On the virial theorem in quantum mechanics

We review the various assumptions under which abstract versions of the quan tum mechanical virial theorem have been proved, We point out a relationship between the virial theorem for a pair of operators HI A and the regularity properties of the map R There Exists s --> e(isA) (z - H)(-1)e(isA). We gi ve an example showing that the statement of the virial theorem in [CFKS] is incorrect.