We prove an optimal semiclassical bound on the trace norm of the following commutators [1_(-∞,](H_ħ) , x] , [1_(-∞,](H_ħ) , - iħ∇] and [1_(-∞,](H_ħ) , e^i⟨t,x⟩] , where H_ħ is a Schrödinger operator with a semiclassical parameter ħ, x is the position operator, -iħ∇ is the momentum operator, and t in R^d is a parameter. These bounds are in the non-interacting setting the ones introduced as an assumption by N. Benedikter, M. Porta and B. Schlein in a study of the mean-field evolution of a fermionic system.