New fundamental quantum mechanical operator-ordering identities for the coordinate and momentum operators

In quantum mechanics theory one of the basic operator orderings is Q-P and P-Q ordering,where Q and P are the coordinate operator and the momentum operator,respectively.We derive some new fundamental operator identities about their mutual reordering.The technique of integration within Q-P ordering and P-Q ordering is introduced.The Q-P ordered and P-Q ordered formulas of the Wigner operator are also deduced which makes arranging the operators in either Q-P or P-Q ordering much more convenient.