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So I have learned that this holds for the trace if A and B are two operators: [itex]\text{Tr}(AB)=\text{Tr}(BA)[/itex]. Now I take the trace of the commutator between [itex]x[/itex] and [itex]p[/itex]: [itex]\text{Tr}(xp)-\text{Tr}(px)=\text{Tr}(xp)-\text{Tr}(xp)=0[/itex]. But the commutator of x and p is [itex]i\hbar[/itex]. Certainly the trace of [itex]i\hbar[/itex] is not zero. What is wrong here?