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arXiv · 2312.09192

A symplectic approach to Schr\"odinger equations in the infinite-dimensional unbounded setting

Javier de Lucas·Julia Lange·Xavier Rivas
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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 Schr\"odinger 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 Schr\"odinger equations onto their projective spaces. Other applications of physical and mathematical relevance are also analysed.

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BibTeXRIS

Javier de Lucas, Julia Lange, Xavier Rivas. 2023-12-14. A symplectic approach to Schr\"odinger equations in the infinite-dimensional unbounded setting. https://doi.org/10.3934/math.20241359

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