The effects of time/frequency squeezing-frequency/time expanding in quantum systems and their nonciassical properties

In this paper, the complete quantum theory is used to study the effects of both time squeezing-frequency expanding and frequency squeezing-time expanding in the quantum systems of both continuous energy spectrum and discrete energy spectrum in detail. Based on the reference 17 in which the time operator t∧ is constructed, it is given the definition of frequency operator ω∧. According to the commutative relation for time operator t∧ and frequency operator ω∧, the Cauchy - Schwartz inequality is used to deduce the uncertainty relation satisfied by both time operator t∧ and frequency operator ω∧, and then the definitions of both time squeezing and frequency squeezing are given, the minimumuncertainty state, the squeezed minimum uncertainty state and the squeezed state of time/frequency are therefore discussed in detail. So the nonclassical properties of both time squeezing-frequency expanding and frequency squeezing-time expanding are revealed. Finally, based upon defining the time quantum-like creation operator τ∧⁺(t), the time quantum-like destruction operator τ∧(t) and the time quantum-like number operator N∧ _τ(t), the formulated theory of the time quantization originated by Yang Zhiyong and Hou Xun is established, and the basic point of view on the time quantization is further presented.