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

Identifier:  imarina:9387495

Handle: https://hdl.handle.net/20.500.11797/imarina9387495

Authors:  de Lucas, Javier; Lange, Julia; Rivas, Xavier

Abstract:
By using the theory of analytic vectors and manifolds modeled on normed spaces, we provide a rigorous symplectic differential geometric approach to t-dependent Schrodinger equations on separable (possibly infinite-dimensional) Hilbert spaces determined by families of unbounded selfadjoint Hamiltonians admitting a common domain of analytic vectors. This allows one to cope with the lack of smoothness of structures appearing in quantum mechanical problems while using differential geometric techniques. Our techniques also allow for the analysis of problems related to unbounded operators that are not self-adjoint. As an application, the Marsden-Weinstein reduction procedure was employed to map the above-mentioned t-dependent Schrodinger equations onto their projective spaces. We also analyzed other physically and mathematically relevant applications, demonstrating the usefulness of our techniques.