The Number-Phase and Position-Momentum Distribution Functions

We present the relationship between the number-phase and position-momentum quantum distribution functions using the extended Liouville space. We also propose an extended Ban’s number-phase distribution function in the extended space, and show that the other distribution functions can be expressed in terms of Ban’s function. Moreover, two new number-phase distribution functions, the Born-Jordan and the Cohen distribution functions, are given in a unified manner. Subject Index: 060