| 1. | In this scheme , the unitary of time evolution operators makes sure that the wavefunction is normalized in time - space propagation
在这种方案中，时间演化算符的幺正性保证了波函数在传播过程中的规范性。 |
| 2. | With the time - evolution operator obtained by means of su ( 2 ) spin coherent states we are able to derive analytic time - evolution of spin probability - current between the two quantum dots for various initial states
我们利用su ( 2 )自旋相干态获得包括库仑相互作用hubbard模型的时间演化算符，得到解析的含时自旋流。 |
| 3. | The energy eigenvalue , eigenfunction , matrix elements of coordinate and momentum operators in energy representation , and evolution operator for a two - dimentional coupled oscillator are presented by using the general linear quantum transformation theory
摘要运用广义线性量子变换理论，给出一类二维耦合量子谐振子的能量本征值、本征函数、坐标和动量算符在能量表象中的矩阵元及演化算符。 |
| 4. | Using lewis - riesenfeld theory , we obtain exact solutions of the time - dependent system , then we recover both n - pulse method based on time - evolution operator of the system and stirap method in terms of instantaneous eigenstates with the help of time - dependent gauge transformation
利用含时规范变换理论得到系统的精确解，我们用时间演化算符同时得到文献中分别采用-位相法和stirap (受激拉曼散射)方法得到的结果，因而更具有普遍性。 |
| 5. | We examin e the generation of bell state in bose - einstein condensates of two interacting species trapped in a double - well configuration analytically and the density of probability for finding the entangled bell state is given . we find that the oscillation amplitude of the probability of density for finding the entangled bell state becomes greater as the ratio of the interspecies interaction strength and the tunneling rate increases , moreover the self - interaction strength of the component a ( b ) has no effect on it . also we use the time - dependent su ( 2 ) gauge transformation to diagonalize the hamilton operator , obtain the berry phase and analytically the time - evolution operator
此外我们还研究了在双阱玻色-爱因斯坦凝聚中纠缠态的演化，研究发现随着组分间相互作用和随穿率的比值的增加系统演化到bell态的概率变大，而且组分自身内在的相互作用对形成bell态的几率没有影响；并且用含时su ( 2 )规范变换对角化哈密顿量得到了系统的berry位相和时间演化算符，并研究了量子随穿过程。 |
| 6. | 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 ) . our results agree well with those derived in [ 3 ] , but the present method is more simple and definite
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。作为一个典型例子，我们得到含时受迫谐振子的演化算符和波函数的精确表达式。 |
| 7. | 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 . we also discuss the squeezing property of the system
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。 |
| 8. | With the hamilto - nian of the interaction between the field and the atom with an intensity - dependent coupling , the evolution operator and the reduced density operators of the field and the atom are derived without taking the influence of the environment into account , then the basic work model without dissipation is established
从光场与原子依赖强度耦合相互作用的哈密顿量，推出了无环境影响的依赖强度耦合j - c模型中系统的一般时间演化算符和光场与原子的约化密度算符，建立了研究不考虑环境影响的j - c模型的一般动力学的基础。 |
| 9. | With time - evolution - operator , it is proved that the population of upper level is in circumstance of cyclic oscillation by laser pulses pair of gaussian line - shape in a homogeneous broadening two - level system . the oscillatory time oxide is the delay time between the laser pulse pairs and the oscillatory frequency equals the one of transition between the lower and upper level
引入时间演化算符，证明均匀增宽二能级体系在飞秒激光脉冲对作用下上能级激发态布居是周期性变化的，它以飞秒脉冲对之间的延时为时间轴，以该原子能级之间的跃迁频率为振荡频率 |
| 10. | Finally , by means of time evolution operator and numerical calculations , the time evolution of the atomic population , the atomic dipole squeezing , the time evolution of the squeezing and coherence properties of the light in the system of the two identical two - level entangled atoms interacting with the coherent optical field have been studied
论文的第三部分工作是采用时间演化算符和数值计算方法，研究了两全同二能级纠缠原子与相干态光场相互作用过程中，原子布居、原子偶极压缩、光场的二阶相干和光场压缩性质的时间演化特性。 |
