Approximate solutions of Schrdinger equation for Eckart potential with centrifugal term

The approximate analytical solutions of the Schrdinger equation for the Eckart potential are presented for the arbitrary angular momentum by using a new approximation of the centrifugal term. The energy eigenvalues and the corresponding wavefunctions are obtained for different values of screening parameter. The numerical examples are presented and the results are in good agreement with the values in the literature. Three special cases, i.e., s-wave, ξ = λ = 1, and β = 0, are investigated.     

Bound states of the SchrSdinger equation for the PSschl-Teller double-ring-shaped Coulomb potential

Poschl-Teller double-ring-shaped Coulomb （PTDRSC） potential, the Coulomb potential surrounded by PSschl- Teller and double-ring-shaped inversed square potential, is put forward. In spherical polar coordinates, PTDRSC potential has supersymmetry and shape invariance in φ,θ and τ coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schr6dinger equation with PTDRSC potential are presented. The normalized φ,θ angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of Laguerre polynomials are presented. Energy spectrum equations are obtained. Wave function and energy spectrum equations of the system are related to three quantum numbers and parameters of PTDRSC potential. The solutions of wave functions and corresponding eigenvalues are only suitable for the PTDRSC potential.     

Bound states of the Dirac equation with position-dependent mass for the Eckart potential

Studying with the asymptotic iteration method, we present approximate solutions of the Dirac equation for the Eckart potential in the case of position-dependent mass. The centrifugal term is approximated by an exponential form, and the relativistic energy spectrum and the normalized eigenfunctions are obtained explicitly.     

Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method

The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation,then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number nr causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function.     

利用Eckart势求玻尔哈密顿量的解析解(英文)

本文中讨论了用Eckart势求解玻尔哈密顿量的新方法.在γ不稳定和γ≈0的两种情况下,对于离心项l/β~2用近似表达的条件下,分别求解了玻尔哈密顿量的解析解,且通过N-U方法,利用Eckart势成功的获得了玻尔哈密顿量解析解的表达式.     

Bound state solutions of d-dimensional Schrödinger equation with Eckart potential plus modified deformed Hylleraas potential

We study the d-dimensional Schrödinger equation for Eckart plus modified deformed Hylleraas potentials using the generalized parametric form of Nikiforov-Uvarov method. We obtain energy eigenvalues and the corresponding wave function expressed in terms of Jacobi polynomial. We also discuss two special cases of this potential comprised of the Hulthen potential and the Rosen-Morse potential in three dimensions. Numerical results are also computed for the energy spectrum and the potentials.     

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     

Exact solutions of the Klein--Gordon equation with Makarov potential and a recurrence relation

In this paper, the Klein--Gordon equation with equal scalar and vector Makarov potentials is studied by the factorization method. The energy equation and the normalized bound state solutions are obtained, a recurrence relation between the different principal quantum number n corresponding to a certain angular quantum number \ell is established and some special cases of Makarov potential are discussed.     

Analytical Approximate Solution of SchrSdinger Equation in D Dimensions with Quadratic Exponential-Type Potential for Arbitrary/-State

We present the bound state solution of Schr6dinger equation in D dimensions for quadratic exponential-type potential for arbitrary l-state. We use generalized parametric Nikiforov-Uvarov method to obtain the energy levels and the corresponding eigenfunction in dosed form. We also compute the energy eigenvalues numerically.     

具有Wood-Saxon势的Dirac方程的束缚态

给出了具有一维Wood-Saxon型标量势大于或等于其矢量势时的Dirac方程的s波束缚态解. 关键词： Wood-Saxon势 Dirac方程 束缚态 精确解     

Hulthen势的微扰计算(英文)

运用一种选择性的近似方法解Hulthen势的薛定谔方程,对于各种本征态的束缚态能量计算到二级近似,并且相应的波函数计算到一级近似.这种微扰方法也可应用于原子物理的其它领域.     

具有Eckart势的Schrödinger方程的任意l波解析解

使用完全量子化规则计算了具有离心项的Eckart势,根据动量积分 和Greene-Aldrich近似化条件,得到了系统的任意l波Schrödinger方程的解析解．讨论了：(1) 基态和激发态下,势能范围参数λ和势阱深度η对具有不同角动量量子数的能量本征值的影响;(2) 径向量子数n和角动量量子数l与能量本征值的关系．     

具有Eckart势的Schrödinger方程的任意l波解析解

使用完全量子化规则计算了具有离心项的Eckart势,根据动量积分 和Greene-Aldrich近似化条件,得到了系统的任意l波Schrödinger方程的解析解．讨论了：(1) 基态和激发态下,势能范围参数λ和势阱深度η对具有不同角动量量子数的能量本征值的影响;(2) 径向量子数n和角动量量子数l与能量本征值的关系．     

具有一维Coulomb型对称势Dirac方程的精确解

在标量势大于矢量势的情况下,一维Dirac方程的束缚态能级是二重简并的.任意两个不同能量本征值的波函数和同一能量本征值的两个波函数都是相互正交的.对于纯标量场,存在零能量束缚态,存在分数电荷 关键词： Coulomb型对称势 Dirac方程 束缚态 分数电荷     

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     

Approximate symmetry reduction for perturbed nonlinear SchrSdinger equation

We investigate the one-dimensional nonlinear SchrSdinger equation with a perturbation of polynomial type. The approximate symmetries and approximate symmetry reduction equations are obtained with the approximate symmetry perturbation theory.     

Approximate solutions of Klein-Gordon equation with improved Manning-Rosen potential in D-dimensions using SUSYQM

In this paper, we present solutions of the Klein–Gordon equation for the improved Manning–Rosen potential for arbitrary l state in d-dimensions using the supersymmetric shape invariance method. We obtained the energy levels and the corresponding wave functions expressed in terms of Jacobi polynomial in a closed form for arbitrary l state. We also calculate the oscillator strength for the potential.     

Manning-Rosen标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态

给出了具有Manning-Rosen型标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态解，其解可用超几何函数表示. 关键词： Manning-Rosen势 Klein-Gordon方程 Dirac方程 束缚态