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A New Kind of Integration Transformation in Phase Space Related to Two Mutually Conjugate Entangled-State Representations and Its Uses in Weyl Ordering of Operators |
| LV Cui-Hong1, FAN Hong-Yi1,2 |
| 1Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026 2Department of Physics, Shanghai Jiao Tong University, Shanghai 200030
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| Cite this article: |
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LV Cui-Hong, FAN Hong-Yi 2010 Chin. Phys. Lett. 27 050301 |
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Abstract Based on the two mutually conjugate entangled state representations |ξ> and |η>, we propose an integration transformation in ξ-η phase space , and its inverse transformation, which possesses some well-behaved transformation properties, such as being invertible and the Parseval theorem. This integral transformation is a convolution, where one of the factors is fixed as a special normalized exponential function. We generalize this transformation to a quantum mechanical case and apply it to studying the Weyl ordering of bipartite operators, regarding to (Q1-Q2)↔(P1-P2) ordered and simultaneously (P1+P2)↔(Q1+Q2) ordered operators.
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| Keywords:
03.65.-w
02.90.+p
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Received: 26 November 2009
Published: 23 April 2010
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| PACS: |
03.65.-w
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(Quantum mechanics)
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02.90.+p
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(Other topics in mathematical methods in physics)
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