变形对称双阱势的束缚态

从第一性原理出发，得到了变形对称双阱势模型的Schroedinger方程束缚态的精确解。应用得到的精确解，给出了对称双阱势和修正Roeschl—Tdler势的能谱和波函数。     

重离子碰撞中的对称势翻转

利用同位旋和动量相关的输运模型IBUU，以Sn,Sn同位素在低能与高能碰撞为例，在两种不同的对称势作用下，研究了重离子碰撞中的对称势翻转现象.我们发现从低能到高能在同位旋相分化、发射核子的中-质比、发射核子的双n/p比，中-质微分横向流观测量中均存在对称势翻转现象.对称势翻转效应的研究有利于确定对称能的密度依赖性. 关键词： 重离子碰撞 对称势翻转 对称能     

超对称WKB近似与一维无限深势阱

证明了一维无限深势阱为非形状不变势.采用超对称WKB近似,得到了一维无限深势阱的精确能谱公式.计算结果表明,把势场具有形状不变性作为超对称WKB近似能够给出精确能谱的充要条件,是一个过强的提法,需要加以弱化.     

含有非谐振势系统能谱的研究

非谐振势V(x)=λx4有着广泛的应用,对其能谱的研究有着重要的意义.采用超对称量子力学和变分法,求解含有非谐振势系统的能谱 关键词： 超对称量子力学 变分法 非谐振势     

阻尼作用下带对称双阱势的原子链中的洞孤子

采用多重尺度法,研究弱阻尼作用下带有对称双阱势的原子链,导出耗散型的非线性薛定谔方程,并对方程进行解析求解,给出阻尼作用下在链中传播的耗散型的洞孤子解.     

球形对称势的能谱计算

球形对称势的能谱计算,在物理学中有着极为重要的意义,对一般的球 形 对称势,扩展了移动1/K展开解法,对任意数量的n和l,准确地给出了截断到1/K 3 项的三级微扰论的结果;并以计算了Morse势、Screened Coulomb势的S态能谱。结果 表明,对于势变化趋势的缓慢情形,这种近似求解结果可靠,收敛良好。     

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.     

外力作用下反馈耦合布朗棘轮的定向输运

本文研究了处于外力作用下双阱棘轮势中两个反馈耦合布朗粒子的定向输运性能. 通过对过阻尼朗之万方程的数值求解, 详细讨论了外力、热噪声与势阱的不对称参数等对耦合布朗粒子的平均速度、 有效扩散系数及Pe数的影响. 研究发现, 平均速度随外力呈周期性的变化规律. 同时耦合系统存在最优噪声强度会使定向输运达到最强. 值得指出的是棘轮系统可通过改变双阱势的结构来获得较强的定向流. 关键词： 耦合布朗棘轮 外力 双阱棘轮势 平均速度     

中能重离子碰撞中的同位旋分馏过程

利用同位旋相关的量子分子动力学模型研究了中能重离子碰撞中同位旋分馏过程.研究结果表明自由粒子中质比与碎片中质比的比值即同位旋分馏强度灵敏地依赖于对称势,而对同位旋相关核子–核子碰撞截面的依赖很弱.同位旋分馏对对称势的灵敏主要来自于气相部分,而液相部分对对称势不够灵敏.气相部分灵敏地依赖于对称势是直接造成同位旋分馏强度对对称势灵敏的主要原因.同时还讨论了各种液相部分的取法,其结果表明不同取法对以上结论的影响不大.因此理论结果与实验数据可以直接比较从而提取对称势的知识.并对引发同位旋分馏的动力学的起因进行了分析和讨论.     

精确的量子化条件和不变量

提出并证明了一维量子系统和三维球对称量子系统的一个精确的量子化条件.在此精确量子化条件中, 除了通常的Nπ项外, 还有一积分项, 称为修正项. 发现该修正项正是在超对称量子力学中所谓的有形状不变势的量子系统的一个不变量，它不依赖于波函数的节点数.对这些系统, 可用基态能级和波函数确定此不变量的值, 从而由精确的量子化条件容易算出全部束缚态的能级. 计算得到能级的正确性又反过来验证了在有形状不变势的量子系统中此修正项确实是不变量.计算的有形状不变势的量子系统, 包括一维的有限方势阱、Morse势及其变形、R 关键词： 量子化条件 超对称量子力学 形状不变势 不变量     

Improved Five-Parameter Exponential-Type Potential Energy Model for Diatomic Molecules

The dissociation energy and equilibrium bond length as explicit parameters are used to establish an improved five-parameter exponential-type potential energy model for diatomic molecules. We demonstrate that the five-parameter exponential-type potential is identical to the Tietz potential for diatomic molecules. It is observed that the improved five-parameter exponential-type potential can well model the internuclear interaction potential energy curve for the ground electronic state of the carbon monoxide molecule by the utilization of the experimental values of three molecular constants.     

Identity for the Exponential-Type Molecule Potentials and the Supersymmetry Shape Invariance

The identity and the supersymmetry shape invariance for a class of exponential-type molecule potentials are studied by introducing a deformed five-parameter exponential-type potential (DFPEP) and via the multi-parameter deformations. It has been shown that the DFPEP is a shape-invariant potential with a translation of parameters. By making use of the shape invariance approach, the exact energy levels are determined for the bound states with zero angular momentum. A class of molecule potentials and their exact energy spectra for the zero angular momentum states are reduced from the DFPEP and a general energy spectrum formula, respectively. The interrelations for some molecule potentials are also discussed.     

Point Canonical Transformation for Solving Five-Parameter Exponential-Type Potential

Using the approach of mapping of shape invariant potentials under point canonical transformations, the energy spectra and wave functions are most easily determined for the bound states of the five-parameter exponential-type potential with a little extra effort.     

An Algebraic Approach to the Generalized Symmetrical Double-Well Potential

We have obtained the energy eigenvalues and the corresponding eigenfunctions for the generalized double-well potential in the non-relativistic Schr?dinger equation. We have calculated the creation and annihilation operators directly from the eigenfunction and we have shown these operators satisfy the commutation relation of the SU(2) group. We have expressed the Hamiltonian in terms of the su(2) algebra. Some interesting result including the standard symmetrical double-well potential, reflectionless-type potential and V ₀tanh ²(r/d) potential are also discussed.     

A mechanistic model of mid-latitude decadal climate variability

A simple heuristic model of coupled decadal ocean-atmosphere modes in middle latitudes is developed. Previous studies have treated atmospheric intrinsic variability as a linear stochastic process modified by a deterministic coupling to the ocean. The present paper takes an alternative view: based on observational, as well as process modeling results, it represents this variability in terms of irregular transitions between two anomalously persistent, high-latitude and low-latitude jet-stream states. Atmospheric behavior is thus governed by an equation analogous to that describing the trajectory of a particle in a double-well potential, subject to stochastic forcing. Oceanic adjustment to a positional shift in the atmospheric jet involves persistent circulation anomalies maintained by the action of baroclinic eddies; this process is parameterized in the model as a delayed oceanic response. The associated sea-surface temperature anomalies provide heat fluxes that affect atmospheric circulation by modifying the shape of the double-well potential. If the latter coupling is strong enough, the model’s spectrum exhibits a peak at a periodicity related to the ocean’s eddy-driven adjustment time. A nearly analytical approximation of the coupled model is used to study the sensitivity of this behavior to key model parameters.     

Six—Parameter Exponential—Type Potential and the Identity for the Exponential—Type Potentials

We propose a six-parameter exponential-type potential (SPEP),which has been shown to be a shapeinvariant potential with a translation of parameters.For this reducible potential,the exact energy levels are obtained by using the supersymmetric shape invariance technique.Choosing appropriate parameters,four classes of exponential-type potentials and their exact energy spectra are reduced from the SPEP and a general energy level formula,respectively.Each class shows the identity except for the different definitions of parameters.     

Nonlinear Transport in Hydrogen-Bonded Systems with Asymmetric Double-Well Potential

We study the nonlinear transport and the motion of the bell-shape soliton in hydrogen-bonded chains with asymmetric double-well potential, based on the new two-component soliton model. Solution, momentum, effective mass, width and energy of bell-shape soliton are found. The theoretical reasults are estimated and compared with experimental ones. The agreement between them is good.     

Localization or tunneling in asymmetric double-well potentials

An asymmetric double-well potential is considered, assuming that the wells are parabolic around the minima. The WKB wave function of a given energy is constructed inside the barrier between the wells. By matching the WKB function to the exact wave functions of the parabolic wells on both sides of the barrier, for two almost degenerate states, we find a quantization condition for the energy levels which reproduces the known energy splitting formula between the two states. For the other low-lying non-degenerate states, we show that the eigenfunction should be primarily localized in one of the wells with negligible magnitude in the other. Using Dekker’s method (Dekker, 1987), the present analysis generalizes earlier results for weakly biased double-well potentials to systems with arbitrary asymmetry.     

Wronskian Approach and One-Dimensional Schrodinger Equation with Double-Well Potential

A Wronskian determinant approach is suggested to study the energy and the wave function for onedimensional Schrodinger equation. An integral equation and its corresponding Green function are constructed. As an example, we employed this approach to study the problem of double-well potential with strong coupling. A series of expansion of ground state energy up to the second order approximation of iterative procedure is given.     

A GENERATION OF EXACTLY SOLVABLE ANHARMONIC SYMMETRIC OSCILLATORS

Using the ideas of supersymmetric quantum mechanics, we exactly solve a continuous family of anharmonic potentials, which are the supersymmetric partners of the linear harmonic oscillators. The family includes a series of potentials in which the excited-state energy is the same as that of the harmonic oscillators, but the ground-state energy can be any value lower than the excited states. The shape of the potential is variable, which includes the double-well and triple-well potentials. All the potentials obtained in this paper are free of singularities, and the supersymmetry of the solutions is unbroken.