第三周期元素正常态原子的四参数解析波函数与能量的计算

本文提出了一套简单适用的四参数变分波函数,对第三周期元素正常态原子进行了系统计算。采用变分法定出了解析波函数的最佳参数,并对各原子的能量进行了系统的大量计算。结果表明,其原子的能量值都较好,且比李光伟等人提出的五参数波函数的计算值还要好。     

类氦原子基态能量的哈密顿替代法研究

首次将哈密顿替代法用于计算类氦原子基态能量.计算结果与单参数变分法给出的数值相同,比一阶微扰法计算的能量更接近实验值.由于计算过程简单直观,不需选取试探波函数,不受微扰项大小限制,而且近似度高,该方法可在教学中采用.     

第四周期过渡元素的原子解析波函数与能量的计算

本文采用修正ls电子解析波函数的基本思想,用因子(1 f~2r~2)修正3d电子波函数,以六参数解析波函数,对第四周期过渡元素的原子多重态能量进行了系统的变分计算。得到较准确的能量值及径向波函数最佳参数值。与类氢五参数的计算结果进行了比较,讨论了能量改进的原因,各参数的变化规律及其物理意义。     

量子激发态最陡下降微扰理论

本文发展了量子激发态能量与波函数的最陡下降微扰理论计算方法,该方法避免了普通微扰理论所需要的对于参考态的无限求和困难,并能通过逐步迭代计算逼近于体系精确的本征函数和本征值。只要保持激发态试探波函数正交于其对称性相同的低激发态或基态的波函数,避免计算过程中的变分坍陷,本文的方法能用于求精确的激发态能量和波函数。 关键词：     

纤锌矿GaN柱形量子点中类氢施主杂质态

在有效质量近似和变分原理的基础上,选取含两个变分参数的波函数,研究了纤锌矿结构的GaN/AlxGa1-xN单量子点中类氢施主杂质体系的结合能随量子点(QD)尺寸以及杂质在量子点中位置的变化,并与以前使用不同尝试波函数的计算结果进行了比较。结果表明:由我们选取的两变分参数波函数得到的结果与前人选取的两变分参数波函数得到的结果相比有所改进,而与选取一个变分参数波函数得到的结果一致。同时我们还计算了体系的维里定理值随量子点半径的变化情况,所得结果与前人工作结果一致,说明本文选取的两变分参数波函数能很好地描述柱形量子点中施主杂质态的运动。     

锂原子低激发态能量的精细结构

利用变分原理，计算出锂原子(类锂离子)第一激发态能量，再用所得到的原子态波函数计算出LS耦合的第一激发态能级的精细结构，将计算结果与实验值比较，误差很小。     

BeAl2O4:Cr3+的能谱和R1线压力移位的理论计算

采用强场方案和三角基,通过对角化三角畸变立方场的d3电子组态完全能量矩阵,拟合得到BeAl2O4:Cr3+的能谱和波函数.利用获得的波函数,计算出了基态g因子和R1 、R2线能谱压致移位值,计算值和实验结果相符合.各参数对能级压力移位率的影响也被定量计算,揭示了R1和R2线压力移位的物理起源.     

BeAl2O4:Cr3+的能谱及R1和R2线压力移位的理论计算

采用强场方案和三角基,通过对角化三角畸变立方场的d3电子组态完全能量矩阵,拟合得到BeAl2O4:Cr3+的能谱和波函数.利用获得的波函数,计算出了基态g因子和R1 、R2线能谱压致移位值,计算值和实验结果相符合.各参数对能级压力移位率的影响也被定量计算,揭示了R1和R2线压力移位的物理起源.     

重夸克偶素的高阶变分-积分微扰修正

利用基于积分方程的改进的变分微扰方法(变分-积分微扰法)求解重夸克偶素激发态.设置含有变分参数的母哈密顿量作为零级哈密顿量,选择该母哈密顿系统的精确解作为试探波函数,得到了只有几项的高阶修正波函数和高阶能量修正.该计算结果更接近精确能量值,修正波函数的有界性和收敛性也得到了证明.结果表明,这种方法不仅可提高计算结果的精度,而且可确保微扰级数解的收敛性. 关键词： 重夸克偶素 变分-积分微扰法 高阶能量修正     

共振价键波函数在高压液氢量子蒙卡模拟中的适用性研究

在共振价键理论基础上, 选取高压液氢电子主要占据轨道的线性组合作为基组, 构建由Jastrow项和反对称孪生函数乘积项 (AGP) 组成的波函数. 考虑电子关联作用的共振价键 (RVB) 波函数得出的能量值低于LDA能量值; 当满足r_s<1.75或T >15000 K时引入backflow项以改善波函数结点面, 改善后的能量值下降约1 mHa/atom, 能量方差值变小. 将构建的RVB波函数与电子-离子耦合的蒙特卡罗法 (CEIMC) 相结合, 计算结果与实验及其他ab-initio结果相符合, 获得的液氘单次冲击Hugoniot曲线基本通过所有加载类型实验误差棒, 液氘在50.3 GPa处具有最大压缩率4.48, 在100–120 GPa内未发现压缩率有急剧增大的现象. 构建的RVB 波函数能够适用于较宽密度与温度范围内(1.0< r_s<2.2, 2800 K< T<60000 K)液氢的模拟, 与CEIMC法相结合可提高液氢冲击特性的模拟精度. 关键词： 共振价键理论 波函数 量子蒙卡法 液氢     

On the validity of the inclusion of geometrical shadowing functions in the multiple-scatter Kirchhoff approximation

The validity of the geometrical shadowing functions for use in calculations of the light distribution scattered from a rough surface is investigated. By the use of the multiple-scatter Kirchhoff approximation, single- and double-scattered contributions are calculated with and without the incident, intrasurface and scatter-shadowing functions. Explicit conditions are given for the validity of the geometrical shadowing functions.     

胶子重组函数的性质

通过协变和非协变的方法研究了领头对数近似(LLA)下扭度为4的QCD演化方程中的胶子重组函数的性质.指出了GLRMQ方程中的胶子重组函数并不适用.讨论了避免红外发散的方法,这种方法可以用于高扭度下演化核和系数函数的推导.     

Investigation of the structural elements of a fullerene within the static-fluctuation approximation of the Hubbard model

The anticommutator Green’s functions, correlation functions, and ground-state energies for closed atomic structures that consist of five or six atoms and are structural elements of a fullerene are calculated within the static-fluctuation approximation of the Hubbard model. The results of the calculations are analyzed and compared with the data available in the literature.     

Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions

Considering the equations for some functions involving the first or the second derivatives of the biconfluent Heun function, we construct two expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta functions. The first series applies single Beta functions as expansion functions, while the second one involves a combination of two Beta functions. The coefficients of expansions obey four- and five-term recurrence relations, respectively. It is shown that the proposed technique is potent to produce series solutions in terms of other special functions. Two examples of such expansions in terms of the incomplete Gamma functions are presented.     

Bi-resonance functions in the theory of collisional broadening of the spectral lines of molecules

In the model of parabolic trajectories, expressions are derived for the bi-resonance functions that appear in the theory of collisional broadening of molecular spectral lines in the case of their interference. The functions required for calculating the cross-relaxation parameters of molecular spectral lines in the case of their broadening by rare gas atoms are obtained numerically in the model of exact trajectories for the isotropic Lennard-Jones 6–12 potential. Analytic models are proposed for these functions, and the corresponding parameters are obtained.     

On the structure of the conformal covariant N-point functions

The conformal covariant n-point functions for the fields with arbitrary spin and scale dimension are found. These functions are determined up to a set of arbitrary functions on $\text{n(n?3)}\text{2}$ independent conformal invariant variables. These arbitrary functions cannot be determined without dynamical assumptions.     

Parametrization of the scattering wave functions of the Paris potential

The neutron-proton scattering wave functions of the Paris nucleon-nucleon potential are parametrized for partial waves of total angular momenta less than 5 at laboratory kinetic energies between 0 MeV and 400 MeV. The inner parts of the wave functions are approximated by polynomials with a continuous transition to the outer parts, which are given by the asymptotic regime and determined by the respective phase shifts. The smooth variation in energy of the phase shifts and of the coefficients of the polynomials permits a further parametrization of these quantities in terms of polynomials of low degree. The scattering wave functions can then be calculated at any given energy below 400 MeV. Special attention is devoted to the zero-energy limit of the low partial waves. An easy-to-use FORTRAN program, which allows the user to calculate these parametrized wave functions, is available via electronic mail.     

Some extensions of the Fermi-Dirac and Bose-Einstein functions with applications to the family of the zeta and related functions

The familiar Fermi-Dirac and Bose-Einstein functions are of importance not only for their rôle in quantum statistics, but also for their several interesting mathematical properties in themselves. Here, in our present investigation, we have extended these functions by introducing an extra parameter in a way that gives new insights into these functions and their relationship to the family of zeta functions. These extensions are dual to each other in a sense that is explained in this paper. Some identities are proved here for each of these general functions and their relationship with the general Hurwitz-Lerch zeta function Φ(z, s, a) is exploited to derive some other (presumably new) identities.     

An examination of the steady-state solution of the differential equation governing indoor sound fields

The use of the characteristic functions to obtain a steady-state sound field is based on the completeness of the set of the characteristic functions. For absorptive boundaries, the characteristic functions are complex functions, and there is no proof in mathematics of whether the set of the characteristic functions is complete. In addition, the use of the characteristic functions to obtain a steady-state sound field of three-dimensional space requires the solving of a huge amount of the complex number k_nx The aims of this paper are to examine whether the set of the characteristic functions can still be complete for strong absorptive boundaries and to provide a practical solving method for k_nx.     

Connection between the 2-body energy of the Kaxiras-Pandey and the Biswas-Hamann potentials

Relationship among interatomic potential functions can be useful in shedding insight on the extent of similarity, and in obtaining a potential function from parameters of another potential function. The 2-body portion of the Biswas-Hamann (BH) and the Kaxiras-Pandey (KP) potential functions are related by equating both functions, as well as their corresponding derivatives up to the third order at the equilibrium bond length. Validity of the parametric relationship is verified by plotting the loose form of the 2-body BH potential in terms of KP parameters and comparing it with the KP potential function. The parametric relationships developed herein are then compared with those that concern other potential functions, with particular emphasis on the scaling factors.