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Physics Letters A

Position-momentum and number-phase Wigner functions and their respective displacement operators

Joan A. Vaccaro, Amitabh Joshi

Published Jun 1, 1998• 3 citations
Publisher
DOI
10.1016/s0375-9601(98)00187-x

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Progress of Theoretical Physics•Jun 1, 2006•2 citations
Abstract We present a method for calculating expectation values of operators in terms of a corresponding c-function formalism which is not the Wigner–Weyl position-momentum phase-space, but another space. Here, the quantity representing the quantum system is the expectation value of the displacement operator, parametrized by the position and momentum displacements, and expectation values are evaluated as classical integrals over these parameters. The displacement operator is found to offer a complete orthogonal basis for operators, and some of its other properties are investigated. Connection to the Wigner distribution and Weyl procedure are discussed and examples are given.
It is shown that the number-phase (or rotational) Wigner function is obtained from the Weyl symmetrization rule for the correspondence between classical functions and quantum operators. In spite of the complicated form of the commutator for the number and phase operators, the Weyl symmetrization rule is similar to that in the case of the position and momentum operators. In addition, it is found that the ordering of the number and phase operators also has the same structure as that for the position-momentum pair.