# Hamiltonian in commutator contradiction [duplicate]

Consider the following: $$[ \hat H, \hat x]=\left[-\frac{\hbar^2 \hat p^2}{2m}+V,\hat x\right]\ne0 \text{ in general}$$ But $$[ \hat H, \hat x]=\left[i\hbar \frac{\partial }{\partial t},\hat x\right]=0$$ Why are these not in contradiction?

## marked as duplicate by Quantum spaghettification, Qmechanic♦Nov 20 '15 at 20:11

• @Joseph In addition to ACuriousMind's link you might find this helpful too, in particular Qmechanic's answer as to why $\hat H\neq i\hbar \partial _t$. physics.stackexchange.com/a/17479 – AngusTheMan Nov 20 '15 at 18:22