基于Schrdinger方程的耦合常数解析延拓方法

基于Schrdinger方程,利用耦合常数解析延拓方法研究了球对称的方势阱、Woods-Saxon势和谐振子势中的单粒子共振态的能量与宽度.分析了耦合常数的取值区间和Pade多项式阶数对计算结果的影响.结果发现,在适当的耦合常数取值范围内,随着Pade多项式阶数的增加可以得到稳定和收剑的单粒子共振态能量与宽度.     

三维非线性Schrdinger方程的直接微扰方法

将直接微扰方法应用于含微扰的三维非线性Schrdinger方程,获得了该方程的包括零阶和一阶修正的近似解析解.借助得到的解析解,分析了微扰对孤子参数的影响。     

原子核的单粒子共振态

采用基于相对论平均场的耦合常数解析延拓方法研究球形核的单粒子共振态.具体计算了Zr同位素链中巨晕核的核芯核122Zr阈值附近的中子共振态的能量、宽度和波函数,其结果同相应的散射相移法的结果一致. Using analytic continuation in the coupling constant (ACCC) method within the framework of the self-consistent relativistic mean field (RMF) theory, the energies, widths and wave functions for single-particle resonant states close to the continuum threshold are evaluated. Predictions are also compared with corresponding results obtained by the scattering phase shift method.     

环状非有心势场中Schrdinger方程的精确解

提出了一个新的环状非有心势模型.利用Nikiforov-Uvarov方法求解了其满足的Schrdinger方程,得到了束缚态波函数的精确解及能谱方程.讨论了角向分量对径向分量的影响及相关参数取特定值时的特殊情况。     

指数型变化有效质量的三维Schrdinger方程的解析解

对随径向坐标指数型变化的有效质量分布,通过坐标变换,得到了与Coulomb型势,Kratzer型势和无限深球方势阱三类势函数相联系的变质量三维Schr dinger方程的解析解,具体给出了这三类系统的能量本征值和本征函数的解析表达式.     

非线性Schrdinger方程的直接间断Galerkin方法

讨论一维和二维非线性Schrdinger(NLS)方程的数值求解.基于扩散广义黎曼问题的数值流量,构造一种直接间断Galerkin方法(DDG)求解非线性Schrdinger方程.证明该方法L2稳定性,并说明DDG格式是一种守恒的数值格式.对一维NLS方程的计算表明,DDG格式能够模拟各种孤立子形态,而且可以保持长时间的高精度.二维NLS方程的数值结果显示该方法的高精度和捕捉大梯度的能力.     

再谈含时Schrdinger方程的求解方法

介绍了线性耦合含时量子系统厄米不变量算符的构造方法，并运用Ｌｅｗｉｓ－Ｒｉｅｓｅｎｆｅｌｄ量子不变量理论得到了一些含时薛定谔方程的精确解．同时也给出了系统时间演化算符的构造方法     

从Schrdinger方程引申到Dirac方程的一种简单方法

从Schrdinger方程出发,结合自旋的唯象描述、简单的相对论考虑和适当的猜测,写出了Dirac方程的正确形式.     

含时Schrdinger方程的高阶辛FDTD算法研究

提出了一种新的算法—高阶辛时域有限差分法(SFDTD(3,4):symplectic finite-difference time-domain)求解含时薛定谔方程.在时间上采用三阶辛积分格式离散,空间上采用四阶精度的同位差分格式离散,建立了求解含时薛定谔方程的高阶离散辛框架;探讨了高阶辛算法的稳定性及数值色散性.通过理论上的分析及数值算例表明:当空间采用高阶同位差分格式时,辛积分可提高算法的稳定度;SFDTD(3,4)法和FDTD(2,4)法较传统的FDTD(2,2)法数值色散性明显改善.对二维量子阱和谐振子的仿真结果表明:SFDTD(3,4)法较传统的FDTD(2,2)法及高阶FDTD(2,4)法有着更好的计算精度和收敛性,且SFDTD(3,4)法能够保持量子系统的能量守恒,适用于长时间仿真.     

依赖强度耦合多光子过程中的缠绕与薛定谔猫态

通过研究领事强度耦合多光子过程中的光场熵演化和光场Ｑ函数，揭示了光场与原子的缠绕特性，讨论原子跃迁过程中吸收或发射的光子数对缠绕特性和薛定谔猫态的影响。     

二维Helmholtz边界超奇异积分方程解析研究

基于常规边界元法及超奇异边界积分方程复线性耦合的Burton-Miller方法应用于无限域声学问题的最大难点在于处理超奇异积分（二维问题）.目前,此类超奇异积分主要使用各种弱奇异/正则化方法求解,而这些弱奇异/正则化方法具有时间消耗大等弱点.基于围道积分定理,本文给出一种使用常值单元的二维Helmholtz边界超奇异积分的解析表达式.在有限部分积分意义下,所有的奇异和超奇异积分可以解析表达.数值算例表明该解析表达式是有效的.     

Coupling Constant of QED in Krein Space Quantization

In this paper, considering the photon self energy in Krein space quantization including quantum metric fluctuation, the running coupling constant of QED is calculated and compared with the conventional result in QED theory.     

A New Method for the Determination of the Dynamic Isotope Effect and the Deuterium Quadrupole Coupling Constant in Liquids

Using a self-consistent NMR method, it is now possible to determine both the deuterium quadrupole coupling constant as well as the rotational dynamic isotope effect in liquids. We successfully tested the method on benzene for temperatures between 280 K and 293 K. The average value of 185(3) kHz for the coupling constant is compared with measurements in solid state and gas phase. As might be expected for liquids without hydrogen bonds, no difference can be detected. A rotational dynamic isotope effect of 6(3)% is observed. This value is significantly smaller than 20(5)%, the only other result reported in the literature. The results are corrected for the influence of vibrational motion.     

Nonminimal Derivative Coupling and the Recovering of Cosmological Constant

We show that the existence of the cosmologicalconstant can be connected to a nonminimal derivativecoupling, in the action of gravity, between the geometryand the kinetic part of a given scalar fieldwithout introducing any effective potential ofscalar fields. Exact solutions are given.     

Strong Coupling Problems of S-Matrix Equations

The analytic continuation of the solutions of nonlinear S-matrix equations for large values of a coupling parameter is investigated.     

A Field Method for Integrating Equations of Motion of Nonlinear Mechanico-Electrical Coupling Dynamical Systems

We deal with the generalization of the field method to weakly non-linear mechanico-electrical coupling systems. The field co-ordinates and field momenta approaches are combined with the method of multiple time scales in order to obtain the amplitudes and phase of oscillations in the first approximation. An example in mechanico-electrical coupling systems is given to illustrate this method.     

On a Counterexample Concerning Unique Continuation for Elliptic Equations in Divergence Form

We construct a second order elliptic equation in divergence form in3, with a nonzero solution which vanishes in a half-space.The coefficients are -Hölder continuous of any order < 1. This improves a previous counterexample of Miller (1972, 1974).Moreover, we obtain coefficients which belong to a finer class ofsmoothness, expressed in terms of the modulus of continuity.     

Renormalization of QCD Coupling Constant in Terms of Physical Quantities

A renormalization scheme is suggested where QCDinput parameters — quark mass and couplingconstant — are expressed in terms ofgauge-invariant and infrared-stable quantities. For theQCD charge renormalization the quark anomalous electromagnetic moment isused. It turns out that in the renormalization procedureQED and QCD do not differ. The examination of the quarkscattering amplitude indicates confinement phenomena inQCD.