Abstract As a natural and important extension of Fan's paper (Fan Hong-Yi 2010 Chin. Phys. B 19 040305) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation this paper finds a new two-fold complex integration transformation about the Wigner operator (in its entangled form) in phase space quantum mechanics, and its inverse transformation. In this way, some operator ordering problems regarding to and can be solved and the contents of phase space quantum mechanics can be enriched, where , are bosonic creation and annihilation operators, respectively.
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174) as well as the President Foundation of Chinese Academy of Sciences.
Cite this article:
Fan Hong-Yi (范洪义), Yuan Hong-Chun (袁洪春) New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case 2010 Chin. Phys. B 19 070301
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