键长-键角和Radau坐标下哈密顿算符在傅里叶基组表象下的厄米性

在量子动力学计算中,有时候为了规避奇点问题或者节省计算量,我们经常需要对哈密顿量进行变换. 然而,在使用傅里叶基矢计算时,哈密顿量的变换形式容易导致哈密顿矩阵失去厄米性,进而有些情况下使数值计算变得不稳定. 本文主要讨论构建具有厄米性的哈密顿算符的方法. 以三原子分子为例,构建了键长—键角和Radau坐标下描述分子运动的各种形式的哈密顿量. 基于这些哈密顿量,采用含时波包方法计算了OClO分子的吸收光谱,讨论了非厄米性矩阵对计算结果的影响. 本文所得到的结论对基于基函数展开的量子动力学计算都是适用的.     

狄拉克δ-函数及有关应用

狄拉克δ-函数实际上是离散情况下的Kronecker δ-函数的连续化,它在数学和物理中都有重要的应用.基于广义函数概念引入狄拉克δ-函数的精确定义,证实狄拉克δ-函数不是通常Lebesgue局部可积意义下的普通函数;文中分别以单位矩形脉冲函数、高斯函数、钟形函数和Sinc函数的序列在弱极限意义下来逼近狄拉克δ-函数....     

δ函数在光学中的应用

以光学中几个典型的例子说明δ函数在光学中的重要应用。     

自傅里叶函数构造法则的研究

研究自傅里叶函数的构造法则，给出了和Ｃａｏｌａ的法则互为补充的法则：ｆ（ｚ）＝ｇ（ｘ）ｇ（－ｘ）＋ｇ＾Ｆ（ｘ）＊ｇ＾Ｆ（－ｘ）。分析了它的优缺点。最后，导出了构造自傅里叶函数法则的最简表达式。     

傅里叶变换的局限性及其改进方法

从对傅里叶变换的局限性分析入手 ,揭示了窗口傅里叶变换、小波变换和分数傅里叶变换的出现是傅里叶变换本身发展的必然 ,阐明了其改进方法产生的原因及其优缺点 ,分析了其改进方法与傅里叶变化的关系 ,这些有助于加深对傅里叶变换的认识。     

Wigner分布函数及非整数傅里叶变换

本文研究了Wigner分布函数的特性,利用Wigner分布函数的旋转,将整数域傅里叶变换推广到了非整数域,描述了自由空间光场的演变过程.     

成像型任意反射面速度干涉仪数据处理方法

 采用傅里叶变换方法,列出了对成像型任意反射面速度干涉仪得到的干涉条纹图进行处理的过程。利用文献结果,处理了冲击波整形时产生的有间断干涉条纹图,对处理结果进行了分析。结果表明：条纹图要干净,条纹间距清晰、均匀,应使用１维傅里叶变换的方法处理条纹图,减小滤波的难度。研究了冲击波测试当中条纹丢失的问题,提出了间断条纹图间断起始点相位确定的方法。对透明和不透明靶产生条纹图的不同进行了讨论,得出对透明靶产生的条纹图应采用适当的条纹外延技术进行预处理后再进行常规处理。     

成像型任意反射面速度干涉仪数据处理方法

采用傅里叶变换方法,列出了对成像型任意反射面速度干涉仪得到的干涉条纹图进行处理的过程。利用文献结果,处理了冲击波整形时产生的有间断干涉条纹图,对处理结果进行了分析。结果表明：条纹图要干净,条纹间距清晰、均匀,应使用１维傅里叶变换的方法处理条纹图,减小滤波的难度。研究了冲击波测试当中条纹丢失的问题,提出了间断条纹图间断起始点相位确定的方法。对透明和不透明靶产生条纹图的不同进行了讨论,得出对透明靶产生的条纹图应采用适当的条纹外延技术进行预处理后再进行常规处理。     

平均场框架下两分量玻色-爱因斯坦凝聚中集体激发的阻尼

研究两分量玻色-爱因斯坦凝聚中集体激发的阻尼,该阻尼包括朗道和巴利耶夫两种机制。采用哈特利-福特-波戈留波夫平均场理论,基于单分量系统理论,构建了两分量系统的理论框架,严格按照单分量系统理论推导公式,并且分析两分量系统和单分量系统在理论框架构建上的主要差别。以理想的能级连续的均匀系统朗道阻尼为例进行半经典近似计算,展示粒子相互作用细节,说明所提理论的物理意义和应用方法。在计算过程中,通过无量纲阻尼函数分析朗道阻尼与温度的依赖关系,分析对阻尼有贡献的准粒子跃迁,包括同类型准粒子之间和不同类型准粒子之间的各种情况,并通过误差函数分析不同能量范围的准粒子跃迁对阻尼的贡献。     

Relationship between dynamic mechanical property and thermodynamic interaction parameter of concentrated polymer solutions

The use of concentrated polymer solutions is one of the basic techniques in the application of polymers. They may be coating materials, plasticized polymers, and oil-extended rubber. In these applications the solubility relation is one of the key requirements. The polymer-solvent interaction is expected to influence the mechanical property of the mixture. It is the intent of this study to explore how the dynamic mechanical property is affected by the change of thermodynamic interaction parameter in concentrated polymer solutions. The theoretical development is based on several assumptions: (1) a polymer chain in the amorphous state and in its own environment assumes unperturbed configuration; (2) a polymer chain in a good solvent (poor) is expanded (contracted) relative to the unperturbed dimension; (3) the expanded (contracted) chain configuration results in the higher (lower) entanglement density; (4) both expanded and contracted chains store an elastic energy, the magnitude of which may be estimated; (5) the elastic energy of the deformed chain is balanced by the thermodynamic energy of interaction. The paper focuses on the development of a theory. Also, limited examples of the application of the theory are presented.     

Relationship between the auger parameter and the energy gap

In this communication we show that for different semiconductors which do not contain transition metal ions, the shift in the extra-atomic relaxation energy for the metal ion with the core hole-as measured by the Wagner Auger parameter shift with respect to the metallic state-is roughly linearly correlated to the energy gap with a slope approximately equal to −1. The relationship, useful from a practical point of view, can be rationalized using the qualitative concepts of local and non-local screening developed by Veal and Paulikas and the direct relation between the band gap and anion electronegativity.

The core-hole screening for the semiconductors that follow the correlation can be described by the non-local screening mechanism. In this case, the polarized ligands transfer electronic charge to the unfilled s-p metal orbitals which are pulled down to the energy level of the local anion valence band by the core hole. Semiconductors containing transition metal ions, for which local screening mechanisms can occur by transferring the charge from the ligands to the localized d electronic levels, do not follow the correlation. This is due to the fact that the Auger parameter of the cation in the compound is similar to that of the atom in the metallic state. This result indicates that the relaxation energy in the transition metal compounds can be similar to the screening energy in the metallic state.     

基于坐标表象的脊波变换研究

在小波变换量子力学机制的启发下, 通过采用Fock空间里双模坐标本征态改写经典Ridgelet变换, 定义了量子光学态的Ridgelet变换. 然后利用IWOP技术给出不对称积分算符的显式, 并推导出了两个有用的双模算符正规乘积公式. 在此基础上, 通过选取双模“墨西哥帽”母小波函数, 分析了相干态、特殊压缩相干态、中介纠缠态表象的Ridgelet变换. 关键词： IWOP技术 Ridgelet变换 相干态     

Impact parameter representation from the Watson-Sommerfeld transform

Using the Watson-Sommerfeld transform the elastic scattering amplitude of two spinless particles is shown to have an exact and unique impact parameter, or Fourier-Bessel (FB) representation. The representation is valid for all physical energies and scattering angles. Wallace's recent work is found to be an asymptotic expansion of the FB amplitude obtained from the partial-wave expansion. The way singularities of the partial-wave amplitude in the l-plane enter in the FB amplitude is also explicitly shown.     

Gravitational perturbations in the expanding universe in a coordinate representation

Gravitational perturbations in the expanding universe are analyzed within the framework of Newtonian cosmology. In contrast to classical work, the perturbations are found not in a Fourier but in a coordinate representation. This makes it possible to obtain general expressions for finding the distributions of perturbations in the density and velocity of matter as a function of the coordinates and time from the known distribution at the initial time. In the simplest cases of plane-symmetric and spherically symmetric distributions, analytical equations are obtained for density perturbations as a function of the coordinates and time. The final conclusion is that it is possible for gravitational perturbations to grow even when the characteristic size of a perturbation is less than the Jeans wavelength. Kazan’ State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 45–52, March, 1997.     

Impact parameter representation for separable potentials

An exact impact parameter representation for nonlocal separable potential has been written down. This representation is valid at all angles and energies. Further, it is shown that the Blankenbecler-Goldberger representation follows naturally for such a potential and has also an $\text{N}\text{D}$ form.     

Supersymmetric representation of order parameter fluctuations

We consider the representation of homogeneous and heterophase fluctuations based on the supersymmetric theory of fields. It is shown that the problem reduces to a mixture of noninteracting Fermi and Bose gases. The thermodynamic features resulting from each type of fluctuations are determined, as well as the correlation functions of the spatial distributions of the order parameter and interphase boundaries.Suma Physicotechnical Institute. RETO Scientific-Industrial Complex. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 49–53, April, 1994.     

自由质点测地线仿射参量时空坐标系

以时序t为自变量,可给出自由质点空间测地线的参数方程组{Xⁱ(t)},借助于仿射参量R(t)变换实现测地线微分方程的齐次化, 推导出仿射参量R满足的一阶微分方程、获得以有理数C_u为标志的序列解析解R.基于R定义平直四维坐标系{t,r,θ,φ}的空间距离单位,建立自由质点测地线仿射参量时空坐标系{t,ξ,θ,φ}.研究{t,ξ,θ,φ}中狭义相对论时空间隔模型度规张量g的对角化过程, 发现与对角化度规对应的特征量t₁(t,ξ), τ₁(τ,ξ),t_t(t,τ,ξ),τ_τ1(t,τ,ξ); 从而推出时空坐标系{t,ξ,θ,φ}维数小于4.