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Differential Completeness Relation in Two-Mode Mass-Weighted |ξ〉- |τ〉Representations
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| 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
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| Cite this article: |
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FAN Hong-yi, LIU Nai-le 1999 Chin. Phys. Lett. 16 625-627 |
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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.
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| Keywords:
03.65.-w
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Published: 01 September 1999
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