等腰直角三角形上混合边界条件的本征函数

假设等腰直角三角形上满足混合边界条件的本征函数是8个平面波函数的线性叠加,由边界条件,确定了8个待定系数.     

关于本征函数系的完全性和封闭性

论证了本征函数系的完全性等价于其封闭性。     

波函数与本征函数的分析

依据量子力学基本理论, 分析了波函数与本征函数的定义、 性质及其意义, 明确两个重要概念的不同     

求解格林函数的本征函数法

从本征函数理论出发，本文介绍了求解第一类格林函数的本征函数法。从而对格林函数的本征函数法建立进行一般的理论概括。最后举例说明应用。     

不对易算符有共同本征函数的必要条件

讨论了不对易算符有共同本征函数的必要条件。     

厄米算符本征函数完备性的一般证明

从一组完备的本征函数开始,以表象原理为前提,建立一个唯象的公式,利用反证法证明了力学量算符的完备性,即这一组完备的本征函数可以投影到力学量算符的本征函数空间中.从而给出了力学量算符本征函数完备性的一般证明.     

基于MATLAB氢原子本征函数的关系图示

应用MATLAB的程序绘制氢原子本征态径向波函数、径向密度函数和径向分布函数与矢径的关系图示、s、P、d等电子角分布函数的图示。     

共轴载流正三角形线圈间的相互作用

从计算回路的磁通量出发,应用虚位移原理,通过Mathematica数学软件,数值计算得到了共轴正三角形载流线圈间的相互作用力和力矩与线圈距离以及交错角度的关系曲线.     

正三角形载流线圈的空间磁场分布

利用一段载流直导线在空间某点的磁场,对正三角形载流线圈进行分段计算,然后根据场强叠加原理,求出正三角形载流线圈的空间磁场分布,并讨论了线圈平面上和中心轴线上的磁场分布情况。     

轨道角动量分量算符的本征函数间的变换

本文讨论了不同轨道角动量分量算符本征函数间的变换关系,给出了对应的变换系数的计算方法,求解了几个比较常见情形l=1,2,3的变换系数,得到了各个变换系数之间的规律.     

量子计算正三角形腔内的氢负离子光剥离截面

用传统量子力学方法研究了横截面为正三角形的腔内氢负离子光剥离, 得到了光剥离截面随能量变化的解析表达公式. 该公式还给出了剥离截面的阈值行为. 进一步研究发现, 当氢负离子处于正三角形一角附近时, 用量子力学方法得到的结果与氢负离子处于60°角域内时使用闭合轨道理论得到的结果一致.     

双三角阵声靶测试系统研究

声靶容易构成较大的测试靶面,常用在大口径弹药的立靶密集度测试中。为了消除声波在空气中传播速度变化对声靶测试精度的影响,采用双三角阵声阵列模型使测量公式中不再引入声波速度。为了使测试系统紧凑、可靠,整个测试系统由双三角阵列、多通道数据采集仪、计算机系统构成。对测试系统进行了实弹射击实验,在2 m×2 m靶面内,弹着点测量误差为±10 mm。     

两个力学量算符具有共同本征态系的条件

量子力学是人们了解微观世界的一门重要的课程.在量子力学中,由于任何实物体都具有波粒二象性,必须用算符来表示力学量,因此算符理论显得尤为重要.在研究多个算符时,有一个非常重要的定理:两个力学量算符能够具有共同本征函数系的充分必要条件是这两个个力学量算符能够互相对易.本文分析了在使用该定理时可能存在的一些问题,并对这些问题进行了澄清.     

Photonic band structure in a two-dimensional hexagonal lattice of equilateral triangles

In this paper, the plane wave expansion method is used to calculate the photonic band structure (PBS) for the transverse electric (TE) polarization in a two-dimensional hexagonal lattice composed air holes with cross-sections in the shape of equilateral triangles embedded in a GaAs background. We consider that the dielectric constant of GaAs is dependent on both hydrostatic pressure and temperature. Further, an increase can be observed in the width of the photonic band gap (PBG) while the lengths of the sides of the equilateral triangles are increased. When the pressure increases in the presence of a constant temperature, the dielectric constant of GaAs decreases; further, the PBS exhibits a more noticeable shift toward regions of higher frequencies than that observed while the temperature is increased at a given pressure. We also observed that the PBG obtained by rotating the triangular holes by an angle θ increases when compared against the results obtained for the lattice of holes without performing any rotation. In addition, the results obtained using the supercell technique denote that the position and width of the PBG remain unchanged while removing a triangular hole from the structure, denoting the presence of a defective band within the PBG.     

正三角型三芯光纤中等腰对称平面波的调制不稳定性分析

详细分析了正三角型三芯光纤中等腰对称平面波的调制不稳定性.等腰对称平面波即两芯中场完全相同,第三芯中场入射功率与其他两芯中不同的平面波,其存在的前提是入射光总功率(P)必须大于某最小值(P_(min)),该最小值取决于光纤的线性耦合系数和非线性系数.对一给定的总功率P≥P_(min),令一芯中的入射功率为P_1,其他两芯中入射功率均为P_2,有两种形式的场分布:一种是P_1始终大于P_2,随着P的增加,P_1越来越大,P_2越来越小,依线性稳定性分析方法,该场分布对应的增益谱主要特征与双芯光纤非对称平面波的增益谱相似;另一种是随着P的增加,P_1越来越小,P_2越来越大,使用同样的分析方法,发现该场分布下增益谱与双芯光纤非对称平面波增益谱截然不同,其显著特征是无扰动下,在正常和反常色散区域均可产生不稳定性增益,且在正常色散区域,零扰动频率对应的增益最强;另一方面,耦合系数色散对增益谱的影响在正常和反常色散区域都非常弱,这与其在双芯光纤中的影响截然不同.该结果对基于多芯光纤的模分复用系统非线性效应的研究具有一定的指导意义.     

Formation Mechanism and Binding Energy for Equilateral Triangle Structure of Li3 Cluster

The formation mechanism for the equilateral triangle structure of Lia cluster is proposed. The curve of the total energy versus the interatomic distance for this structure has been calculated by using the method of Gou＇s Modified Arrangement Channel Quantum Mechanics. The result shows that the curve has a minimal energy of-22.338 60 a.u at R = 5.82 ao. The total energy of Lia when R approaches co has the value of-22.284 09 a.u. This is also the total energy of three lithium atoms dissociated from Lia. The difference value of 0.0545 08 a.u. for the above two energy values is the dissociation energy of Li3 cluster, which is also its binding energy. Therefore the binding energy per lithium atom for Lia is 0.018 169 a.u. = 0.494 eV, which is greater than the binding energy of 0.453 eV per atom for Li2 calculated in a previous work. This means that the Li3 cluster may be formed in the equilateral triangle structure of side length R = 5.82ao stably with a stronger binding from the symmetrical interaction among the three lithium atoms.     

Formation Mechanism and Binding Energy for Equilateral Triangle Structure of Li3 Cluster

The formation mechanism for the equilateral triangle structure of Li3 cluster is proposed. The curve of the total energy versus the interatomic distance for this structure has been calculated by using the method of Gou‘s Modified Arrangement Channel Quantum Mechanics. The result shows that the curve has a minimal energy of-22.338 60 a.u at R = 5.82 a0. The total energy of Li3 when R approaches ∞ has the value of-22.284 09 a.u. This is also the total energy of three lithium atoms dissociated from Li3. The difference value of 0.0545 08 a.u. for the above two energy values is the dissociation energy of Li3 cluster, which is also its binding energy. Therefore the binding energy per lithium atom for Li3 is 0.018 169 a.u. = 0.494 eV, which is greater than the binding energy of 0.453 eV per atom for Li2 calculated in a previous work. This means that the Li3 cluster may be formed in the equilateral triangle structure of side length R = 5.82a0 stably with a stronger binding from the symmetrical interaction among the three lithium atoms.     

一类非常规斯特姆-刘维问题的本征函数完备性与节点

端点与质点(集中质量)连结的弦或杆的振动等问题在分离变量后归结为一类非常规的斯特姆一刘维本征值问题,证明了此类本征值问题的本征函数族具有完备性.证明了第n个本征函数具有n-1个节点(零点).     

Formation Mechanism and Binding Energy for Equilateral Triangle Structure of He3+ Cluster

The formation mechanism for the equilateral triangle structure of the He3 cluster is proposed. The curveof the total energy versus the internuclear distance R for this structure has been calculated by the method of a modifiedarrangement channel quantum mechanics. The result shows that the curve has a minimal -7.81373 a.u at 1 = 1.55 a0.The binding energy of He3 with respect to He He He was calculated to be 0.1064 a.u. (about 2.89 eV). This meansthat the He3 cluster may be formed in the equilateral triangle structure stably by the interaction of He with two heliumatoms.