本征态

First of all, we use approximate method of the super-symmetric quantum mechanics to calculate super-potential and eigenvalues of spheroidal functions in the first several terms. Further more , we derive the ground eigenfunction in the first order terms, which is very useful for applying of the spheroidal wave function probably

首先我们使用近似的超对称量子力学方法计算出前几阶超势和广义椭球函数的本征值；接着根据之前所求得的超势和本征值推导出广义椭球函数一阶基态波函数，该超对称量子力学方法的引入及一阶基态波函数形式将有利于广义椭球函数深入研究

Resultantly, the individual warm/cold events in ENSO cycle appear to be partially locked to the annual cycle, and also exhibit obvious irregularity both in amplitude and in lasting time.

本文第四章研制设计了一包含海洋表面边界层和大气辐合反馈过程的热带太平洋海气耦合异常模式，进而利用该模式对ENSO循环进行了较为真实的模拟，通过对模式ENSO循环的演变特征及其形成机制的细致分析，建立了-ENSO循环的非线性分析模式，并提出了ENSO循环形成的一种更为客观的理论，指出：1）和观测事实类似，模式ENSO循环确实涉及了三种主要时间尺度过程即LF、QB和AC，其中LF为3-4年主周期振荡，QB占总方差10～20%；2）ENSO循环的正反馈机制是不稳定海气相互作用过程，且这一不稳定过程的发展在暖态中明显强于冷态；3）ENSO循环的负反馈机制在冷暖态中表现不同，在冷态消亡过程中，这种负反馈过程主要表现为西边界反射产生的时滞效应，但在暖态消亡过程中不存在类似的时滞效应，其负反馈过程主要表现为在海气耦合不稳定充分发展时伴随的赤道两侧冷水上翻过程的加强以及非线性过程的衰减作用抑制了不稳定的发展并最终使得系统回复至冷态；4）ENSO循环的3-4年主周期振荡是一非线性系统的自激振荡现象，其形成是线性系统的本征模即准两年振荡通过非线性机制产生的周期加倍所致，其中&单向性&大气辐合反馈加热过程对其形成至关重要；5）虽然年循环过程对ENSO循环形成没有本质影响，但它可明显影响ENSO循环的具体振幅和位相，使得ENSO对季节循环有明显的&锁相&特征，并且也使得ENSO循环在振幅大小和时间长短方面呈现出明显的不规则性。

We lay these eigenstates out flat on the ground and orthogonal to each other.

我们将这些本征态放在平面上并互相垂直。

Then, new soliton eigenstates and bifurcation behavior are obtained.

并且在此基础上讨论了孤子本征态和分岔结构。

The lion then collapses into one of the eigenstates, which is rolled up and placed inside the cage.

然后狮子就被瓦解成一系列本征态并重新积累安置在笼子里面。

For linear quantum systems,our new phase becomes a statistical average of the Berry phases for all eigenstates involve...

在线性量子系统中，新定义的几何相位是各个本征态Berry相位的权重平均。

This new phase applies to both linear quantum systems and nonlinear quantum systems,and should be particularly useful for the latter for which the adiabatic evolution of a general quantum state cannot be described in terms of a superposition of eigenstates.

这个新的几何相位同时适用于线性量子系统和非线性量子系统。它对于后者尤其重要因为非线性量子系统的绝热演化不能通过本征态的线性叠加来描述。

On condition that there exist weak excitations in the two-component BEC, the SO (3, 2) Lie algebraic description still work. The eigenstates and energy-gap equation have been obtained.

对存在弱激发的双分量BEC，SO（3，2）代数方法仍然近似有效，我们由此求得了系统的本征态和弱激发能隙方程。

In this space, we construct two kinds independent phase operators by improving supersymmetric annihilation operator and supersymmetric creation operator, and then obtain their eigenstates.

我们进一步将它推广到用超对称谐振子的产生算符和湮灭算符来构造适用于超对称谐振子的双摸相位空间里的二类独立的相位算符并相应地求出了其归一化的本征态。

The results show that the number of the squeezed atomic dipoles is decided by the coherence of the atom, the direction of the quantum information entropy squeezing is decided by the phases of the field and the atom, and the quantum information entropy squeezing is a precision tool for the squeezing of the atom, especially when the atom is in the eigenstates of the dipole operators.

结果表明：原子偶极矩分量出现信息熵压缩的数目依赖于原子的分布角；信息熵压缩的方向由原子和场的位相决定；量子信息熵是原子压缩的精密量度工具，尤其适合于原子处在偶极矩算符的本征态时压缩情况的描述。

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。