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 $\Delta(\mu, \nu)$ (in its entangled form) in phase space quantum mechanics, and its inverse transformation. In this way, some operator ordering problems regarding to $(a^\dagger_1-a_2)$and $(a_1+a^\dagger_2)$ can be solved and the contents of phase space quantum mechanics can be enriched, where $a_i$, $a_i^\dagger$ 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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