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.     

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     

Classical mechanics in non-commutative phase space

In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space. The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity. First, new Poisson brackets have been defined in non-commutative phase space. They contain corrections due to the non-commutativity of coordinates and momenta. On the basis of this new Poisson brackets, a new modified second law of Newton has been obtained. For two cases, the free particle and the harmonic oscillator, the equations of motion are derived on basis of the modified second law of Newton and the linear transformation (Phys. Rev. D, 2005, 72: 025010). The consistency between both methods is demonstrated. It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space, but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative.     

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.     

The scattering states of the generalized Hulthén potential with an improved new approximate scheme to the centrifugal term

This paper finds the approximate analytical scattering state solutions of the arbitrary l-wave Schrdinger equation for the generalized Hulth’en potential by taking an improved new approximate scheme for the centrifugal term.The normalized analytical radial wave functions of the l-wave Schrdinger equation for the generalized Hulth’en potential are presented and the corresponding calculation formula of phase shifts is derived.Some useful figures are plotted to show the improved accuracy of the obtained results and two special cases for the standard Hulth’en potential and Woods-Saxon potential are also studied briefly.     

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.     

BmN (m=1-8)团簇结构和稳定性的密度泛函理论研究

使用泛函密度理论的B3LYP 方法,在6-311G*水平上对BmN（m=1-8）团簇的几何结构、电子结构、振动频率等进行了研究。结果表明,以Bm团簇作为设计母体,考虑在不同位置上结合N原子可以较快找到BmN类团簇基态结构;团簇的最稳定结构是平面结构,N原子倾向于在B团簇外端与两个B原子成键。通过对基态结构的平均束缚能和能量二次差分的计算,得到m=2和5的BmN团簇较为稳定。     

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.     

具有运动边界与含时频率的一类环状非球谐振子模型势的精确解(英文)

在球坐标系中研究了一类具有运动边界与含时频率的环状非球谐振子模型势的Schrdinger方程.应用坐标变换将运动边界转化为固定边界,从而获得了系统的精确波函数.研究表明,系统的角向波函数是一个推广的缔合勒让德多项式,径向波函数可以表示为贝赛耳函数.最后我们简单讨论了指数运动边界和指数含时频率这一特殊情况.     

双光子Tavis-Cummings模型中的量子纠缠

我们对两个全同二能级原子通过双光子跃迁与单模辐射场发生相互作用的Tavis-Cummings(T-C)模型中的量子纠缠特性进行了研究.通过数值计算与分析,结果表明:双光子T-C模型的量子纠缠比单光子T-C模型的量子纠缠要保持得好一些;另外分析了双光子T-C模型中原子间偶极-偶极相互作用强度系数、原子与场的耦合系数、光子数对两原子间纠缠特性与场熵的影响.