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

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.

27 pages

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Cited by in corpus (1)

• Mixed superposition rules for Lie systems, compatible geometric structures, and applications