伪自旋对称情形下Rosen-Morse类型势场中相对论粒子的束缚态

在伪自旋对称情形下研究了Rosen-Morse类型势场中相对论粒子的束缚态,利用Nikiforov-Uvarov方法求解了伪自旋对称情形下的Klein-Gordon和Dirac方程,得到了相对论粒子被束缚在Rosen-Morse类型势场的精确束缚态解.     

Rosen-MorseⅡ势函数的Klein-Gordon方程和Dirac方程束缚态的精确解

在标量势和矢量势相等的情形, 研究了Rosen-MorseⅡ势的相对论效应, 应用超对称和形状不变势方法通过求解Klein-Gordon方程和Dirac方程得到了束缚态能量本征值, 最后, 讨论了Rosen-MorseⅡ势的一种特殊情况.     

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     

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     

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     

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     

具有Kratzer型标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态

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

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

给出了具有Poschl-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.     

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.     

Bound states of the Klein－Gordon and Dirac equation for scalar and vector pseudoharmonic oscillator potentials

The exact bound state solutions of the Klein－Gordon equation and Dirac equation with scalar and vector pseudoharmonic oscillator potentials are obtained in this paper. Furthermore, we have used the supersymmetric quantum mechanics, shape invariance and alternative method to obtain the required results.     

Exact solution of the one-dimensional Klein-Gordon equation with scalar and vector linear potentials in the presence of a minimal length

Using the momentum space representation, we solve the Klein-Gordon equation in one spatial dimension for the case of mixed scalar and vector linear potentials in the context of deformed quantum mechanics characterized by a finite minimal uncertainty in position. The expressions of bound state energies and the associated wave functions are exactly obtained.     

Where and why the generalized Hamilton-Jacobi representation describes microstates of the Schrödinger wave function

A generalized Hamilton-Jacobi representation describes microstates of the Schrödinger wave function for bound states. At the very points that boundary values are applied to the bound state Schrödinger wave function, the generalized Hamilton-Jacobi equation for quantum mechanics exhibits a nodal singularity. For initial value problems, the two representations are equivalent.     

Molecular Dynamics Study of gases H2,D2 and T2

The classical Molecular dynamics simulation has been used to study the equation of state of gas H2,D2 and T2.It has also been investigated that the isotope mass affects on the accuracy of equation of state.Our calculated Iesults show that the classical effect is principal and the isotope mass effects on the equation of state are obvious for the much light gases.At the same time,some useful theoretical data of equation of state for these gases have been provided.It is found that the classical simulation is still effective to the quantum gas.However,the quantum mechanics simulation and the improvement of intermolecular interaction potential are necessary if more accurate computational results are expected.     

Exact solutions of the Klein-Gordon equation with Makarov potential and a recurrence relation

In this paper, the Klein--Gordon equation with equal scalar and vector Makarov potentials is studied by the factorization method. The energy equation and the normalized bound state solutions are obtained, a recurrence relation between the different principal quantum number n corresponding to a certain angular quantum number \ell is established and some special cases of Makarov potential are discussed.     

最弱受约束电子势模型的径向波函数的两类递推关系

应用简单的方法———Laplace变换法来求最弱受约束电子势模型(WBEPM势)的径向Schrdinger方程.通过这种方法使得两阶微分方程变为一阶微分方程,这样可以直接运用积分得到WBEPM势束缚态能量方程和归一化的波函数,所得结果与文献一致.更重要的是用Laplace变换得到径向波函数的两类新的递推关系.这种递推关系是有效主量子数和角量子数之间关系,在计算原子和分子跃迁几率时有着广泛的应用.     

Some stochastic aspects of quantization

From the advent of quantum mechanics, various types of stochastic-dynamical approach to quantum mechanics have been tried. We discuss how to utilize Nelson’s stochastic quantum mechanics to analyze the tunneling phenomena, how to derive relativistic field equations via the Poisson process and how to describe a quantum dynamics of open systems by the use of quantum state diffusion, or the stochastic Schrödinger equation.     

MIMO量子信道的空间自由度研究

量子通信是一个量子密钥分发过程,目前采用的通信技术严重制约了量子密钥分发的比特率.将多输入多输出（MIMO）技术应用于量子通信系统,提高量子密钥分发的比特率,促进量子通信向高速大容量发展.然而,量子场本身不可避免地存在量子噪声约束容量的增长,限制了可利用空间资源,即空间自由度.文中采用光子场的量子化和满足Schrdinger方程条件的电磁场波动方程推导出MIMO量子信道的空间自由度上限,为开发稳健的MIMO量子通信空时处理算法和优化设计高性能MIMO量子通信系统提供理论基础和技术支持. 关键词： 多输入多输出 量子密钥分发 Schrdinger方程 光子场的量子化     

Logarithmic Quantum Mechanics: Existence of the Ground State

We study nonlinear logarithmic Schrödinger equation in three dimensions. We examine energy levels in this setting, we are especially interested in the ground state. We also show some topological properties of the spectrum. The main contribution of this paper is the first rigorous proof of existence of the ground state in logarithmic quantum mechanics.     

Approximate analytical solutions and mean energies of stationary Schrödinger equation for general molecular potential

The Schrödinger equation is solved with general molecular potential via the improved quantization rule. Expression for bound state energy eigenvalues, radial eigenfunctions, mean kinetic energy, and potential energy are obtained in compact form. In modeling the centrifugal term of the effective potential, a Pekeris-like approximation scheme is applied. Also, we use the Hellmann-Feynman theorem to derive the relation for expectation values. Bound state energy eigenvalues, wave functions and meanenergies of Woods-Saxon potential, Morse potential, Möbius squared and Tietz-Hua oscillators are deduced from the general molecular potential. In addition, we use our equations to compute the bound state energy eigenvalues and expectation values for four diatomic molecules viz. H₂, CO, HF, and O₂. Results obtained are in perfect agreement with the data available from the literature for the potentials and molecules. Studies also show that as the vibrational quantum number increases, the mean kinetic energy for the system in a Tietz-Hua potential increases slowly to a threshold value and then decreases. But in a Morse potential, the mean kinetic energy increases linearly with vibrational quantum number increasing.