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

Abstract

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.