bogoliubov transformation

Using the formulized approach to the SU(1,1) h(4) time-dependent system, which is derived from the combination of the formulation of the time-dependent Bogoliubov transformation and the evolution equation of the system, we obtain the time evolution operator , state function and Heisenberg uncertainty relation of the parametric oscillator with cavity losses under the weak coupling approximation.

本文利用含时波戈留波夫变换与时间演化方程相结合得到的求解SU(1，1)⊕h(4)量子系统的时间演化算符和演化态的普遍公式，我们导出了带腔损耗的参数振子在弱耦合近似下的演化算符，态函数和不确定乘积，并讨论了系统的压缩特性。

In this paper, the exact expressions of the evolution operator and wave function for a driven time-dependent quantum oscillator are obtained by means of the combination of the inhomogeneous Bogoliubov transformation (IBT) and the evolution equation associated with a su(1, 1) h(4).

非齐次波戈留波夫变换与su(1，1)⊕h(4)量子系统的演化方程相结合，给出了求该系统时间演化算符和波函数的精确表达式。