvable problem of wave fronts and applications to the asymptotic theory ⋮ Rational KdV potentials and differential Galois theory ⋮ Elliptic solitons, Fuchsian equations, and algorithms ⋮ Spectral Picard-Vessiot fields for algebro-geometric Schrödinger operators

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