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 Δ (μ, ν) (in its entangled form) in phase space quantum mechanics, and its inverse transformation. In this way, some operator ordering problems regarding to (a†1 – a2) and (a†1 – a2) can be solved and the contents of phase space quantum mechanics can be enriched, where ai, a†i are bosonic creation and annihilation operators, respectively.
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