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A symplectic approach to Schrodinger equations in the infinite-dimensional unbounded setting

  • Identification data

    Identifier: imarina:9387495
    Handle: https://hdl.handle.net/20.500.11797/imarina9387495
    Authors:
    de Lucas, JavierLange, JuliaRivas, Xavier
    Abstract:
    By using the theory of analytic vectors and manifolds modeled on normed spaces, we provide a rigorous symplectic differential geometric approach to t-dependent Schrodinger equations on separable (possibly infinite-dimensional) Hilbert spaces determined by families of unbounded selfadjoint Hamiltonians admitting a common domain of analytic vectors. This allows one to cope with the lack of smoothness of structures appearing in quantum mechanical problems while using differential geometric techniques. Our techniques also allow for the analysis of problems related to unbounded operators that are not self-adjoint. As an application, the Marsden-Weinstein reduction procedure was employed to map the above-mentioned t-dependent Schrodinger equations onto their projective spaces. We also analyzed other physically and mathematically relevant applications, demonstrating the usefulness of our techniques.

  • Others:

    Author, as appears in the article.: de Lucas, Javier; Lange, Julia; Rivas, Xavier
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: Rivas Guijarro, Xavier
    Keywords: Analytic vector Geometrization Hamiltonian system Infinite-dimensional symplectic manifold Integrabilit Marsden-weinstein reduction Mathematical exposition Normed space Projective schro<spacing diaeresis>dinger equation Quantum-mechanics Representations Unbounded operato
    Abstract: By using the theory of analytic vectors and manifolds modeled on normed spaces, we provide a rigorous symplectic differential geometric approach to t-dependent Schrodinger equations on separable (possibly infinite-dimensional) Hilbert spaces determined by families of unbounded selfadjoint Hamiltonians admitting a common domain of analytic vectors. This allows one to cope with the lack of smoothness of structures appearing in quantum mechanical problems while using differential geometric techniques. Our techniques also allow for the analysis of problems related to unbounded operators that are not self-adjoint. As an application, the Marsden-Weinstein reduction procedure was employed to map the above-mentioned t-dependent Schrodinger equations onto their projective spaces. We also analyzed other physically and mathematically relevant applications, demonstrating the usefulness of our techniques.
    Thematic Areas: General mathematics Mathematics Mathematics (all) Mathematics (miscellaneous) Mathematics, applied
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: xavier.rivas@urv.cat
    Record's date: 2024-10-26
    Papper version: info:eu-repo/semantics/publishedVersion
    Papper original source: Aims Mathematics. 9 (10): 27998-28043
    APA: de Lucas, Javier; Lange, Julia; Rivas, Xavier (2024). A symplectic approach to Schrodinger equations in the infinite-dimensional unbounded setting. Aims Mathematics, 9(10), 27998-28043. DOI: 10.3934/math.20241359/math.20241359
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2024
    Publication Type: Journal Publications

  • Keywords:

    Mathematics,Mathematics (Miscellaneous),Mathematics, Applied
    Analytic vector
    Geometrization
    Hamiltonian system
    Infinite-dimensional symplectic manifold
    Integrabilit
    Marsden-weinstein reduction
    Mathematical exposition
    Normed space
    Projective schrodinger equation
    Quantum-mechanics
    Representations
    Unbounded operato
    General mathematics
    Mathematics
    Mathematics (all)
    Mathematics (miscellaneous)
    Mathematics, applied

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