查询词典 eigenstate

The quantum amplitude amplification is the generalization of quantum Grover search algorithm. In this strategy, the Grover iteration has been replaced by two different quantum amplitude amplification operations. This makes it possible to collapse the system with probability 1, in other words, with certainty. The measurement operation in this scheme is only used to cancel the phase factor. Finally, one can use the admissible control to drive the system from the eigenstate to the target state and the control task is accomplished.

量子幅值放大是Grover迭代思想的一般化，该控制方案中采用两种不同的量子幅值放大操作替换了Grover迭代，使得期望本征态的概率幅的模在经过一定次数的迭代之后精确的等于1，然后借助于测量来消除相位因子，使系统的波函数确定性的塌缩到期望的本征态，最后再借助幺正演化，将系统从本征态控制到目标态，实现期望的控制任务。

In this scheme, the description of unitary evolution and quantum measurement is unified and the quantum control operation is represented by probability state transition. The algorithm works as follows. At first a measurement is applied on the system. If the state after collapse is not the desired eigenstate, then system evolution will go on. After a period of time, the system is measured again. The process will go on like this until we get the desired eigenstate by measurement. Finally the system is driven to the target state with admissible control as before.

4把本征态能控性概念进一步向前发展，提出了概率能控性的概念，将幺正演化和量子测量这两种量子控制手段统一的用概率状态转移来描述，并针对一类特殊的本征态能控的系统，提出了幺正演化和测量交替进行的量子反馈控制策略：如果单步测量所得到的本征态不是期望的本征态，则让系统以这一本征态作为新的初态进行下一步的幺正演化，然后在适当的时候再次测量，让系统塌缩到某一本征态，如此重复进行，直到达到期望的目标态为止。

First, one. analyzes the eigenstates-from reachable sets and seeks the one which the target state belongs to. Then using the Grover iteration to amplify the probability amplitude of the desired eigenstate (the modul square of which is the probability of the corresponding eigenstate that the system will collapse to when it is measured). By measuring, the system will then collapse to the desired eigenstate with a probability of almost unity. Finally, one can use the admissible control to drive the system from the eigenstate to the target state.

该策略的核心思想是对本征态能控的系统，通过分析控制目标态与本征态的关系，寻找给定目标态所属的本征态可达集，然后利用量子非结构化搜索的Grover算法，将任意给定的系统初始态经过一定次数的Grover迭代，放大该本征态所对应的概率幅(概率幅的模方对应测量时波函数塌缩到对应本征态的概率)，然后对迭代后的态进行一次测量操作，使系统以接近1的概率塌缩到所需的本征态(前面分析得到的本征态可达集所对应的本征态)，最后用容许的控制将系统从该本征态控制到期望的目标态。

It can be shown that the wavelength is equal to h/p, where h is Planck's constant and p is the momentum of the eigenstate.

波长可以表示为h/p，这里h 是普朗克常数而p是特征态动量。

An eigenstate of momentum, on the other hand, has the form of a plane wave.

在其它方面一个动量特征态具有一平面波形。

We compare the results with the analytic results from the weak coupling limit and the strong coupling limit. As an extension, when think about the dispersion relations for SU(2) trapped bosons, we find that we can not get the inverse effective mass directly from the dispersion relations of the holon-isospin excitation for the wave function from Bethe equation is not the eigenstate wave function of the total momentum.

作为推广，我们还研究了无限深势阱中SU(2)玻色子的各类激发态的色散关系，发现由于直接的Bethe Ansatz 波函数不是总动量的本征态，所以不同通过直接的色散关系来给出质量有效质量比。

This is called an eigenstate of position.

这个就叫做位置的特征态。

For a certain kind of eigenstate controllable system, the convergence of this algorithm can be proved.

对于一类特殊的本征态能控系统(量子控制操作的不变子空间不可约的系统)，该策略可以证明是收敛的。

The eigenstate controllability is presented and a control algorithm based on Grover iteration and quantum measurement is designed for eigenstate controllable system. The process of this algorithm is as follows.

2首次提出了本征态能控性的概念，并借鉴量子Grover搜索算法的主要思想，创造性的利用量子测量自身的特点，给出了一种适用于本征态能控系统的量子控制策略。

Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate.

每个可见特征值符合操作者一特征向量，而相关的特征值符合特征值里的可见值。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。