Differential completeness relation in two-mode mass-weighted vertical bar xi >-vertical bar tau > representations

The explicit form of the common eigenstates \tau] of the mass-weighted rela tive coordinate m(2)Q(1) - m(1)Q(2) and the mass-combinatorial momentum m(1 )P(1) + m(2)P(2) Of two particles is given. On the basis of \t] and their c onjugate states \x] we find that there exist new differential completeness relations (DCR). The applications of the new DCR in deriving the normally o rdered two-mode squeezing operators for the mass-related coordinates and mo menta are demonstrated. Throughout the discussion the technique of differen tiation within an ordered product of operators is fully employed.