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

2023/12/14 by de Lucas, Javier, Lange, Julia, Rivas, Xavier · 1 citation
#34A26 #34A34 (primary) 17B66 #53Z05 (secondary) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2312.09192

Abstract

By using the theory of analytic vectors and manifolds modelled on normed spaces, we provide a rigorous symplectic differential geometric approach to t-dependent Schrödinger equations on separable (possibly infinite-dimensional) Hilbert spaces determined by unbounded t-dependent self-adjoint Hamiltonians satisfying a technical condition. As an application, the Marsden--Weinstein reduction procedure is employed to map above-mentioned t-dependent Schrödinger equations onto their projective spaces. Other applications of physical and mathematical relevance are also analysed.

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• Mixed superposition rules for Lie systems and compatible geometric structures

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