本征态

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 In this strategy, the Grover iteration has been replaced by two different quantum amplitude amplification operations.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。

Two basic theorems are given by researching Hamilton's two steps linear differential equations of bender equations which provide widespread application methods of normal differential operator correspond to ladder operators,then the solutions of general equations are obtained by taking advantage of the two above theorems: The energy eigenvalue equation of one-dimensional oscillator; the common state of ; the radial equation of a bondage state of hydrogen atom; the radial equation isotropic three-dimensional harmonic oscillator; the infinity deep potential well of ball

本文通过研究束缚态本征方程里的哈密顿算符的二阶线性常微分形式，给出两个基本定理并证明，提供构造二阶线性常微分算符相应的阶梯算符的普遍实用的方法，然后利用这两个定理构造量子力学中常见力学量的阶梯算符，并用以计算其能量本征值和对应本征函数：一维谐振子的能量本征方程；共同本征态；氢原子束缚态径向方程；三维各向同性谐振子的径向方程；无限深球势阱。

In order to research the influence of polyaniline on acrylic anticorrosive coating, the polyaniline/acrylic anticorrosive coating that the mass rate of emeraldine base form of polyaniline in coating was 0%, 1.5%, 3%, 5%, 10% were prepared, and theirs anticorrosive performance in 3.5% NaCl solution was studied by Tafel and EIS.

为了研究本征态聚苯胺对丙烯酸涂层防腐性能的影响，制备了本征态聚苯胺质量分数分别为0%，1%，3%，5%及10%的聚苯胺／丙烯酸防腐涂层，应用Tafel极化曲线和电化学阻抗谱方法对比了其在3.5% NaCl溶液中的防腐性能。

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。

Naturally, we can take as basis the eigenstates of the unperturbed Hamiltonian and expand the perturbed states in this basis.

很自然地，我们可以取未扰动哈密顿量的本征态做为基矢，来展开被扰动哈密顿量的本征态。

The transfer relationships between two-mode squeezed state and eigenstates of both coordinate and momentum operators are presented. Some properties of two-mode squeezed state are discussed.

导出了双模压缩态与质心系下坐标本征态和动量本征态之间的转换关系，并讨论了双模压缩态的若干性质。

In this paper, coordinate and momentum eigenstates of two-particle have been introduced in the centre-of-mass system. New formalisms of two-mode squeeze operator and two-mode squeezed state have been given in coordinate and momentum pictures.

在质心坐标系下引入了双粒子坐标本征态和动量本征态，得到双模压缩算符和双模压缩态在坐标表像和动量表像中的新形式表示。

The bond electronic densities of the ground state can be mapped out by the bond polarizabilities at the final stage of relaxation and the relaxation time is shown to be proportional to the wavelength of the exciting light in agreement with Heisenberg's uncertainty principle.

激发虚态并不是本征态(这是对于非共振拉曼而言的，另一种情形是共振的状态，它的激发态是本征态，但这一问题我们在这里先不作讨论)，如果用量子力学来描述的话，激发虚态是所有可能的本征激发态的线性叠加。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。