用不变本征算符法求一维线性谐振子的量子化能谱

采用不变本征算符法与积分变换法相当简捷地求出一维线性谐振子的量子化能谱.     

用代数方法求算符的本征值

本文表明了通常在量子力学初级课程里研究的简单量子力学模型的本征值，可以用一种非常简单的代数方法得到，并讨论了量子力学中的几个主要模型．     

外场与介观约瑟夫森结相互作用的不变本征算符法研究

本文首先详细介绍了场与介观约瑟夫森结相互作用系统的哈密顿量,进一步讨论了系统的量子化方案,然后简要介绍了不变本征算符法及其基本应用.在此基础上,用不变本征算符法求得外场与介观约瑟夫森结相互作用系统的能级间隔.     

一维晶格振动声子谱的全量子理论和"不变量本征算符"方法

建立一维晶格振动声子谱的全量子理论,其哈密顿量是自动包含了Born-von-Karmann边界条件的环链量子哈密顿量,然后用不变本征算符方法简捷地求出其声子谱.     

不变本征算符方法求解含不同在位势的一维双原子链的色散关系

本文运用全量子化的不变本征算符方法, 求解了含有不同简谐在位势的一维双原子链模型, 得到其色散关系并讨论了不同在位势系数之比和力常数对于色散关系高频支和低频支的影响, 分析发现在位势的存在使得低频支和高频支的频谱都有一定程度的抬高; 在一定的条件下, 布里渊区边界的高频支与低频支存在交点, 意味着在某些在位势下, 高频支与低频支的频隙为零. 关键词： 在位势 一维双原子链 不变本征算符方法 色散关系     

不变本征算符法计算各向异性海森伯亚铁磁系统的自旋波能量

利用不变本征算符法计算了X-Y-Z模型各向异性海森伯亚铁磁系统的自旋波能量,并讨论了此系统特殊情形下的自旋波能量及不变本征算符法的优点与不足.     

光子消灭算符高次幂的本征态及其性质

本文提出一种构造光子消灭算待高次幂α^N的正交归一本征态的一般方法,并着重研究了N=3场合下正交归一本征态的数学结构和量子统计性质,发现这些本征态均具有非经典效应,它们组成一个以非经典光场态作基矢的完备表象。 关键词：     

q-玻色湮没算符二次方的本征态

明显构造了a_q²的两个正交归一本征态,并证明这两个本征态组成一个完备Hilbert空间。 关键词：     

体积算符对任意价顶角的本征作用与本征值谱

利用体积算符所含抓三元组对自旋网任意价顶角中圈线作用的反称化和双元恒等式，证明了这种作用均为本征作用，本征值为-2.用代数方法给出了对任意价顶角求体积算符本征值的系统程式，得到了普遍情况下的3，4，5和6顶角体积本征值的具体代数表式. 关键词： 体积算符 任意价顶角 本征作用证明 本征值谱     

Normal coordinate in harmonic crystal obtained virtue of the classical correspondence of the invariant eigen-operator

Noticing that the equation with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation （2004 Phys. Left. A. 321 75）, we can find normal coordinates in harmonic crystal by virtue of the invaxiant eigen-operator method.     

Normal coordinate in harmonic crystal obtained by virtue of the classical correspondence of the invariant eigen-operator

Noticing that the equation frac d²O_ndt²={H_c,{H_c,O_n}} =λO_n with double-Poisson bracket, where O_n is normal coordinate, H_c is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation (2004 Phys. Lett. A. 321 75), we can find normal coordinates in harmonic crystal by virtue of the invariant eigen-operator method.     

Concentration dependence of the mixed crystal modes of vibration

The concentration dependence of the reststrahl absorption in various mixed crystals exhibiting one, two and mixed mode behaviour is investigated using the coherent potential approximation (cpa). The phonon Green’s function, the impurity mode frequencies and the strength of absorption are calculated in the Einstein model from the generalizedcpa proposed by Tripathi and Behera which takes into account both mass and force constant changes. The introduction of a phenomenological concentration dependence of the force constant change parameter is shown to provide a satisfactory explanation of the concentration dependence of the experimental data for the twenty mixed crystal systems analysed. It is conjectured that the nearest neighbour force constant of an impurity atom substituted at a host site is very much different from that of a perfect crystal consisting of these impurity atoms and that both these play an important role in determining the one, two and mixed mode behaviour of the mixed crystals.     

有限周期性弦球链系统的振动模

用实验和数值模拟的方法研究了一个有限周期性弦球链系统的振动模.观察到了振动谱的带状结构,表面态模.考察了表面态模的振动频率与第一个小球距弦端的距离τ的关系.用离散差分法对该弦球链系统作了数值模拟并对实验和数值模拟结果作了简单讨论.     

具有在位势的一维双原子链中杂质引起的对称局域模

对具有在位势且含杂质的一维双原子链的晶格振动方程组进行求解,得到了局域振动的解析解,给出了在位势对局域振动影响的基本特征,并简要讨论了对称局域模的存在形式.     

Effect of surface tension on the mode selection of vertically excited surface waves in a circular cylindrical vessel

Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate patternforming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term,an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tensionwas introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important.However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.     

Analysis of nonlinear steady state vibration of a multi-degree-of-freedom system using component mode synthesis method

In this paper, an analytical approach for nonlinear forced vibration of a multi-degree-of-freedom system is proposed using the component mode synthesis method. The whole system is divided into some components and a nonlinear modal equation of each component is derived using the free-interface vibration modes. The modal equations of all components and the conjunction conditions are solved simultaneously, and then the modal responses of components are derived. Finally, the dynamic responses of the whole system can be obtained. The degrees of freedom of modal equations can be reduced when the lower vibration modes are only adopted in each component. As a numerical example, a nine-degree-of-freedom system is considered, in which all spring have cubic type nonlinearity. As a result, it is shown that when there are no rigid modes in components, the compliance by the proposed method agrees very well with the exact one even if the lower vibration modes of components are only adopted. The other hand, in the case with rigid modes in components, the compliance has a little error compared with the exact result. It is recognized that the method proposed is very effective in the case without rigid modes in components for the actual application.     

晶格振动和晶粒尺度对磁记录膜矫顽力的竞争影响研究)

对晶格自旋相互作用的交换积分进行了晶格振动的修正,依此修正,导出了振动对磁记录膜矫顽力的影响关系;分析了磁晶量子尺度效应对磁记录膜矫顽力的影响机制;讨论了振动效应和量子尺度效应相互影响,共同竞争的物理内涵.结果显示:①振动的存在将减小薄膜的矫顽力;②磁晶微粒的量子尺度效应将使薄膜的矫顽力增加;③振动效应和量子尺度效应相互影响,共同竞争,为薄膜提供矫顽力;④要提高薄膜完备系的矫顽力,可将磁记录膜制成纳米级薄膜.     

一维双原子链中杂质引起的局域振动模

对含杂质的一维双原子链,在链中所有原子之间近邻相互作用力常数均相等的情况下,数值求解晶格振动的运动方程组,得到不同局域振动模的振动图像和产生条件,给出了局域模关于杂质原子质量和原胞中两种晶格原子质量比分布的相图．