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

作者：Lv Cui Hong; Fan Hong Yi^*

来源：Chinese Physics Letters, 2010, 27(5): 050301.

DOI：10.1088/0256-307X/27/5/050301

Based on the two mutually conjugate entangled state representations vertical bar xi > and vertical bar eta >, we propose an integration transformation in xi - eta phase space integral integral d(2)xi d(2)eta/pi(2)e((xi-mu)(eta*-nu*)-(eta-nu)(xi*-mu*)) F(xi, eta) equivalent to D(mu, nu), 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 (Q(1) - Q(2)) <-> (P(1) - P(2)) ordered and simultaneously (P(1) P(2)) <-> (Q(1) Q(2)) ordered operators.

• 出版日期2010-5
• 单位上海交通大学