Deriving new operator identities by alternately using normally, antinormally, and Weyl ordered integration technique

Dirac’s ket-bra formalism is the language of quantum mechanics. We have reviewed how to apply Newton-Leibniz integration rules to Dirac’s ket-bra projectors in previous work. In this work, by alternately using the technique of integration within normal, antinormal, and Weyl ordering of operators we not only derive some new operator ordering identities, but also deduce some new integration formulas regarding Laguerre and Hermite polynomials. This may open a new route of directly deriving some complicated mathematical integration formulas by virtue of the quantum mechanical operator ordering technique, without really performing the integrations in the ordinary way.