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     

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     

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     

开放Ⅴ型系统相对位相对LWI增益瞬态演化的影响

数值计算具有自发辐射诱导相干性的开放V型三能级原子系统密度矩阵运动方程,分析无反转激光(LWI)增益的瞬态演化.结果表明:无论是否存在非相干抽运,探测场和驱动场间的相对位相(Ф)对增益的瞬态演化都有显著的影响;通过选择Ф的取值可以获得更大的瞬态和稳定增益;不存在非相干抽运时,系统达到瞬态增益最大值及获得增益稳定值所需要的时间更长,演化过程中振荡幅度更大,获得的增益更大;原子退出速率r₀(原子注入速率比S)的变化将使增益瞬态演化的具体过程发生改变,在r₀(S)的一定取值范围内,瞬态和稳定增益随S(r₀)的增大而增大.     

环形非球谐振子标量势与矢量势的Klein-Gordon和Dirac方程的束缚态

通过求解环形非球谐振子势的 Klein-Gordon 和 Dirac方程,给出了束缚态波函数与能量方程的精确解,并指出非相对论Schr?dinger方程与具有相等标量势和矢量势的Klein-Gordon 方程以及Dirac方程之间具有数学结构上的等价性。     

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     

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     

高次正幂与逆幂势函数的叠加的径向薛定谔方程的解析解

当薛定谔方程中出现高次非谐振子势，电偶极矩势，分子晶体势，极化等效势等高次正幂与逆幂势函数以及它们的叠加时，薛定谔方程的求解变得非常复杂，采用奇点邻域附近的级数解法与求解渐近解相结合，在多种相互作用幂函数紧密耦合的条件下，得到势函数为V(r)=a₁r⁶+a₂r²+a₃r^{-4关键词： 级数解法 幂势函数 径向波函数 渐近解}     

环形非球谐振子势Klein-Gordon方程的束缚态

用分离变量方法讨论了在环形非球谐振子标量势和矢量势相等条件下的Klein-Gordon方程的束缚态解.给出了用广义连带勒让得多项式表示的归一化角向波函数和用合流超几何函数表示的归一化径向波函数，获得了精确的束缚态能谱方程. 关键词： 环形非球谐振子势 Klein-Gordon方程 束缚态     

新环状非球谐振子势的Dirac方程束缚态解

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Dirac 方程的束缚态解.通过分离变量得到Dirac方程相应的角向方程和径向方程,得出了用广义连带勒让德多项式表示的归一化角向波函数和用合流超几何函数表示的归一化径向波函数;获得了精确的束缚态能谱方程并对结果作适当讨论与结论.     

(1+1)-Dirac Particle with Position-Dependent Mass in Complexified Lorentz Scalar Interactions: Effectively $\mathcal{PT}$ -Symmetric

The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the “quasi-parity” on the Dirac particles’ spectra is also studied. A Dirac particle with PDM and complexified scalar interactions of the form S(z)=S(x−ib) (an inversely linear plus linear, leading to a symmetric oscillator model), and S(x)=S _r (x)+iS _i (x) (a -symmetric Scarf II model) are considered. Moreover, a first-order intertwining differential operator and an η-weak-pseudo-Hermiticity generator are presented and a complexified -symmetric periodic-type model is used as an illustrative example.     

The Klein-Gordon equation with the Kratzer potential in <Emphasis Type="Italic">d</Emphasis> dimensions

We apply the Asymptotic Iteration Method to obtain the bound-state energy spectrum for the d-dimensional Klein-Gordon equation with scalar S(r) and vector potentials V(r). When S(r) and V(r) are both Coulombic, we obtain all the exact solutions; when the potentials are both of Kratzer type, we obtain all the exact solutions for S(r) = V(r); if S(r) > V(r) we obtain exact solutions under certain constraints on the potential parameters: in this case, a possible general solution is found in terms of a monic polynomial, whose coefficients form a set of elementary symmetric polynomials.      

Hypervirial perturbation theory for eigenenergies for two types of atomic potentials

Eigenenergies are calculated for the potentialsV ₁(r)=−(a/r)[1+(1+br)e^−2br ] andV ₂(r)=−(v/r)[1 −λr(1−Z ⁻¹)(1+λr)⁻¹], using renormalized series technique. Accurate results produced here for various eigenstates agree with those available in the literature.     

Scalar Charged Particle in Presence of Magnetic and Aharonov–Bohm Fields Plus Scalar–Vector Killingbeck Potentials

The generalized form of Killingbeck potential is an attractive Coulomb term plus a linear term and a harmonic oscillator term, i.e. ?a/r + br + λr ², which has a useful application in quarkonium spectroscopy. The ground state energy with the corresponding wave function are obtained for any arbitrary m-state in two-dimensional Klein–Gordon equation with equal mixture of scalar–vector Killingbeck potentials in the presence of constant magnetic and singular Ahoronov–Bohm flux fields perpendicular to the plane where the interacting charged particle is confined. The analytical exact iteration method is used in our solution. We obtain the energy eigensolutions for particle and antiparticle corresponding to S(r) = V(r) and S(r) = ?V(r) cases, respectively. Some special cases like the Coulomb, harmonic oscillator potentials and the nonrelativistic limits are found in presence and absence of external fields.     

Analysis of the Initial Slope of the Small‐Angle Scattering Correlation Function of a Particle

The small‐angle scattering correlation function of a particle γ(r) results from scattering experiments. This function possesses a well‐defined slope γ′(0) at the origin. This slope is defined by the particle volume V and the whole surface area S of the particle via γ′(0) = –S/(4V). In this paper it is demonstrated that this slope defines the mean chord length of the particle, . This theorem involves non‐convex particles, especially the case of particles with hollow parts. Consequently, for a large class of particle shapes the mean chord length is defined in terms of V and S. This extension of the Cauchy theorem is developed by closer analysis of the set covariance C(r), of the small‐angle scattering correlation function γ(r), and of the so‐called linear erosion P(r) near the origin r→0. The cases of a single hollow sphere, of two touching spheres, and of the single hollow cylinder are discussed.     

Estimates of the number of quantal bound states in one and three dimensions

Using the relation between the number of bound states and the number of zeros of the radial eigen-functionψ(r), or equivalently, that ofφ(r)=rψ(r) in the range 0⩽r⩽∞, the upper bounds on the number of bound states generated by potentialV(r) in different angular momentum channels are obtained in three dimension. Using a similar procedure, the upper bound on the number of bound states in one dimension is also deduced. The analysis is restricted to a class of potentials for whichE=0 is the threshold. By taking a number of specific examples, it is demonstrated that both in one and three dimensions, the estimate of the upper bound obtained by this procedure is very close to or equal to the exact number of bound states. The correlation of the present method with the Levison’s theorem and WKB approximation is discussed.     

Nuclear mean fields through self-consistent semiclassical calculations

Semiclassical expansions derived in the framework of the Extended Thomas-Fermi approach for the kinetic energy density τ( r) and the spin-orbit density J( r) as functions of the local density ρ( r) are used to determine the central nuclear potentials V _n( r) and V _p( r) of the neutron and proton distribution for effective interactions of the Skyrme type. We demonstrate that the convergence of the resulting semiclassical expansions for these potentials is fast and that they reproduce quite accurately the corresponding Hartree-Fock average fields. Received: 12 February 2000 / Accepted: 14 March 2002     

Integral equation theory of the exchange potential,HOMO–LUMO properties,and sum rules for the exchange-correlation force

Recently, a formally exact integral equation for the exchange potential V _x(r) has been presented by the authors. In the admittedly simplistic limit in which Slater–Kohn–Sham and Hartree–Fock determinants become equal, this integral equation reduces to that given by Della Sala and Görling. Here, a proposal is made to relate, but now approximately, the formally exact equation for V _x(r) to HOMO–LUMO properties. The addition of a correlation contribution V _c(r) to V _x(r), the sum being the exchange-correlation potential V _xc(r), is finally considered, some exact properties and especially sum rules for the force ??V _xc/?r being the focus.