光子增加混沌场的退相干和非经典效应

将产生算符作用在混沌场上,构造了光子增加混沌场.利用有序算符内的积分技术和热纠缠态表象求解密度矩阵主方程的方法,研究了振幅衰减模型中光子增加混沌场的退相干和非经典效应.通过解振幅衰减模型中的密度算符的主方程,得到了初态为光子增加混沌场的密度算符的演化公式.计算了终态密度算符的P表示和Wigner函数,并数值计算了耗散对其P表示和Wigner函数的影响.结果表明:随耗散时间的增长,光子增加混沌场的非经典效应减弱.另一方面,随光子增加数的增加,其非经典效应也减弱.     

利用热纠缠态表象获得Caldeira-Leggett密度算符方程的积分形式解

开放量子系统,即系统-热库模型,可以用一个关于密度算符的主方程来描述,比如,用来描述固态物理中耗散现象的Caldeira.Leggett主方程.虽然已经有人为了求解此主方程的约化密度矩阵的精确表达式而做过一些努力,但迄今还未见有解答.本文使用了一种全新的方法来求解Caldeira-Leggett方程,用这个新方法可以得到积分形式的显式表达.该方法的要点在于利用有序算符内积分技术把关于密度算符的微分方程首先转化成关于密度态矢量的微分方程,再将密度态矢量投影到热纠缠态表象中,Caldeira-Leggett方程就转变成了关于波函数的微分方程,而波函数是函数.这样就可以使用数学中求解微分方程的方法来求解出波函数.再次利用有序算符内积分技术,再将波函数转化为态矢量和算符,就得到了Caldeira-Leggett方程的积分形势解.     

海森伯矩阵力学

重述了矩阵力学的理论框架,包括位置动量不对易关系,算符的海森伯运动方程,非简并微扰论,给出了一维谐振子的矩阵力学求解过程.     

正切平方势阱中线性与非线性光学折射率变化的研究

利用正切平方势把电子的Schrodinger方程化为了超几何方程，并用超几何函数严格求解了电子的本征值和本征函数利用量子力学中的密度矩阵算符理论导出了正切平方势阱中的线性与三阶非线性光学折射率的解析表达式计算了该系统中的线性与非线性光学折射率变化的大小，讨论了影响折射率变化因素文章以典型的GaAs/AlGaAs势阱为例作了数值计算,数值计算结果表明，势阱的形状和入射光强对光学折射率的变化有着重要的影响.     

离子键分子振-转能级与光谱

对离子键分子内部势能函数进行了几何与物理分析,全面分析了4种分子键的贡献,克服了仅考虑马德隆势的不足,引入极化势与范德华势,建立了较全面精准适用的离子相互作用能量函数.求解了相应薛定谔方程,并引入了马德隆势的能量表象的Kramer公式,导出了能级的解析解.对氯化钠分子基态能量和基跃迁频率作了计算,其结果与实验值很好的符合.量子力学,量子理论是本科教学重要基础,本文在加深微扰论、表象理论、算符矩阵运算和矩阵元计算等内容的理解与应用是具体生动的,对本科生今后从事教学(大学)和升入更深层次的学习是很重要的.     

同调谐振子参数与基态能量的关系

采用升降算符方法研究了同调谐振子(包括一维谐振子)定态薛定谔方程的严格解,详细讨论了谐振子参量不同取值范围形成不同基态能量的关系.对于有关文献的一些欠完善的提法给予了分析和澄清 关键词： 同调谐振子 升算符 降算符 基态能量     

扩散过程中弱相干光场的退相干

研究了扩散过程中弱相干光场量子特性的演化.利用正规乘积、反正规乘积和Weyl编序算符内的积分技术,采用热纠缠态表象求解密度矩阵主方程,利用Kraus算符给出扩散过程中密度算符解的表达式,导出初态为弱相干态的量子态密度算符演化规律.讨论了扩散对光场压缩效应和反聚束效应的影响.结果表明:随着扩散过程的进行,弱相干场压缩深度和压缩范围均在减小;扩散初期光场呈反聚束效应,扩散时间大于一定值后反聚束效应消失.     

光学形式量子化算符法与矩阵法的对应关系

本文从光学位置坐标算符和正则动量算符的定义以及线性光学系统光学算符的幺正性假设出发,由线性系统的普遍性质建立光学系统算符表示和矩阵表示的关联方程,进而利用该方程实现了光学算符和光学矩阵的互为导出,因此证明了光学算符法和矩阵法的等效对应关系。最后,本文说明了光学算符的物理意义。 关键词：     

利用强飞秒激光脉冲串传递相干波包

用一维两态波包动力学模型从理论上研究了碘分子在两个激光脉冲串作用下有泵浦－拉下过程。计算中碘分子的基态和激发态势能面采用莫尔斯势能面,含时薛定谔方程通过分裂算符快速富里叶变换方法求解,基电子态的振动本征函数采采不连续变量方法计算,初步波包选择为电子基态的振动基本征函数,两个势能面之间的耦合采用偶极近似,激光脉冲的形状选择为高斯脉冲。利用上述的含时波包法实时地模拟了碘分子通过中间Ｂ态向基电子Ｘ态的高     

非球谐振子势的精确解

严格求解了三维非球谐振,势的Schrodinger方程给出了精确的能谱方程和归一化的径向波函数.获得了径向幂次算符r^s的矩阵元和平均值的计算公式及其递推关系.     

Trajectory approach to the Schrödinger–Langevin equation with linear dissipation for ground states

The Schrödinger–Langevin equation with linear dissipation is integrated by propagating an ensemble of Bohmian trajectories for the ground state of quantum systems. Substituting the wave function expressed in terms of the complex action into the Schrödinger–Langevin equation yields the complex quantum Hamilton–Jacobi equation with linear dissipation. We transform this equation into the arbitrary Lagrangian–Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation is simultaneously integrated with the trajectory guidance equation. Then, the computational method is applied to the harmonic oscillator, the double well potential, and the ground vibrational state of methyl iodide. The excellent agreement between the computational and the exact results for the ground state energies and wave functions shows that this study provides a synthetic trajectory approach to the ground state of quantum systems.     

Four-Parameter Scheme for Ground Level of Helium Atom

In this paper, the ground state wave function of four parameters is developed and the expression of the ground state level is derived for the helium atom when the radial Schrödinger equation of the helium atom is solved. The ground energy is respectively computed by the optimized algorithms of Matlab 7.0 and the Monte Carlo methods. Furthermore, the ground state wave function is obtained. Compared with the experiment value and the value with the variation calculus in reference, the results of this paper show that in the four-parameter scheme, not only the calculations become more simplified and precise, but also the radial wave function of the helium atom meets the space symmetry automatically in ground state.     

Properties of One Oxygen Hole Motion in a Quantum Antiferromagnet

By making use of the equation of motion of the Green's function method and the selfconsistent nondiagonal Fock approximation technique, we present a systematic analysis of the ground state properties of one-hole doping in the cupric oxides for the two-band model. The quant urn Bogoliu bov-de Gennes formalism is developed to study the renormalized hole motion with the effects of local distortion of spin configurations. The ground state wave function, the ground state energy and the effective mass are derived. The calculations are carried out with the variational approach.     

An upper bound for the ground-state energy of an antiferromagnetic chain with next-nearest-neighbor interaction

A trial function for the ground state of the antiferromagnetic linear chain leads to an equation for an upper bound of the ground-state energy per spin. This equation is solved exactly.     

基于Gross-Pitaevskii能量泛函求解谐振势阱中玻色凝聚气体基态波函数

基于Gross-Pitaevskii(G-P)平均场能量泛函和变分方法，对囚禁在谐振势阱中的玻色凝聚气体，在T=0K时的基态波函数提出一种新解法.运用这一方法能得到基态波函数的解析表达式，求解出系统的化学势与凝聚原子数的关系等.其结果与Edwards和Dalfovo等人直接数值求解G-P方程所得到的结果相一致，并在Na_s/a1大原子数N的极限条件下，与托马斯-费米近似模型的结论也趋向一致.该方法计算简单，而且能够进行解析处理. 关键词： 玻色凝聚气体 G-P泛函 谐振势阱 基态波函数     

束缚态径向方程和■~-超核的结合能(英文)

无论从薛定谔方程或是Dirac方程的低能近似出发都可导出同一标准形式的径向方程,这种径向方程可用三点中央差分格式从中心两点出发向外递推求解,给出了一种求解束缚态的能量本征值及其径向波函数的方法并计算分析了几个Ξ~-超核的基态结合能。     

四参数法计算氦原子基态能级研究

在求解氦原子径向Schr dinger方程时,设计了含有四参数的基态波函数,推导出含有四参数的氦原子基态能级表达式,分别采用Matlab 7.0最优化运算和Monte-Carlo法,计算了氦原子的基态能量,得到了相应的波函数.将计算结果与其它文献采用变分法所得计算值及实验值进行了比较,结果表明:这种方法不仅计算简便有效,准确性较高,而且所得氦原子基态空间波函数自动满足空间对称性的要求.     

A Particle Interacting with V-shaped Potential Decorated by a Dirac Delta Function Interaction at Center

The Schrodinger equation for a particle in the V-shaped potential decorated by a repulsive or attractive Dirac delta function interaction at the center is solved, demonstrating the crucial influence of point interaction on the even-parity states of the original system without decoration. As strength of the attraction increases, the ground state energy falls down without limit; and in limit of infinitely large attraction, the ground state approaches a singular state. Our analysis and conclusion can be readily generalized to any one-dimensional system a particle interacts with symmetrical potential plus the Dirac delta function interaction at the center.     

Radial Equation of Bound State and Binding Energies of Ξ－ Hypernuclei

The radial equation in its standard form, which can be solved by using the threepoint central difference method from central two points towards outside point by point, is reduced from Schrodinger equation or from the low energy approximation of Dirac equation. In this paper, a method for solving the radial equation of the bound state to get the binding energy and the radial wave function is given, and the binding energies of the ground state (GS) of several Ξ^－ hypernuclei are calculated.     

Electric-field effect on shallow impurity ground state in nanowire superlattice

We have developed a variational formalism to analyze the effect of electric field on the donor ground state in a nanowire superlattice with cylindrical cross-section. The trial function is taken as a product of the free-electron ground state wave function with an envelope function that is a solution of a differential equation arising from the Schrödinger variational principle. We establish a close relationship between the donor ground state energy and density of charge induced by the unbound electron at the point of donor location. Also, we show that electric field applied along the crystal growth direction can easily shift the peak position of the free-electron density distribution from the central well toward one of the nanowire ends, providing a variation of the average electron-ion separation and a considerable alteration of the donor ground state energy.