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
Link to the original source: https://www.aimspress.com/article/doi/10.3934/math.20241359
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/
Article's DOI: 10.3934/math.20241359
Entity: Universitat Rovira i Virgili
Journal publication year: 2024
Publication Type: Journal Publications
Repositori URV