Time-Dependent Quantum Perturbations Uniform in the Semiclassical Regime

We present a time-dependent quantum perturbation result, uniform in the Planck constant for a potential whose gradient is bounded almost everywhere. We show also that the classical limit of the perturbed quantum dynamics remains in a tubular neighbourhood of the classical unperturbed one, the size of this neighbourhood being of the order of the square root of the size of the perturbation. We treat both Schrodinger and von Neumann-Heisenberg equations.

Automated summary

We propose a time-dependent quantum perturbation result that is applicable to a potential with bounded gradient almost everywhere, with the perturbation being independent of the Planck constant. We demonstrate that the perturbed quantum dynamics in the classical limit remains in a tubular neighborhood of the unperturbed classical dynamics, with the size of the neighborhood proportional to the square root of the perturbation. We consider both the Schrodinger and von Neumann-Heisenberg equations.