The Essence of Operators' Weyl Ordering Scheme and New Operator Identities for Converting Q− P Ordering to Weyl Ordering.

We find new operator formulas for converting Q− P and P− Q ordering to Weyl ordering, where Q and P are the coordinate and momentum operator. In this way we reveal the essence of operators' Weyl ordering scheme, e.g., Weyl ordered operator polynomial ${_{:}^{:}}\;Q^{m}P^{n}\;{_{:}^{:}}$, where ${}_{:}^{:}$ ${}_{:}^{:}$ denotes the Weyl ordering symbol, and H is the two-variable Hermite polynomial. This helps us to know the Weyl ordering more intuitively. [ABSTRACT FROM AUTHOR]