Differential Completeness Relation in Two-Mode Mass-Weighted |ξ〉- |τ〉Representations
FAN Hong-yi1,2, LIU Nai-le2
1Department of Applied Physics, Shanghai Jiao Tong University, Shanghai 200030
2Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026
Differential Completeness Relation in Two-Mode Mass-Weighted |ξ〉- |τ〉Representations
FAN Hong-yi1,2;LIU Nai-le2
1Department of Applied Physics, Shanghai Jiao Tong University, Shanghai 200030
2Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026
Abstract： 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.
1999, Vol. 16 
