  In this letter, firstly, the Schr$\ddot{o}$dinger equation on noncommutative
phase space is given by using a generalized Bopp's shift. Then the anomaly term
of commutator of arbitrary physical observable operators on noncommutative
phase space is obtained. Finally, the basic uncertainty relations for
space-space and space-momentum as well as momentum-momentum operators in
noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary
physical observable operators in NCQM are discussed.
