Quantum phase: A different approach

It is generally thought that, in the same way that position and momentum are canonical variables in quantum mechanics, the number operator should have a canonical operator, i.e., there should be a possibility of defining a well-defined phase operator associated with it. From the point of view of the phase space, it becomes clearer as position and momentum uncertainties are well reflected. Indeed, the same occurs in the phase space for phase and intensity. In this contribution, we do a small survey on the possibilities of defining a phase operator via discrete Fourier operators and introduce some possible applications.