A symplectic approach to Schr\'odinger equations in the infinite-dimensional unbounded setting
- Resource Type
- Working Paper
- Authors
- de Lucas, Javier; Lange, Julia; Rivas, Xavier
- Source
- Subject
- Mathematical Physics
Mathematics - Differential Geometry
Quantum Physics
34A26, 34A34 (primary) 17B66, 53Z05 (secondary)
- Language
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.
Comment: 27 pages