Systematic Derivation of the Number-Phase Distribution Functions

We propose a unified method for obtaining the number-phase distribution functions in the extended Fock space and apply it to various distribution functions. A physical number-phase distribution function is easily obtained; it is the expectation value of an extended Wigner operator in a physical state. This method corresponds to Cohen’s method for the positionmomentum Wigner functions. The properties of the number-phase distribution functions and their relations are presented in a unified manner. Also, through the distribution functions, the correspondence between classical functions and quantum operators is obtained explicitly.