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By using the pseudo-metric introduced in Golse and Paul (Arch Ration Mech Anal 223:57–94, 2017), which is an analogue of the Wasserstein distance of exponent 2 between a quantum density operator and a classical (phase-space) density, we prove that the convergence of time splitting algorithms for the von Neumann equation of quantum dynamics is uniform in the Planck constant $$\hbar $$ ħ . We obtain explicit uniform in $$\hbar $$ ħ error estimates for the first-order Lie–Trotter, and the second-order Strang splitting methods.

On the Convergence of Time Splitting Methods for Quantum Dynamics in the Semiclassical Regime