On the Definition of the Phase Operator of Harmonic Oscillator and Some Related Paradoxes

Owing to negligence of the non-hermiticity of the phase operator, the early definitions resulted in some contradictions. In this paper, three paradoxes are discussed showing that the problem could be solved by taking into consideration the fact that the phase operator φ is non-hermitian.X-V.And it is proved that φ is non-hermitian indeed.