For any even order p, the p-th order Trotter-Suzuki splitting approximates semiclassical Schrödinger observables with error O(Δt^p) uniformly in the semiclassical parameter h, proven by algebraic commutator estimates.
For completeness, we begin by introducing the underlying Lie algebra in a spatially continuous setting and reviewing its key properties
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Uniform semiclassical observable error bound of Trotter-Suzuki splitting: a simple algebraic proof
For any even order p, the p-th order Trotter-Suzuki splitting approximates semiclassical Schrödinger observables with error O(Δt^p) uniformly in the semiclassical parameter h, proven by algebraic commutator estimates.