By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even-and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even-and odd-Hermite polynomials.

By introducing the Hermite-polynomial-operator Hn(X), where X is the coordinate operator (or the quadrature operator in quantum optics theory), and combining the technique of integration within an ordered product of operators, we derive some new operator identities about quantum squeezing, which are useful for studying the squeezed number state.

We derive some new generating function formulae of the two-variable Hermite polynomials, such asn!m! H 2n+l,2m+k (x, y). We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.

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