Differential Completeness Relation in Two-Mode Mass-Weighted |ξ〉- |τ〉Representations

The explicit form of the common eigenstates |τ〉of the mass-weighted relative coordinate μ₂Q₁–μ₁Q₂ and the mass-combinatorid momentum μ₁P₁+μ₂P₂ of two particles is given. On the basis of |τ〉and their conjugate states |ξ〉, we find that there exist new differential completeness relations (DCR). The applications of the new DCR in deriving the normally ordered two-mode squeezing operators for the mass-related coordinates and momenta are demonstrated. Throughout the discussion the technique of differentiation within an ordered product of operators is fully employed.