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Russian Physics Journal

Calculation of mean values for physical quantities in the Wigner quantum distribution

V. N. Gorshenkov, V. L. Kon'kov

Published Jul 1, 1973• 0 citations
Publisher
DOI
10.1007/bf00891527

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It is possible to calculate expectation values and transition probabilities from the Wigner phase-space distribution function. Based on the canonical transformation properties of the Wigner function, an algorithm is developed for calculating these quantities in quantum optics for coherent and squeezed states. It is shown that the expectation value of a dynamical variable can be written in terms of its vacuum expectation value of the canonically transformed variable. Parallel-axis theorems are established for the photon number and its variant. It is also shown that the transition probability between two squeezed states can be reduced to that of the transition from one squeezed state to vacuum.
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.