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

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.