The quasiprobability operator of positions and momenta in quantum mechanics

On the basis of the linearity constraints on the rule for constructing quantum operators we introduce the quasiprobability operator of positions and momenta (if positive definite, the probability operator). The quantum operators for any physical quantity can be constructed by means of the quasiprobability operator. We derive the general form of the probability operator in terms of a set of several functions. © 1978 Plenum Publishing Corporation.