In this note we study the properties of a sequence of approximate propagators for the
Schrödinger equation, in the spirit of Feynman's path integrals. Precisely, we consider
Hamiltonian operators arising as the Weyl quantization of a quadratic form in phase space,
plus a bounded potential perturbation in the form of a pseudodifferential operator with a
rough symbol. The corresponding Schrödinger propagator belongs to the class of
generalized metaplectic operators, a fact that naturally motivates the introduction of a …

What about rates of convergence for En (t)→ U (t) in Ls (L2 (Rd))? What about convergence
in operator norm? The lack of information in this connection is a well-known limitation of the
unitary Trotter formula–it is a qualitative strong convergence result that can be hardly refined
or extended to other topologies.