The s-ordered expansions of the operator function about the combined quadrature µX + νP

Abstract

A general framework applicable to deriving the s-ordered operator expansions is presented in this paper. We firstly deduce the s-ordered operator expansion formula of density operator ρ a † , a and introduce the technique of integration within the sordered product of operators (IWSOP). Based on the deduction and the technique, we derive the s-ordered expansions of operators (μX + νP) n and H n (μX + νP) (linear combinations of the coordinate operator X and the momentum operator P, H n (x) is Hermite polynomial), respectively, and discuss some special cases of s = 1, 0, −1. Some new useful operator identities are obtained as well.s-ordered operator expansion formula, combined quadrature μX + νP, Hermite polynomial, IWSOP technique 03.65.Ta, 42.50.Ar

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