线型分子的电子能级之Λ分裂的新解释

认为电子态能级发生Λ分裂虽然是角动量引起的,但不是耦合而是运动牵连作用的结果.从这一认识出发,利用欧拉方程和拉格朗日方程分别得到了包含Λ分裂的分子转动哈密顿函数和哈密顿算符,所得结果与Van.Vleck的著名结论完全一致 关键词： Λ分裂 线型分子 欧拉方程 哈密顿算符     

氦原子自旋-自旋相互作用精细结构参数的理论计

利用多电子原子的精细结构哈密顿算符的球张量形式,通过计算氦原子的自旋-自旋相互作用哈密顿算符在|LSJMJ〉表象中的矩阵元,导出了氦原子的自旋-自旋相互作用精细结构参数的理论计算式,并就氦原子(n1s)(n2p)组态具体计算参数B之值.     

第一类PschlTeller势的非线性代数结构

在形变李代数理论的基础上 ,利用哈密顿算符和自然算符 ,构造出第一类P schl Teller势的非线性谱生成代数 .该非线性代数能够完全确定势场的能量本征态集合和本征值谱 ,在适当的非线性算符变换下可以化为谐振子代数 ,显示了该系统具有新的对称性     

第一类P?schl-Teller势的非线性代数结构

在形变李代数理论的基础上,利用哈密顿算符和自然算符,构造出第一类P?schl-Teller势的非线性谱生成代数.该非线性代数能够完全确定势场的能量本征态集合和本征值谱,在适当的非线性算符变换下可以化为谐振子代数,显示了该系统具有新的对称性 关键词： P?schl-Teller势 自然算符 非线性谱生成代数     

第一类Poschl-Teller势的非线性代数结构

在形变李代数理论的基础上,利用哈密顿算符和自然算符,构造出第一类Poschl-Teller势的非线性谱生成代数。该非线性代数能够完全确定势场的能量本征态集合和本征值谱,在适当的非线性算符变换下可以化为谐振子代数,显示了该系统具有新的对称性。     

复合函数算符的微商法则及其在量子物理中的应用

给出了在量子物理学、量子统计学、算符排序理论、矩阵论以及控制理论中有着重要用途的复合函数算符的一般微分法则,利用这一法则研究了Wigner算符和Weyl对应规则中的积分问题,证明了两类典型的算符恒等公式.给出了Wigner算符的有序算符内的微分形式,并得到了一些重要函数的新的微分式.最后,引入了一个参数型的Wigner算符来统一正规序、Weyl编序以及反正规序三种算符排序.     

IEO方法在求解哈密顿量能谱中的应用

利用IEO方法,通过选取合适的不变本征算符,使之满足所谓的"本征算符方程",其本征值与体系的能隙对应;从而直接、方便地推导出体系的能谱.本文以有外场时双原子分子体系和光场非线性相互作用的两个哈密顿为例,介绍IEO方法在分子与原子物理中的应用.     

含时波包法研究NaH分子的光解截面

采用傅立叶格点哈密顿方法求解含时薛定谔方程、劈裂算符方法传播波函数,计算了NaH分子在三组势能曲线下从初始态X1Σ (v″=0)跃迁到激发态B1Π的光解截面.研究表明影响光解截面最大值及相应光子能量的关键因素是解离阈能,势能曲线间相对小的平移对计算结果影响不大.应用含时量子力学方法计算光解截面时,车比雪夫多项式方案和劈裂算符方法能够给出基本相同的结果.     

在局域子空间中计算给定范围内的能量本征值

通过能量算符δ函数作用于完全随机格点波函数,构造了可用于直接计算给定范围[Emin,Emax]内能量本征值和本征函数的局域子空间.在非正交局域基下详细推导了交迭积分和哈密顿算符在分立位置表象中的表示,讨论了广义本征值问题的解法.以Morse势和Henon-Heiles势的多个能量范围为例检验了算法     

几类粒子密度算符和粒子流密度算符的讨论

从粒子密度和粒子流密度出发,分析了几类相关的算符,讨论了它们的性质与相互关系;从具体的物理意义出发,明确了合适的粒子密度算符和粒子流密度算符的表达形式.     

Approximate calculation of electronic energy levels of axially symmetric quantum dot and quantum ring by using energy dependent effective mass

Calculations of electronic structures about the semiconductor quantum dot and the semiconductor quantum ring are presented in this paper. To reduce the calculation costs, for the quantum dot and the quantum ring, their simplified axially symmetric shapes are utilized in our analysis. The energy dependent effective mass is taken into account in solving the Schr?dinger equations in the single band effective mass approximation. The calculated results show that the energy dependent effective mass should be considered only for relatively small volume quantum dots or small quantum rings. For large size quantum materials, both the energy dependent effective mass and the parabolic effective mass can give the same results. The energy states and the effective masses of the quantum dot and the quantum ring as a function of geometric parameters are also discussed in detail.     

Electronic states in a step quantum well in a magnetic field

The quantum states and energy spectrum of an electron in a rectangular step quantum well in a magnetic field parallel to the plane of two-dimensional electronic gas are investigated. It is shown that the joint effect of a magnetic field and confining potential of quantum well results in radical change of the electron energy spectrum. The energy dependencies on the parameters of the quantum well and magnetic field induction are investigated. Numerical calculations are carried out for an AlAs/ GaAlAs/ GaAs/ AlAs step quantum well.     

量子点中极化子的内部激发态性质

采用Huybrechts线性组合算符和幺正变换方法研究了抛物量子点中的强、弱耦合极化子的激发态性质。分别导出强、弱耦合情况下,抛物量子点中的极化子的第一内部激发态能量、激发能量、共振频率与量子点的有效受限长度和电子-声子耦合强度的关系。数值计算结果表明,量子点中弱耦合和强耦合极化子的内部激发态能量、激发能量和共振频率都随量子点的有效受限长度的减小而迅速增大。弱耦合极化子的第一内部激发态能量随电子-声子耦合强度的增加而减少;而强耦合极化子的振动频率随量子点的有效受限长度的减小而迅速增加。弱耦合极化子的第一内部激发态能量、激发能量和共振频率随电子-声子耦合强度的增加而减小。     

极性晶体量子点中强耦合激子的内部激发态

在有效质量近似下,采用线性组合算符和幺正变换方法研究了极性晶体量子点中强耦合激子的内部激发态性质,导出了极性晶体量子点中强耦合激子的基态能量、第一内部激发态能量和激发能量随量子点半径的变化关系。对TlCl晶体进行数值计算,结果表明,量子点中强耦合激子的基态能量、第一内部激发态能量和激发能量随量子点半径的减小而增大。     

电荷离散化时相干态下介观金属环中电荷与电流以及能量的量子涨落

基于电荷量子化的事实,运用最小平移算符Q∧的性质等,计算对应的相干态下介观金属环中电荷、电流及能量的量子涨落,研究影响量子涨落的因素.结果表明:计及电荷的离散性,在相干态下介观金属环中电荷、能量的量子涨落不为零,分别与电荷量子、相干态参量等因素有关;此外,能量的量子涨落还决定于金属环的电感、外磁通及其时间变化率的大小.     

The effect of impurity on transition frequency of bound polaron in quantum rods

The Hamiltonian of a quantum rod with an ellipsoidal boundary is given after a coordinate transformation that changes the ellipsoidal boundary into a spherical one. The properties of the quantum rods constituting the bridge between two-dimensional quantum wells, zero-dimensional quantum dots and one-dimensional quantum wires are explored theoretically using linear combination operator method. The first internal excited state energy, the excitation energy and the transition frequency between the first internal excited and the ground states of the strong-coupled impurity-bound polaron in the rod with Coulomb-bound potential, the transverse effective confinement length, the ellipsoid aspect ratio and the electron–phonon coupling strength are studied. It is found that the first internal excited state energy, the excitation energy and the transition frequency are increasing functions of the Coulomb-bound potential and the electron–phonon coupling strength, whereas they are decreasing functions of the ellipsoid aspect ratio and the transverse effective confinement length. These results can be attributed to the interesting quantum size confining effects.     

Quantum energy and charging energy in point contact MOSFETs acting as single electron transistors

The charging energy and quantum energy in silicon single electron transistors have been investigated. The devices were fabricated in the form of point contact MOSFETs, some of which show the Coulomb blockade oscillations at room temperature. The charging energy and quantum energy were derived by fitting the simulation results to the experimental data. It was clearly found that the quantum energy became comparable with the charging energy when the dot size is smaller than 10–20 nm and the charging energy is more than 20 meV. These results indicate that the quantum effects should be taken into account even in silicon devices when silicon single electron transistors or MOSFETs smaller than about 20 nm are designed.     

有限深抛物势量子盘中极化子的激发态性质

量子点作为一种重要的低维纳米结构, 近年来在单光子光源和新型量子点单光子探测器的研究引起了人们的广泛关注, 对各种势阱中量子点性质的研究已取得了重要成果. 但是大多理论研究都局限于无限深势阱, 而有限深势阱更具有实际意义. 利用平面波展开、幺正变换和变分相结合的方法研究了有限深势阱中极化子激发态能量及激发能随势阱形状和量子盘大小的变化规律. 数值计算结果表明: 极化子的激发态能量、激发能随势垒高度或宽度的增大而增大, 原因是势垒愈高、愈宽, 电子穿透势垒的可能性愈小, 电子在阱内运动的可能性愈大, 进而导致极化子的激发态能量和激发能均随势垒高度和宽度的增大而增大; 极化子的激发态能量和激发能随量子盘半径的增大而减小, 表明量子盘具有显著的量子尺寸效应; 极化子的激发态能量随有效受限长度的增加而减小, 原因是有效受限长度愈大, 有效受限强度愈小, 电子受到的束缚愈弱、振动愈慢、势能愈小, 进而导致基态能量、激发态能量减小; 同时由于激发态能量较基态能量减小慢, 使得激发能随之增加. 研究结果对量子点的应用具有一定的理论指导意义.     

氮化物抛物量子阱中类氢杂质态能量

采用变分方法研究氮化物抛物量子阱(GaN/Al_xGa_1-xN)材料中类氢杂质态的能级,给出基态能量、第一激发态能量、结合能和跃迁能量等物理量随抛物量子阱宽度变化的函数关系.研究结果表明,基态能量、第一激发态能量、基态结合能和1s→2p±跃迁能量随着阱宽L的增大而减小,最后接近于GaN中3D值.GaN/Al_0.3Ga_0.7N抛物量子阱对杂质态的束缚程度比GaAs/Al_0.3Ga_0.7As抛物量子阱强,因此,在GaN/Al_0.3-Ga_0.7N抛物量子阱中束缚于杂质中心处的电子比在GaAs/Al_0.3Ga_0.7As抛物量子阱中束缚于杂质中心处的电子稳定.     

Hydrogenic impurity in double quantum dots

The ground state binding energy and the average interparticle distances for a hydrogenic impurity in double quantum dots with Gaussian confinement potential are studied by the variational method. The probability density of the electron is calculated, too. The dependence of the binding energy on the impurity position is investigated for GaAs quantum dots. The result shows that the binding energy has a minimum as a function of the distance between the two quantum dots when the impurity is located at the center of one quantum dot or at the center of the edge of one quantum dot. When the impurity is located at the center of the two dots, the binding energy decreases monotonically.