最弱受约束电子势模型的径向波函数的两类递推关系

应用简单的方法———Laplace变换法来求最弱受约束电子势模型(WBEPM势)的径向Schrdinger方程.通过这种方法使得两阶微分方程变为一阶微分方程,这样可以直接运用积分得到WBEPM势束缚态能量方程和归一化的波函数,所得结果与文献一致.更重要的是用Laplace变换得到径向波函数的两类新的递推关系.这种递推关系是有效主量子数和角量子数之间关系,在计算原子和分子跃迁几率时有着广泛的应用.     

用Laplace变换求一维谐振子势的Schrdinger方程束缚态解

用Laplace变换把二阶一维谐振子的Schr dinger微分方程退化为一阶微分方程,用直接积分法求出一阶微分方程的解.然后用波函数的单值性得到束缚态能谱,用级数展开,再进行Laplace逆变换,得到其本征函数.     

Hartmann势的Klein-Gordon方程束缚态解及递推关系

给出了在Hartmann型标量势与矢量势相等的条件下其Klein-Gordon方程束缚态解.结果表明 ，径向波函数可用广义Laguerre多项式表示，其角向波函数可用Legendre多项式表示.另外 ，给出了径向波函数关于角量子数l和量子数n的二类新递推关系. 关键词： Hartmann势 Klein-Gorgon方程 束缚态 递推关系     

用Laplace变换求一维谐振子势的Schr(o)dinger方程束缚态解

用Laplace变换把二阶一维谐振子的Schrodinger微分方程退化为一阶微分方程,用直接积分法求出一阶微分方程的解．然后用波函数的单值性得到束缚态能谱,用级数展开,再进行Laplace逆变换,得到其本征函数．     

二维各向同性谐振子的升降算符解法

本文利用角动量算符的Ｓｃｈｗｉｎｇｅｒ表示，用代数方法研究了二维各向同性谐振子的能量本征函数．求出了（Ｈ，ｌｚ）共同本征函数　Ｎｍ（θ，）　，找到了量子数Ｎ，ｍ的升降算符以及各本征函数之间的递推关系，包括径向波函数的递推关系．给出了（Ｈ１，Ｈ２）表象与（Ｈ，ｌｚ）表象之间的变换关系，这关系和转动矩阵有密切联系．     

Makarov势的Dirac方程的束缚态解

给出了Makarov型标量势与矢量势相等条件下的Dirac方程的束缚态解. Dirac方程的角向方程用因子分解方法求解，在得出角向波函数的过程中，自然地得到了属于同一本征值的不同角向波函数间的递推操作. 径向束缚态波函数用合流超几何函数表示，束缚态的能量方程可由径向波函数满足的边界条件得到. 关键词： Makarov势 Dirac方程 束缚态 因子分解方法     

非球谐振子势的精确解

严格求解了三维非球谐振,势的Schrodinger方程给出了精确的能谱方程和归一化的径向波函数.获得了径向幂次算符r^s的矩阵元和平均值的计算公式及其递推关系.     

二维氢原子径向方程的两种解法

本文利用两种方法求解二维氢原子的径向方程：一是升降算符法，由所定义的关于量子数ｍ的升降算符，给出了径向波函数之间的递推公式，求出了二维氢原子的能级和径向波函数的表达式；二是通过与三维氢原子径向方程的类比，在三维氢原子径向波函数的基础上，直接给出了二维氢原子径向波函数的一般表示式．两种解法所得结果完全一致．     

束缚态径向方程和Ξ-超核的结合能

无论从薛定谔方程或是Dirac方程的低能近似出发都可导出同一标准形式的径向方程,这种径向方程可用三点中央差分格式从中心两点出发向外递推求解. 给出了一种求解束缚态的能量本征值及其径向波函数的方法并计算分析了几个Ξ-超核的基态结合能.     

环形振子径向矩阵元的通项表达式及其递推关系

利用文献1给出的环形振子的归一化的径向波函数,推导出环形振子径向矩阵元的通项表达式及其递推关系.解决了环形振子径向矩阵元的计算问题.     

Exact solutions of the Klein—Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform

We present exact solutions for the Klein-Gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central oscillator potential. The angular functions are expressed in terms of the hypergeometric functions. The radial eigenfunctions have been obtained by using the Laplace integral transform. By means of the Laplace transform method, which is efficient and simple, the radial Klein-Gordon equation is reduced to a first-order differential equation.     

Pseudospin Symmetry in Position-Dependent Mass Dirac-Coulomb Problem by Using Laplace Transform and Convolution Integral

The exact pseudospin symmetry solutions of Dirac equation with position-dependent mass (PDM) Coulomb potential in the presence of Colulomb-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 given. By using Laplace convolution integral, the corresponding radial wave functions are presented in terms of confluent hypergeometric functions.     

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.     

Analytical Solutions of the Gravitational Field Equations in de Sitter and Anti-de Sitter Spacetimes

The generalized Laplace partial differential equation, describing gravitational fields, is investigated in de Sitter spacetime from several metric approaches—such as the Riemann, Beltrami, Börner-Dürr, and Prasad metrics—and analytical solutions of the derived Riccati radial differential equations are explicitly obtained. All angular differential equations trivially have solutions given by the spherical harmonics and all radial differential equations can be written as Riccati ordinary differential equations, which analytical solutions involve hypergeometric and Bessel functions. In particular, the radial differential equations predict the behavior of the gravitational field in de Sitter and anti-de Sitter spacetimes, and can shed new light on the investigations of quasinormal modes of perturbations of electromagnetic and gravitational fields in black hole neighborhood. The discussion concerning the geometry of de Sitter and anti-de Sitter spacetimes is not complete without mentioning how the wave equation behaves on such a background. It will prove convenient to begin with a discussion of the Laplace equation on hyperbolic space, partly since this is of interest in itself and also because the wave equation can be investigated by means of an analytic continuation from the hyperbolic space. We also solve the Laplace equation associated to the Prasad metric. After introducing the so called internal and external spaces—corresponding to the symmetry groups SO(3,2) and SO(4,1) respectively—we show that both radial differential equations can be led to Riccati ordinary differential equations, which solutions are given in terms of associated Legendre functions. For the Prasad metric with the radius of the universe independent of the parametrization, the internal and external metrics are shown to be of AdS-Schwarzschild-like type, and also the radial field equations arising are shown to be equivalent to Riccati equations whose solutions can be written in terms of generalized Laguerre polynomials and hypergeometric confluent functions.     

Axisymmetric wave propagation of thermoelastic transversely isotropic half-space under buried loading using potential functions

By virtue of a new scalar potential function and Hankel integral transforms, the wave propagation analysis of a thermoelastic transversely isotropic half-space is presented under buried loading and heat flux. The governing equations of the problem are the differential equations of motion and the energy equation of the coupled thermoelasticity theory. Using a scalar potential function, these coupled equations have been uncoupled and a six-order partial differential equation governing the potential function is received. The displacements, temperature, and stress components are obtained in terms of this potential function in cylindrical coordinate system. Applying the Hankel integral transform to suppress the radial variable, the governing equation for potential function is reduced to a six-order ordinary differential equation with respect to z. Solving that equation, the potential function and therefore displacements, temperature, and stresses are derived in the Hankel transformed domain for two regions. Using inversion of Hankel transform, these functions can be obtained in the real domain. The integrals of inversion Hankel transform are calculated numerically via Mathematica software. Our numerical results for displacement and temperature are calculated for surface excitations and compared with the results reported in the literature and a very good agreement is achieved.     

Scattering of a Klein-Gordon particle by a black hole

By using the curved space-time Klein-Gordon equation, the form of the wave function of a scalar particle near a nonrotating black hole is obtained. It is shown that although the radial wave function oscillates infinitely rapidly near the black hole, the probability density remains finite even on the event horizon. This is consistent with the fact that the Schwarzschild surface is nonsingular. An expression is given for the large angular momentum scattering differential cross section by comparing the asymptotic form of the radial wave equation with the corresponding Coulomb radial wave equation in ordinary quantum mechanics.     

弱光场下电子与库仑势散射的微扰解

外光场下电子与库仑势散射的schrodinger 方程可用Floque 分波法分离变量. 径向波动方程是一组无限祸合的二次线性微分方程组, 当弱外光场可视为微扰, 方程组将近似为二次常微分方程并且可积, 由此可得径向波函数、s 矩阵、截面. 无论何种极化或是否作偶极近似,共振谱线是普遍存在的, 井给出共振能量和强度的计算公式. 关键词：     

弱光场下电子与库仑势散射的微扰解

外光场下电子与库仑势散射的Schr?dinger方程可用Floquet分波法分离变量,径向波动方程是一组无限耦合的二次线性微分方程组,当弱外光场可视为微扰,方程组将近似为二次常微分方程并且可积,由此可得径向波函数、S矩阵、截面。无论何种极化或是否作偶极近似,共振谱线是普遍存在的,并给出共振能量和强度的计算公式。     

Determining the cutoff frequencies of weakly guiding optical fibres by the Laplace transform

We investigate the Laplace transform of the reduced radial Helmholtz equation for the electromagnetic fields in weakly guiding optical fibres. In the Laplace transform space we derive an integral condition for the cutoff frequencies of the LP modes. We apply our equation to several refractive index profiles of practical interest.