Consider two Hermitian operator A, B; Define [A,B]=iC, then operator C is also Hermitian. we calculate the expectation value with respect to |a>, one eigenstate of A with the eigenvalue a. From the left side, we have: <a|[A,B]|a>=<a|(AB-BA)|a>=(a-a)<a|B|a>=0, while on the right side, <a|iC|a> does not necessarily vanish. That is :<a|[A,B]|a> ≠ <a|iC|a>, which is absurd !!!!!! So what is wrong in my calculation?