Wood-Saxon势中相对论粒子的束缚态

给出了具有Wood-Saxon型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解.     

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     

无反射势阱中相对论粒子的束缚态

给出了具有无反射势型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 关键词： 无反射势 Klein-Gordon方程 Dirac方程 束缚态     

具有P?schl-Teller型标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态

给出了具P?schl-Teller型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 关键词： P?schl-Teller势 Klein-Gordon方程 Dirac方程 束缚态     

四参数双原子分子势阱中相对论粒子的束缚态

给出了具有四参数双原子分子势型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 关键词： 四参数双原子分子势 Klein-Gordon方程 Dirac方程 束缚态     

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     

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     

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     

tan~2(πηr)型势阱中相对论粒子的束缚态

给出了具有tan2(πηr)型标量势和矢量势的KleinGordon方程和Dirac方程的s波束缚态解,并与无限深球方势阱的情况进行了比较. 关键词： tan~2(πηr)势 KleinGordon方程 Dirac方程 束缚态     

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     

Analytical solutions of the Dirac equation under Hellmann–Frost–Musulin potential

The approximate analytical solutions of the Dirac equation with Hellmann–Frost–Musulin potential have been studied by using the generalized parametric Nikiforov–Uvarov (NU) method for arbitrary spin–orbit quantum number k under the spin and pseudospin symmetries. The Hellmann–Frost–Musulin potential is a superposition potential that consists of Yukawa potential, Coulomb potential, and Frost–Musulin potential. As a particular case, we found the energy levels of the non-relativistic limit of the spin symmetry. The energy equation of Yukawa potential, Coulomb potential, Hellmann potential and Frost–Musulin potential are obtained. Energy values are generated for some diatomic molecules.     

Conservation laws and hierarchies of potential symmetries for certain diffusion equations

We show that the so-called hidden potential symmetries considered in a recent paper [M.L. Gandarias, New potential symmetries for some evolution equations, Physica A 387 (2008) 2234-2242] are ordinary potential symmetries that can be obtained using the method introduced by Bluman and collaborators [G.W. Bluman, S. Kumei, Symmetries and Differential Equations, Springer, New York, 1989; G.W. Bluman, G.J. Reid, S. Kumei, New classes of symmetries for partial differential equations, J. Math. Phys. 29 (1988) 806-811]. In fact, these are simplest potential symmetries associated with potential systems which are constructed with single conservation laws having no constant characteristics. Furthermore we classify the conservation laws for classes of porous medium equations, and then using the corresponding conserved (potential) systems we search for potential symmetries. This is the approach one needs to adopt in order to determine the complete list of potential symmetries. The provenance of potential symmetries is explained for the porous medium equations by using potential equivalence transformations. Point and potential equivalence transformations are also applied to deriving new results on potential symmetries and corresponding invariant solutions from known ones. In particular, in this way the potential systems, potential conservation laws and potential symmetries of linearizable equations from the classes of differential equations under consideration are exhaustively described. Infinite series of infinite-dimensional algebras of potential symmetries are constructed for such equations.     

基于原子晶体构型的高压固氩中的多体相互作用

X射线衍射实验显示固氩是面心立方(fcc)晶格结构,目前对晶体氩的研究只限于两体,三体以及四体相互作用势.本文利用多体展开方法和超分子单、双(三)重激发耦合簇理论(CCSD(T))对固氩fcc晶格结构的三体和四体的几何构型、几何参数、不同体积下所有三体和四体构型的势能以及各构型所占比例等几个方面进行了准确的量子化学计算.结果表明:所有三体构型中对总的三体势能贡献最大的是构型1、构型6、构型12和构型23;三体势及其交换部分和色散部分的计算结果与现有解析经验势在长程部分符合得非常好,但在短程部分有较小差异.所有的四体构形中对总的四体势能贡献最大的是构型1,构型2,构型4,构型5,构型7和构型8;四体势及其交换势部分和色散部分的计算结果尚无解析经验势可比较.利用这些特殊构型的相关数据并结合其它构型,可拟合出更准确的三体经验势函数及其参数,也为拟合四体经验势函数及其参数提供了重要的参考价值.     

基于原子晶体构型的高压固氩中的多体相互作用

X射线衍射实验显示固氩是面心立方(fcc)晶格结构,目前对晶体氩的研究只限于两体,三体以及四体相互作用势。本文利用多体展开方法和超分子单、双 (三)重激发耦合簇理论(CCSD(T))对固氩fcc晶格结构的三体和四体的几何构型、几何参数、不同体积下所有三体和四体构型的势能以及各构型所占比例等几个方面进行了准确的量子化学计算。结果表明:所有三体构型中对总的三体势能贡献最大的是构型1、构型6、构型12和构型23;对三体势及其交换部分和色散部分的计算结果与现有解析经验势在长程部分符合得非常好,但在短程部分有较小差异。所有的四体构形中对总的四体势能贡献最大的是构型1,构型2,构型4,构型5,构型7和构型8;对四体势及其交换势部分和色散部分的计算结果尚无解析经验势可比较。利用这些特殊构型的相关数据并结合其它构型,可拟合出更准确的三体经验势函数及其参数,也为拟合四体经验势函数及其参数提供了重要的参考价值。     

Eigen solutions of the D-dimensional Schrӧdinger equation with inverse trigonometry scarf potential and Coulomb potential

The approximate analytical solutions of the D-dimensional space of the Schrӧdinger equation is studied with a newly proposed potential model. The proposed potential is a combination of Coulomb potential and inverse trigonometry scarf-type potential. The energy equation and the corresponding wave function are obtained using parametric Nikiforov–Uvarov method. The energy equations for Coulomb potential and inverse trigonometry scarf-type potential are respectively obtained by changing the numerical values of the potential strengths. It is found that the results obtained are equivalent to that previously obtained for Hellmann potential which is a combination of Coulomb potential and Yukawa potential. It is also found that the results for inverse trigonometry scarf potential are equivalent to the results previously obtained for Yukawa potential. Also, the Onicescus information energy of a system under the influence of the newly proposed potential is investigated in detail.     

The Quasi-Exactly Solvable Problems in Relativistic Quantum Mechanics

We study the quasi-exactly solvable problems in relativistic quantum mechanics. We consider the problems for the two-dimensional Klein-Gordon and Dirac equations with equal vector and scalar potentials, and try to find the general form of the quasi-exactly solvable potential. After obtaining the general form of the potential, we present several examples to give the specific forms. In the examples, we show for special parameters the harmonic potential plus Coulomb potential, Killingbeck potential and a quartic potential plus Cornell potential are quasi-exactly solvable potentials.     

A Global Investigation About Hard Core Attractive Yukawa Approximation and Adhesive Hard Sphere Approximation for Structure of Colloidal Dispersion Systems

The accuracy of hard core attractive Yukawa (HCAY) potential and adhesive hard sphere (AH) potential in representing the structure factor of short range square well potential and Asakura and Oosawa (AO) depletion potential is examined by comparing theoretical predictions with the existing simulation data and the present numerical results from the non-linear optimized random phase approximation closure for Ornstein-Zernike equation. For the case of square-well (SW) potential, it is shown that the structure factor of HCAY potential based on a recently proposed semi-analytical expression for the radial distribution function can describe the structure factor of SW potential with reduced well width λ≤2 only if the reduced contact potential βε_SW≤0.25, while the analytical expression for the structure factor of AH potential under Percus-Yevick (PY) approximation completely fails for the case of λ>1.2. For the case of AO depletion potential, the domain of validity of both HCAY potential and AH potential is complementary. With the above analysis and considering the solid-liquid transition of the AH potential with an adhesive parameter τ below 1.31 cannot be predicted by modified weighted density approximation, the role played by the HCAY potential about the mapping manipulation should not be ignored.     

AlH+离子A2∏态势能函数的变分研究简

采用双原子分子离子XY+的能量自洽法(Energy-consistent-method for ion XY+,ECMI)研究了氢化铝离子AlH+激发态A2∏的解析势能函数,并与采用中性双原子分子势能函数Morse势和HuxleyMurrell-Sorbie(HMS)势分析该离子该电子态的势能行为的结果、基于实验的Rydberg-Klein-Ress(RKR)数据和MCSCF方法的理论研究结果进行了比较.结果表明,由ECMI方法得到的解析势能函数ECMI势明显优于Morse势和HMS势的表现及MCSCF方法的结果,与RKR数据符合得很好,并能得到RKR数据缺乏的离解区和渐近区数据以及正确的离解极限,而正确的全程势能数据对研究各种散射问题都是非常必要的.     

激光场中极化势对电子-氦原子散射影响

构建含有极化势的静电屏蔽势和单纯的静电屏蔽势这两种原子势模型,应用第二玻恩近似（SBA）理论,分别对激光场中电子-氦原子散射截面进行了理论计算。对比实验结果发现含有极化势的静电屏蔽势给出的结果与实验符合较好。表明极化势在激光辅助电子-原子散射中起着重要作用。     

激光场中极化势对电子-氦原子散射影响

构建含有极化势的静电屏蔽势和单纯的静电屏蔽势这两种原子势模型,应用第二玻恩近似(SBA)理论,分别对激光场中电子-氰原子散射截面进行了理论计算.对比实验结果发现含有极化势的静电屏蔽势给出的结果与实验符合较好.表明极化势在激光辅助电子-原子散射中起着重要作用.