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In this note we study the properties of a sequence of approximate propagatorsfor the Schr\"odinger equation, in the spirit of Feynman's path integrals.Precisely, we consider Hamiltonian operators arising as the Weyl quantizationof a quadratic form in phase space, plus a bounded potential perturbation inthe form of a pseudodifferential operator with a rough symbol. It is known thatthe corresponding Schr\"odinger propagator is a generalized metaplecticoperator. This naturally motivates the introduction of a manageable timeslicing approximation consisting of operators of the same type. By means oftechniques and function spaces of time-frequency analysis it is possible toobtain several convergence results with precise rates in terms of the mesh sizeof the time slicing subdivision. In particular, we prove convergence in thenorm operator topology in $L^2$, as well as pointwise convergence of thecorresponding integral kernels for non-exceptional times.

On the convergence of a novel family of time slicing approximation operators for Feynman path integrals