Generalized phase-space distributions associated with a pseudo-oscillator

Abstract

The problem of mapping the operator functions of $$\hat b$$ and $$\hat b^\dag $$ , which are the annihilation and creation operators associated with a pseudo-oscillator, onto thec-number functions is studied from a unified point of view. The approach is similar to the one recently developed by Agarwal and Wolf for the case of the ordinary oscillator. The results are illustrated by means of a number of examples. The phase-space distributions corresponding to Weyl’s, normal and antinormal orderings are studied in detail and the explicit representations for them in terms of coherentstate matrix elements are given. The connection with the so-called semiclassical description is also established.