I am reading about the recovery of some classical rules from quantum mechanics. My text (Shankar) considers a Hamiltonian operator in a one-dimensional space H = P^2 / 2m + V(X) where P and X are the momentum and position operators respectively. It then asserts that [X,H] = [X,P^2/2m] That is, it has discarded the potential term of the Hamiltonian without comment or explanation. How is that justified? I would have thought that if, as indicated, V is a function of X, the hamiltonian operator should be expressed in terms of that function. For example, if V is a gravitational potential V(X) = -k/X, I would expect the above commutator to be [X,H] = [X,P^2/2m-k/X] = [X,P] - k[X,1/X] Why does Shankar discard the second term? If one didn't discard it, what would [X,1/X] mean? Is there any way to handle the reciprocal of an operator? Thanks for any help.