New Operator Ordering Formulas Related to Hermite Polynomials Derived by Virtue of IWOP Technique

摘要

By virtue of the technique of integration within an ordered product of operators and the fundamental operator identity H_n(X) = 2~n : X~n :, where X is the coordinate operator and H_n is the n-order Hermite polynomials, : : is the normal ordering symbol, we not only simplify the derivation of the main properties of Hermite polynomials, but also directly derive some new operator identities regarding to H_n(X). Operation for transforming f(X) → : f(X) : is also discussed.