Massive Dirac particles based on gapped graphene with Rosen-Morse potential in a uniform magnetic field

We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an external uniform magnetic field.In order to describe the corresponding structure,we consider the propagation of electrons in graphene as relativistic fermion quasi-particles,and analyze it by the wave functions of two-component spinors with pseudo-spin symmetry using the Dirac equation.Next,to solve and analyze the Dirac equation,we obtain the eigenvalues and eigenvectors using the Legendre differential equation.After that,we obtain the bounded states of energy depending on the coefficients of Rosen-Morse and magnetic potentials in terms of quantum numbers of principal n and spin-orbit k.Then,the values of the energy spectrum for the ground state and the first excited state are calculated,and the wave functions and the corresponding probabilities are plotted in terms of coordinates r.In what follows,we explore the band structure of gapped graphene by the modified dispersion relation and write it in terms of the two-dimensional wave vectors K_(x) and K_(y).Finally,the energy bands are plotted in terms of the wave vectors K_(x) and K_(y) with and without the magnetic term.

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 twocomponent 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 a →0.

Continuum states of modified Morse potential

Using a proper approximation scheme to the centrifugal term, we study any l-wave continuum states of the Schrodinger 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.

Bound State Solutions of Schrodinger Equation for Generalized Morse Potential with Position-Dependent Mass

The effective mass one-dimensional Schroedinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the constant mass case. Energy eigenvalues are computed numerically for some diatomic molecules. They are in agreement with the ones obtained before.

Discrete breathers in a model with Morse potentials

Under harmonic approximation, this paper discusses the linear dispersion relation of the one-dimensional chain. The existence and evolution of discrete breathers in a general one-dimensional chain are analysed for two particular examples of soft （Morse） and hard （quartic） on-site potentials. The existence of discrete breathers in one-dimensional and two-dimensional Morse lattices is proved by using rotating wave approximation, local anharmonic approximation and a numerical method. The localization and amplitude of discrete breathers in the two-dimensional Morse lattice with on-site harmonic potentials correlate closely to the Morse parameter a and the on-site parameter к.

Binding energy of the donor impurities in GaAs-Ga_(1-x)Al_xAs quantum well wires with Morse potential in the presence of electric and magnetic fields

The behavior of a donor in the GaAs–GaAlAs quantum well wire represented by the Morse potential is examined within the framework of the effective-mass approximation. The donor binding energies are numerically calculated for with and without the electric and magnetic fields in order to show their influence on the binding energies. Moreover, how the donor binding energies change for the constant potential parameters(De, re, and a) as well as with the different values of the electric and magnetic field strengths is determined. It is found that the donor binding energy is highly dependent on the external electric and magnetic fields as well as parameters of the Morse potential.

The bound state solution for the Morse potential with a localized mass profile

We investigate an analytical solution for the Schr o¨dinger equation with a position-dependent mass distribution, with the Morse potential via Laplace transformations. We considered a mass function localized around the equilibrium position.The mass distribution depends on the energy spectrum of the state and the intrinsic parameters of the Morse potential. An exact bound state solution is obtained in the presence of this mass distribution.

The rotating Morse potential energy eigenvalues solved by using the analytical transfer matrix method

We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix（ATM） method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris approximation,which can be used to calculate the energies of higher rotational states from the energies of lower states.The energies of rotational states of the hydrogen molecule are calculated by the ATM condition,and comparison of the results with those from the hypervirial perturbation method reveals that the accuracy of the approximate expression of Pekeris for the eigenvalues of the rotating Morse potential can be improved substantially in the framework of supersymmetric quantum mechanics.

A Generalized Frenkel-Kontorova Model with Morse Potentials

A generalized Frenkel-Kontorova model with the Morse potentials is studied.The phase diagram reflects the nonlinear nature of the Morse potential.The correspondences of the ground states and the orbits of the area-preserving map are studied numerically.Our results present a better simulation to the real systems.

Unbiased Fuzzy Global Optimization of Morse Clusters with Short-Range Potential for N≤400

Global optimization of Morse clusters with shortrange potential is a great challenge.Here,we apply our recently developed unbiased fuzzy global optimization method to systematically study Morse clusters with the potential rangeρ=14 and the number of atoms N up to 400.All the putative global minima reported in the literature have been successfully reproduced with relatively high success ratios.Compared to the available results for N≤240 and several larger Morse clusters,new global minima(and local minima)with lower energies have been found out for N=164,175,188,193,194,197,239,246,260,318,and 389.Clusters with magic numbers are figured out through fitting the size-dependent global minimum energies.The cluster structures tend to be close-packed for short-range potential with large N.

Feynman Perturbation Series for the Morse Potential

In this paper we give an alternative treatment of the Schrodinger equation with the Morse potential, which based on the exact summation of the Feynman perturbation series in its original form. Using Fourier transform we establish a recurrence equation between terms of the perturbation series. Finally, by the inverse Fourier transform and some technical tools of the ordinary differential equations of the second order, we can compute the exact sum of the perturbation series which is the Green’s function of the problem.

Wave Functions for Time-Dependent Morse Potentials

The one dimensional Schrodinger equation associated with a time-dependent Morse potentials is studied. We use the invariant operator method （Lewis and Riesenfeld） to obtain approximate solution of the Schrodinger equation in terms of solution of second order ordinary differential equation describes the amplitude of the Morse potentials.

Hellmann-广义Morse势Schrdinger方程的散射态解

基于对离心项的恰当近似,本文研究了具有Hellmann-广义Morse势的薛定谔方程的散射态问题,得到了归一化的散射态波函数和相应的散射相移,同时利用散射振幅解析性质获得了束缚态能级满足的方程。最后,数值求解特征值方程并和真实值数据进行了对比。

一维Morse势的Dirac方程的束缚态

在标量型和矢量型Morse势相等的条件下 ,给出了Dirac方程束缚态的一维二分量波函数和一维四分量波函数的精确解。并且在求精确解时 ,运用一种新的自变量变换方法 。

China’s Potential Economic Growths during 2015-2025 under Different Scenarios~

China has entered a crucial period of further growth and restructuring that will last until 2025. Based on a review of the major factors affecting China＇s potential economic growth, this paper has created an integrated economic system model consisting of system dynamics, econometrics, and input-output for the forecast of China＇s economic size and structure by 2025. Analysis shows that prior to 2025, China will be able to maintain a potential annual economic growth rate of 5.7%-7.2%. Faced with an international environment of a possible slowdown of advanced economies and diminishing demographic dividends, China needs to further expedite its urbanization process, enhance R＆D and education spending, increase total factor productivity （TFP）, vigorously develop the tertiary sector, and expand consumption in order to achieve the optimistically estimated growth of 6.6%-7.4% during the period of 2015-2025. Economic growth should be accompanied by the upgrade of industry structure and improvement of investment and consumption structures.

C_(60)分子间相互作用的Morse势函数及应用

利用C60晶体的升华焓、晶胞参数等性质,得到C60分子间相互作用的Morse势函数,其解析表达式为u(r)=30.05exp犤-24.96(r-1.005)犦-60.10exp犤-12.48(r-1.005)犦采用该作用势研究了C60及其晶体的一些性质,如计算得到C60晶体(100)面的表面能为7.46×10-2J·m-2,在650～4500K温度范围内计算了C60分子的第二维里系数,研究了C60面心立方晶体的晶格振动,并计算得到了晶格振动的态密度分布,还利用该作用势研究了不同晶型时C60晶体的稳定性.

Morse-3型S波段测波雷达比对试验结果分析

为了评价Morse-3型S波段测波雷达试验数据的有效性和实际观测效果,在遮浪岛附近以MKIII型波浪骑士浮标作为比对仪器进行试验。比对结果显示,所有参数的测量结果均略高于比对仪器的测量结果,且两者的相关性较好,平均波高和对应波周期测量结果最好。波高数据相关系数为0.936,误差介于（-0.1～0.1）m和（-0.2～0.2）m的概率分别为58.59%和99.38%;波周期误差介于（-1.5～1.5）s的概率为64.18%,误差标准偏差为0.50 s。

一维Morse势动量算符矩阵元的通项公式

导出一维Morse势中动量算符矩阵元〈n|^pq|n′〉的通项计算公式

Morse势中矩阵元X_(νν′)、P_(νν′)的计算

矩阵元Ｘνν′和Ｐνν′在有关量子力学问题中有相当重要的应用，本文利用广义拉盖尔多项式的正交性和分部积分的方法，推导Ｍｏｒｓｅ 势中 Ｘνν′、Ｐνν′的计算公式．

Hellmann-广义Morse势Klein-Gordon方程的散射态解

对非线性离心项采用恰当的近似办法,研究了具有Hellmann-广义Morse势的Klein-Gordon方程的散射态问题,推导了归一化的散射态波函数和相应的散射相移公式,同时利用散射振幅解析性质获得了束缚态能级满足的方程.最后,数值求解特征值方程并和真实值数据进行了对比.