The Relativistic Scattering States of the Hulthén Potential with an Improved New Approximate Scheme to the Centrifugal Term

The approximately analytical scattering state solutions of the l-wave Klein-Gordon equation with the unequal scalar and vector Hulthén potentials are carried out by an improved new approximate scheme to the centrifugal term. The normalized analytical radial wave functions of the l-wave Klein-Gordon equation with the mixed Hulthén potentials are presented and the corresponding calculation formula of phase shifts is derived. It is well shown that the energy levels of the continuum states reduce to those of the bound states at the poles of the scattering amplitude. Some useful figures are plotted to show the improved accuracy of our results and two special cases for s-wave (l=0) and for l=0 and equal scalar and vector Hulthén potentials are also studied briefly.     

具有Manning-Rosen标量势与矢量势的Klein-Gordon方程的任意l波束缚态近似解析解

在球坐标系中研究了具有离心项的Manning-Rosen型标量势与矢量势的Klein-Gordon方程.在标量势等于矢量势的条件下,运用合适的指数近似将具有离心项的径向Klein-Gordon方程转化成超几何微分方程,从而获得了系统的任意l波Klein-Gordon方程解析束缚态径向波函数.最后,对l=0和α=0或1两种特殊情况进行了简单讨论. 关键词： Manning-Rosen势 Klein-Gordon方程 束缚态 近似解析解     

The scattering of the Manning-Rosen potential with centrifugal term

In this Letter the approximately analytical scattering state solutions of the l-wave Schrödinger equation for the Manning-Rosen potential are carried out by a proper approximation to the centrifugal term. The normalized radial wave functions of l-wave scattering states are presented and the calculation formula of phase shifts is derived. It is well shown that the poles of the S-matrix in the complex energy plane correspond to bound states for real poles and scattering states for complex poles in the lower half of the energy plane. We consider and verify two special cases: the l=0 and the s-wave Hulthén potential.     

Arbitrary Wave Relativistic Bound State Solutions for the Eckart Potential

The approximately analytical bound state solutions of the l-wave Klein-Gordon and k-state Dirac equations with the mixed Eckart potentials are carried out by a proper approximation to the centrifugal term. The analytical radial wave functions of the l-wave Klein-Gordon and k-state Dirac equations with the mixed Eckart potentials are presented and the corresponding energy equations are derived. Two special cases for k=1 and for k=1 and β=0 are studied briefly. Finally, we also verify the rationality of this approximation.     

Approximately analytical solutions of the Manning-Rosen potential with the spin-orbit coupling term and spin symmetry

In this Letter the approximately analytical bound state solutions of the Dirac equation with the Manning-Rosen potential for arbitrary spin-orbit coupling quantum number k are carried out by taking a properly approximate expansion for the spin-orbit coupling term. In the case of exact spin symmetry, the associated two-component spinor wave functions of the Dirac equation for arbitrary spin-orbit quantum number k are presented and the corresponding bound state energy equation is derived. We study briefly two special cases; the general s-wave problem and the equal scalar and vector Manning-Rosen potential.     

Continuum states of modified Morse potential

Using a proper approximation scheme to the centrifugal term, we study any l-wave continuum states of the Schrdinger equation for the modified Morse potential. The normalised analytical radial wave functions are presented, and a corresponding calculation formula of phase shifts is derived. It is shown that the energy levels of the continuum states reduce to those of the bound states at the poles of the scattering amplitude. Some numerical results are calculated to show the accuracy of our results.     

Approximate analytical solution of continuous states for the l-wave Schrödinger equation with a diatomic molecule potential

The continuous states of the l-wave Schrödinger equation for the diatomic molecule represented by the hyperbolical function potential are carried out by a proper approximation scheme to the centrifugal term. The normalized analytical radial wave functions of the l-wave Schrödinger equation for the hyperbolical function potential are presented and the corresponding calculation formula of phase shifts is derived. Also, we interestingly obtain the corresponding bound state energy levels by analyzing analytical properties of scattering amplitude.     

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     

Path integral treatment for the generalized Ginocchio potentials

The solution for the generalized Ginocchio potentials is exactly constructed by the path integral approach combined to the summation of the spectral representation. The energy spectrum and the wave functions of bound and scattering states are explicitly evaluated. The scattering functionS _l for each angular momentuml is also deduced.     

The arbitrary l continuum states of the hyperbolic molecular potential

Within the framework of partial-wave method, we study in this Letter the arbitrary l continuum states of the Schrödinger equation with the hyperbolic molecular potential in terms of an improved approximation to the centrifugal term. We present the normalized radial wave functions and obtain analytical formula of phase shifts. In addition, the corresponding bound states are also discussed by studying the analytical properties of the scattering amplitude. We calculate the energy spectra and scattering phase shifts by the improved, previous approximations and the accurate methods, respectively and find that the improved approximation is better than the previous one since the present results are in better agreement with the accurate ones.     

Solutions of Dirac equations with the Pöschl-Teller potential

By using the basic concepts of the supersymmetric quantum mechanics formalism and the function analysis method, we solve the Dirac equation with vector and scalar potentials and obtain the bound-state solutions for the nuclei in the relativistic P?schl-Teller potential. All of the analyses are prepared under the conditions of the exact spin symmetry and pseudospin symmetry. The exact energy equation and corresponding two-component spinor wave functions for s -wave bound states are obtained analytically.     

库仑势加新环形势的相对论束缚态

在标量势等于矢量势的条件下，获得了库仑势加新环形势的Klein-Gordon方程和Dirac方程的束缚态的精确解. 对于Klein-Gordon方程，获得了精确的能谱方程和归一化的波函数. 对于Dirac方程，给出了精确的能谱方程和归一化的旋量波函数. 关键词： 库仑势加新环形势 束缚态 精确解     

Approximate analytical solutions of scattering states for Klein-Gordon equation with Hulthén potentials for nonzero angular momentum

In this paper, using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Klein-Gordon equation with the vector and scalar Hulthén potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of t-waves scattering states are presented. The normalized wave functions expressed in terms of hypergeometric functions of scattering states on the “k/2π scale” and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solution is discussed.      

在赝自旋对称性势场中运动的相对论粒子的束缚态

在赝自旋对称性条件下,分别求解了在Kratzer型、Hulthén型和Poschl-Teller型标量势与矢量势场中运动的相对论粒子的Klein-Gordon方程和Dirac方程,给出了它们的束缚态能谱和相对论性波函数.     

Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential

The Klein-Gordon equation in D-dimensions for a recently proposed ring-shaped Kratzer potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound states and the corresponding wave functions of the Klein-Gordon are obtained in the presence of the non-central equal scalar and vector potentials. The results obtained in this work are more general and can be reduced to the standard forms in three dimensions given by other works.      

Levinson's theorem for the Klein-Gordon equation in one dimension

In terms of the modified Sturm-Liouville theorem, the Levinson theorem for the one-dimensional Klein-Gordon equation with a symmetric potential V(x) is established. It is shown that the number N₊ (N_-) of bound states with even (odd) parity is related to the phase shift of the scattering states with the same parity at zero momentum as and The solution of the one-dimensional Klein-Gordon equation with the energy M or -M is called as a half bound state if it is finite but does not decay fast enough at infinity to be square integrable. Received 22 December 1999     

具有n维氢原子型标量势与矢量势的Klein-Gordon方程的束缚态

研究了具有n维氢原子型标量势和矢量势的Klein-Gordon方程的束缚态性质，获得了束 缚态的精确解-给出了精确的能谱方程和归一化的解析波函数，推导出径向平均值的两个递 推关系和部分低幂次径向平均值的解析表达式- 关键词： n维氢原子势 Klein-Gordon方程 束缚态 精确解     

Bound state solution of the Klein-Gordon equation for vector and scalar Hellmann plus modified Kratzer potentials

In this study, the analytical solutions of the Klein–Gordon equation for any l states of the scalar and vector Hellmann plus modified Kratzer potential are derived by using an approximation method to the centrifugal potential term. The analytical expressions for eigenvalues and corresponding normalized eigenfunctions of the spin-zero particle have been estimated by using the parametric Nikiforov-Uvarov method. The solution for the radial part of the Klein-Gordon equation is formulated in terms of the generalized Jacobi polynomials. The energy state equation and the wave function for special cases are in good agreement with the previous literature. In addition, we have measured the numerical results of the energy eigenvalues and also the trend of the eigenvalues concerning of different potential parameters have been plotted. Furthermore, it was shown that the energy levels E and quantum numbers n and l are inversely proportional to each other.     

Hartmann势加新环型势的相对论束缚态解(英文)

在矢势与标势相等的情况下,对Hartmann势加新环型势的Klein-Gordon方程精确求解.给出了归一化的角向和径向波函数,同时获得了能谱方程.     

Any l-state solutions of the Klein-Gordon equation with the generalized Hulthén potential

We present analytical solutions of the Klein-Gordon equation with non-zero l values for the general Hulthén potential within the framework of an approximation to the centrifugal potential for any l-states. The explicit expressions of bound state energy eigenvalues and eigenfunctions are derived. Three special cases, s-wave, standard Hulthén potential and ground state are discussed.