Rosen-MorseⅡ势函数的Klein-Gordon方程和Dirac方程束缚态的精确解

在标量势和矢量势相等的情形, 研究了Rosen-MorseⅡ势的相对论效应, 应用超对称和形状不变势方法通过求解Klein-Gordon方程和Dirac方程得到了束缚态能量本征值, 最后, 讨论了Rosen-MorseⅡ势的一种特殊情况.     

Rosen-Morse势阱中相对论粒子的束缚态

给出了具有Rosen-Morse型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 运用超对称量子力学和形不变性得到了束缚态能谱，通过变量代换求得波函数. 把上述方法推广到相对论量子力学. 关键词： Rosen-Morse势 Klein-Gordon方程 Dirac方程 束缚态     

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.     

相对论情况下赝自旋对称性势场中运动粒子的束缚态

在赝自旋对称性条件下,分别求解了在M rse型和Tan2(πηr)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.     

类Quesne环状球谐振子势场中的赝自旋对称性

提出了一种新的类Quesne环状球谐振子势,应用二分量方法求解1/2-自旋粒子满足的Dirac方程, Dirac哈密顿量由标量和矢量类Quesne环状球谐振子势构成.在Σ=S(r)+V(r)=0的条件下,得到了Dirac旋量波函数下分量的束缚态解和能谱方程, 显示出类Quesne环状球谐振子势场中的赝自旋对称性.讨论了束缚态波函数和能谱方程的有关性质. 关键词： 类Quesne环状球谐振子势 Dirac方程 赝自旋对称性 束缚态     

赝自旋对称性条件下四参量双原子分子势中相对论粒子的束缚态

在赝自旋对称性条件下,严格求解了四参量双原子分子势中运动粒子的s波Klein-Gordon方程和Dirac方程,并给出了相应的束缚态能谱和相对论性波函数.     

相对论类空方程

根据Dirac类空自洽性条件的思想,通过引入类空因子定义了类空波函数.它的物理部分与Bethe-Salpeter波函数相一致.利用普适的相互作用核的重排技术,导出了对于束缚态和散射态的相对论类空方程,并且将它们推广到多粒子的情形.也得到了束缚态类空波函数的归一化条件和散射态类空方程的非齐次项的解.因此,建立起了相对论类空方程体系.     

广义非对称Hartmann势Klein-Gordon方程的严格解(英文)

在标量势和矢量势相等的条件下,严格求解了在广义非对称Hartmann势场中粒子运动的Klein Gordon方程;并利用束缚态边界条件,获得了束缚态能谱表达式和由超几何函数表示出的波函数.     

一类相对论性非球谐振子系统的束缚态

给出了具有形式为12r²+A2r²的非球谐振子型标量势和矢量势 的相对论系 统在两种势相等的条件下三维Klein-Gordon方程，二维和三维Dirac方程的s波束缚态解. 关键词： 三维非球谐振子势 Klein-Gordon方程 Dirac方程 束缚态     

具有Coulomb势的N维Klein-Gordon方程的束缚态精确解

研究了在具有Coulomb势的N维Enclidean空间中运动的相对论性无自旋粒子的束缚态,给出了粒子的能级及相应径向波函数.所得结果适用于N维π介子原子.     

Pseudospin symmetric solutions of the Dirac equation with the modified Rosen—Morse potential using Nikiforov—Uvarov method and supersymmetric quantum mechanics approach

Employing the Pekeris-type approximation to deal with the pseudo-centrifugal term, we analytically study the pseudospin symmetry of a Dirac nucleon subjected to equal scalar and vector modified Rosen-Morse potential including the spin-orbit coupling term by using the Nikiforov-Uvarov method and supersymmetric quantum mechanics approach. The complex eigenvalue equation and the total normalized wave functions expressed in terms of Jacobi polynomial with arbitrary spin-orbit coupling quantum number k are presented under the condition of pseudospin symmetry. The eigenvalue equations for both methods reproduce the same result to affirm the mathematical accuracy of analytical calculations. The numerical solutions obtained for different adjustable parameters produce degeneracies for some quantum number.     

Bound-state solutions of the Dirac-Rosen-Morse potential with spin and pseudospin symmetry<Superscript>⋆</Superscript>

The energy spectra and the corresponding two-component spinor wave functions of the Dirac equation for the Rosen-Morse potential with spin and pseudospin symmetry are obtained. The s -wave ( k \kappa = 0 state) solutions for this problem are obtained by using the basic concept of the supersymmetric quantum mechanics approach and function analysis (standard approach) in the calculations. Under the spin symmetry and pseudospin symmetry, the energy equation and the corresponding two-component spinor wave functions for this potential and other special types of this potential are obtained. The extension of this result to the k \kappa 1 \neq 0 state is suggested.     

相对论谐振子下的自旋和赝自旋轨道伙伴态劈裂

通过求解具有谐振子势的径向标量势与矢量势的Dirac方程, 分别分析了原子核中赝自旋和自旋双重态的能级劈裂和波函数劈裂随着谐振子的振动频率参数ω和描述谐振子势阱底偏离中心参数r₀的变化关系. 研究发现, 这些参数对于赝自旋和自旋双重态的能级劈裂和波函数劈裂都有着显著的影响. 此外, 也研究了能级劈裂和波函数劈裂随着量子数的变化关系. 由于参数ω与核子数有关, 而参数r₀与形变核有关, 所以以这些参数为变量对于赝自旋劈裂和自旋劈裂的研究是有意义的, 研究的结果至少可以定性地应用到大部分原子核中.     

Spin symmetry in the relativistic modified Rosen-Morse potential with the approximate centrifugal term

By applying a Pekeris-type approximation to the centrifugal term, we study the spin symmetry of a Dirac nucleon subjected to scalar and vector modified Rosen-Morse potentials. A complicated energy equation and associated two-component spinors with arbitrary spin-orbit coupling quantum number k are presented. The positive-energy bound states are checked numerically in the case of spin symmetry. The relativistic modified Rosen-Morse potential cannot trap a Dirac nucleon in the limiting case α→ 0.     

包含非中心电耦极矩的环状非谐振子势场赝自旋对称性的三对角化表示

提出了一个包含非中心电耦极矩分量的环状非谐振子势模型,在能够负载Dirac波动算子三对角化表示的完全平方可积L~2空间讨论了这一势场的赝自旋对称性.利用三对角化矩阵方案,使得求解Dirac方程转换为寻求波函数展开系数满足的三项递推关系式.角向波函数和径向波函数分别以Jacobi多项式和Laguerre多项式表示.由径向分量展开系数递推关系式的对角化条件得到束缚态的能量谱,显示出这一势模型具有严格的赝自旋对称性     

Pseudoscalar Cornell potential for a spin- 1/2 particle under spin and pseudospin symmetries in 1 ＋ 1 dimension

The Cornell potential that consists of Coulomb and linear potentials has received a great deal of attention in particle physics. In this paper, we present the exact solutions of the Dirac equation with the pseudoscalar Cornell potential under spin and pseudospin symmetry limits. The energy eigenvalues and corresponding eigenfunctions are given in closed form.     

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.     

Dirac equation for the Hulthén potential within the Yukawa-type tensor interaction

Using the Nikiforov-Uvarov (NU) method, pseudospin and spin symmetric solutions of the Dirac equation for the scalar and vector Hulthén potentials with the Yukawa-type tensor potential are obtained for an arbitrary spin-orbit coupling quantum number κ. We deduce the energy eigenvalue equations and corresponding upper- and lower-spinor wave functions in both the pseudospin and spin symmetry cases. Numerical results of the energy eigenvalue equations and the upper- and lower-spinor wave functions are presented to show the effects of the external potential and particle mass parameters as well as pseudospin and spin symmetric constants on the bound-state energies and wave functions in the absence and presence of the tensor interaction.     

Exploration of Pseudospin Symmetry in the Resonant States

Taking ^120Sn as an example, we discuss the pseudospin symmetry in the single proton resonant states by examining the energies, widths and the wavefunctions. The information of the single proton resonant states in spherical nuclei are extracted from an analytic continuation in the coupling constant method within the framework of the self-consistent relativistic mean field theory under the relativistic boundary condition. We find small energy splitting in a pair of pseudospin partners in the resonant states. The lower components of the Dirac wavefunctions of a pseudospin doublet agree well in the region where nuclear potential dominates. It is concluded that the pseudospin symmetry is also well conserved for the resonant states in realistic nuclei.     

Solutions of Dirac Equation for Makarov Potential with Pseudospin Symmetry

The pseudospin symmetry in the Makarov potential is investigated systematically by solving the Dirac equation. The analytical solution forthe Makarov potential with pseudospin symmetry is obtained byNikiforov-Uvarov (N-U) method. The eigenfunctions and eigenenergies arepresented with equal mixture of vector and scalar potentials in oppositesigns, for which is exact.