二维谐振子的双波描述

采用双波函数量子理论,研究了二维谐振子力学量的时间演化方程及其经典极限,并给出了二维各向同性谐振子守恒量的表达式。     

非保守Nielsen方程的形式不变性导致的非Noether守恒量

研究非保守Nielsen方程由形式不变性直接导致的非Noether守恒量．函数对时间的全导数采 用沿运动轨道曲线的方式，给出非保守Nielsen方程的非点的形式不变性的定义和判据，并 研究其Noether守恒量．得到形式不变性导致非Noether守恒量的条件以及守恒量的形式，并 给出三种特殊情形的推论．举例说明结果的应用． 关键词： Nielsen方程 形式不变性 非Noether守恒量     

一类环状非球谐振子势场中相对论粒子的束缚态解

提出了一种新的环状非球谐振子势, 在标量势与矢量势相等的条件下，给出了其Klein-Gordon方程和Dirac方程的束缚态解. Klein-Gordon方程的θ角向波函数以超几何函数表示，径向波函数可用合流超几何函数或广义拉盖尔多项式表示，能谱方程由径向波函数满足的束缚态边界条件得到. Dirac方程的旋量波函数可用Klein-Gordon方程的解构造. 关键词： 环状非球谐振子势 Klein-Gordon方程 Dirac方程 束缚态     

Poincaré-Chetaev方程的统一对称性

研究Poincaré-Chetaev方程的统一对称性及其导致的守恒量. 给出Poincaré-Chetaev方程统一对称性的定义和判据, 得到Poincaré-Chetaev方程统一对称性的三种守恒量: Noether守恒量、Hojman守恒量和Mei守恒量. 关键词： Poincaré-Chetaev方程 统一对称性 守恒量     

含速率平方阻力项的一维相对论谐振子的Lagrange函数与守恒量

用Taylor级数展开的方法得到含速率平方阻力项的一维相对论谐振子的运动微分方程.从守恒量的性质及运动微分方程出发得到了系统的Lagrange函数和守恒量的表达式. 关键词： 相对论谐振子 Lagrange函数 守恒量     

准坐标下广义非保守系统Lagrange方程的积分因子与守恒定理

用积分因子方法研究准坐标下广义非保守系统Lagrange方程的守恒定理.列写系统的运动微分方程，给出它的积分因子的定义.研究守恒量存在的必要条件.建立系统的守恒定理及其逆定理，并举例说明结果的应用. 关键词： 准坐标 Lagrange方程 积分因子 守恒量     

Birkhoff系统的一类新型守恒量

给出了Birkhoff系统的一类新型守恒量。首先，建立了Birkhoff系统的运动方程及其Mei对称性的定义和判据；其次，给出了系统的一类新型守恒量的存在定理，并导出了用于确定无限小生成元的广义Killing方程；最后，建立了守恒定理的逆定理 关键词： Birkhoff系统 Mei对称性 守恒量 Killing方程     

线性谐振子的非定态波函数

引入初坐标算符和初动量算符为线性谐振子的力学量完全集，求解薛定谔方程，可得到线性谐振子的两类非定态波函数。     

用不变量方法求含时谐振子的波函数

利用辅助方程从含量谐振子的哈密量出发得到了两个不变量，利用这两个不变量求得了系统薛定谔方程的解。     

Vacco动力学方程的Mei对称性、Lie对称性和Noether对称性

研究Vacco动力学方程的形式不变性即Mei对称性，给出其定义和确定方程，研究Vacco动力学方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量，给出一 个例子说明结果的应用. 关键词： Vacco动力学方程 Mei对称性 Noether对称性 Lie对称性 守恒量     

The equation-transform model for Dirac–Morse problem including Coulomb tensor interaction

The approximate solutions of Dirac equation with Morse potential in the presence of Coulomb-like tensor potential are obtained by using Laplace transform (LT) approach. The energy eigenvalue equation of the Dirac particles is found and some numerical results are obtained. By using convolution integral, the corresponding radial wave functions are presented in terms of confluent hypergeometric functions.     

Potential Symmetries and Associated Conservation Laws to Fokker-Planck and Burgers Equation

Kara and Mahomed have derived an identity, which does not rely on use of a Lagrangian as needed to obtain conservation laws by Noethers theorem. By using the identity and symbolic computation, conservation laws arising from nonlocal symmetries are obtained for Fokker-Planck equation and burgers equation.     

Spin and Pseudospin Symmetries of Hellmann Potential with Three Tensor Interactions Using Nikiforov-Uvarov Method

The Dirac equation with Hellmann potential is presented in the presence of Coulomb-like tensor (CLT), Yukawa-like tensor (YLT), and Hulthen-type tensor (HLT) interactions by using Nikiforov-Uvarov method. The bound state energy spectra and the radial wave functions are obtained approximately within the framework of spin and pseu- dospin symmetries limit. We have also reported some numerical results and figures to show the effects of the tensor interactions. Special cases of the potential are also discussed.     

中心力场中散射角的简洁推导

本文从牛顿方程及角动量守恒定律出发 ,利用矢量函数的微积分运算技巧简捷地推导出中心力场中散射角 φ,避免了经典教科书中从轨道方程出发推导出 φ的繁琐性 ,不仅计算简洁 ,而且物理过程明确 .     

Dirac Equation with a New Tensor Interaction under Spin and Pseudospin Symmetries

The approximate analytical solutions of the Dirac equation under spin and pseudospin symmetries are examined using a suitable approximation scheme in the framework of parametric Nikiforov-Uvarov method. Because a tensor interaction in the Dirac equation removes the energy degeneracy in the spin and pseudospin doublets that leads to atomic stability, we study the Dirac equation with a Hellmann-like tensor potential newly proposed in this study. The newly proposed tensor potential removes the degeneracy from both the spin symmetry and pseudospin symmetry completely. The proposed tensor potential seems better than the Coulomb and Yukawa-like tensor potentials.     

Double Reduction and Exact Solutions of Zakharov-Kuznetsov Modified Equal width Equation with Power Law Nonlinearity via Conservation Laws

The conservation laws for the (1+2)-dimensional Zakharov-Kuznetsov modified equal width (ZK-MEW) equation with power law nonlinearity are constructed by using Noether's approach through an interesting method of increasing the order of this equation. With the aid of an obtained conservation law, the generalized double reduction theorem is applied to this equation. It can be shown that the reduced equation is a second order nonlinear ODE. Finally, some exact solutions for a particular case of this equation are obtained after solving the reduced equation.     

CONSERVATION LAWS FOR SELF-ADJOINT FIRST-ORDER EVOLUTION EQUATION

We consider the problem on group classification and conservation laws for first-order evolution equations. Subclasses of these general equations which are quasi-self-adjoint and self-adjoint are obtained. By using the recent new conservation theorem due to Ibragimov, conservation laws for equations admiting self-adjoint equations are established. The results are illustrated applying them to the inviscid Burgers equation. In particular an infinite number of new symmetries of this equation are found.     

Spin Symmetry in Dirac-Attractive Radial Problem and Tensor Potential

In this paper,we solve the Dirac equation under spin symmetry limit for attractive radial potential including a Coulomb-like tensor interaction.By using the parametric generalization of the Nikiforov-Uvarov method,the energy eigenvalues equation and the corresponding wave functions have been obtained in closed forms.Some numerical results are given too.     

Exact pseudospin symmetry solution of the Dirac equation for spatially-dependent mass Coulomb potential including a Coulomb-like tensor interaction via asymptotic iteration method

In this Letter, the Dirac equation is exactly solved for spatially-dependent mass Coulomb potential including a Coulomb-like tensor potential under pseudospin symmetry limit by using asymptotic iteration method with arbitrary spin-orbit coupling number κ. The energy eigenvalues and corresponding eigenfunctions are obtained and some numerical results are given.     

Relativistic symmetry of position-dependent mass particle in Coulomb field including tensor interaction

The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction under the spin and pseudospin symmetric limit. Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number κ. Some numerical results are given too. The effect of the tensor interaction on the bound states is presented. It is shown that the tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under the conditions of the spin symmetric limit in the absence of tensor interaction.