Weyl ordering, normally ordering of Husimi operator as the squeezed coherent state projector and its applications

By introducing a new kind of squeezed coherent states |p,q〉κ we propose so-called Husimi operator Δh(q,p,κ) corresponding to the Husimi distribution functions in phase space. Remarkably, we show Δh(q,p,κ)=|p,q〉k〈p,q|k, i.e. the Husimi operator actually is a squeezed coherent state projector. The Weyl ordered form and the normally ordered form of Δh(q,p,κ) are derived that provides us with an operator version to examine various properties of the Husimi distribution, which is concise and neat. In so doing, a new operator-representation theory which underlies the Husimi distribution is established. Throughout the Letter we have fully employed the technique of integration within an ordered product of operators.