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Modern Physics Letters B

Two-Mode Wigner Operator in <η| Representation

Wu He-jun, Hong-Yi Fan

Published Jun 10, 1997• 20 citations
Publisher

Abstract

We derive the <η| representation of two-mode Wigner operator, where the <η| state is the common eigenstate of two particles' relative position and total momentum. By virtue of this representation we can conveniently obtain Wigner functions of some two-mode states and the Weyl correspondence functions of two-mode unitary phase operators.

DOI
10.1142/s0217984997000670

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We derive the <η| representation of two-mode Wigner operator, where the <η| state is the common eigenstate of two particles' relative position and total momentum. By virtue of this representation we can conveniently obtain Wigner functions of some two-mode states and the Weyl correspondence functions of two-mode unitary phase operators.
We point out that there is a close connection between the Weyl correspondence and coherent state correspondence. By virtue of differential and integral method within normal ordered products we demonstrate that the essence of the Weyl correspondence is just coherent state correspondence in both boson and fermion cases. Furthermore, coherent state form and explicit operator form for the Wigner function are given. With these forms we can derive some important operator formulas from the Weyl correspondence. The Wigner function's zero-point value is also discussed.