氢原子和谐振子的能级、波函数的联系

求氢原子和谐振子的能级、波函数是解两个不同的定态薛定谔方程的问题。实际上，我们从三维谐振子的径向方程出发，应用适当的变换，就能由三维谐振子的能级和波函数导出氢原子与类氢离子的能级和波函数．     

相对论谐振子下的自旋和赝自旋轨道伙伴态劈裂

通过求解具有谐振子势的径向标量势与矢量势的Dirac方程, 分别分析了原子核中赝自旋和自旋双重态的能级劈裂和波函数劈裂随着谐振子的振动频率参数ω和描述谐振子势阱底偏离中心参数r₀的变化关系. 研究发现, 这些参数对于赝自旋和自旋双重态的能级劈裂和波函数劈裂都有着显著的影响. 此外, 也研究了能级劈裂和波函数劈裂随着量子数的变化关系. 由于参数ω与核子数有关, 而参数r₀与形变核有关, 所以以这些参数为变量对于赝自旋劈裂和自旋劈裂的研究是有意义的, 研究的结果至少可以定性地应用到大部分原子核中.     

幂函数叠加势的径向薛定谔方程的解析解(英文)

当薛定谔方程中出现高次非谐振子势,电偶极矩势,分子晶体势,极化等效势等高次正幂与逆幂势函数以及它们的叠加时,薛定谔方程的求解变得非常复杂,本文采用奇点邻域附近的级数解法与求解渐近解相结合并且通过系数比较法,得到势函数为V(r)=a1r6 a2r2 a3r-4 a4r-6的径向薛定谔方程的一系列定态波函数解析解以及能级结构,并作了适当讨论与结论.     

类Quesne环状球谐振子势场中的赝自旋对称性

提出了一种新的类Quesne环状球谐振子势,应用二分量方法求解1/2-自旋粒子满足的Dirac方程, Dirac哈密顿量由标量和矢量类Quesne环状球谐振子势构成.在Σ=S(r)+V(r)=0的条件下,得到了Dirac旋量波函数下分量的束缚态解和能谱方程, 显示出类Quesne环状球谐振子势场中的赝自旋对称性.讨论了束缚态波函数和能谱方程的有关性质. 关键词： 类Quesne环状球谐振子势 Dirac方程 赝自旋对称性 束缚态     

线性谐振子的非定态波函数

引入初坐标算符和初动量算符为线性谐振子的力学量完全集，求解薛定谔方程，可得到线性谐振子的两类非定态波函数。     

几个量子力学问题的统一解法

通过变换求得连带Laguerre方程的变通形式，它包括了量子力学中-维谐振子、三维谐振子和类氢离子所满足的径向薛定谔方程，因此可用统一的方法对这三个问题的能级和波函数求解。     

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     

求解径向Schrodinger方程解析解的一种方法以及由此延伸的讨论--叠加势基态能级与势参数关系

采用转化法.可得到一系列具有球对称势函数的径向Schrodinger方程的解析解和能级方程.这种方法是用一个恰当的尝试波函数代入Schrodinger方程后,将微分方程变成简单的可解的代数方程组,由此大大简化了运算.本文给出了库仑势、库仑势与谐振子势的叠加势以及离子与原子相互作用势的径向Schrodinger方程解析解,并得到能级方程.由于此方法中涉及一个势参数制约关系,为此以叠加势V(r)=-A1r-1-A2r-3+A3r-4为例,讨论其基态能级.得出重要结论:在库仑势上叠加上两项逆幂指数势作用后基态能量将增大,但是并不是单调增大,而是与各项势参数有关.     

求解径向Schrdinger方程解析解的一种方法以及由此延伸的讨论——叠加势基态能级与势参数关系

采用转化法.可得到一系列具有球对称势函数的径向Schr dinger方程的解析解和能级方程.这种方法是用一个恰当的尝试波函数代入Schr dinger方程后,将微分方程变成简单的可解的代数方程组,由此大大简化了运算.本文给出了库仑势、库仑势与谐振子势的叠加势以及离子与原子相互作用势的径向Schr dinger方程解析解,并得到能级方程.由于此方法中涉及一个势参数制约关系,为此以叠加势V(r)=-A1r-1-A2r-3+A3r-4为例,讨论其基态能级.得出重要结论:在库仑势上叠加上两项逆幂指数势作用后基态能量将增大,但是并不是单调增大,而是与各项势参数有关.     

辛和非辛算法求解薛定谔方程误差分析

在哈密尔顿体系下,提出气体声波传播的一种新的谐振子模型,并引入群论确定气体声波传播过程中的分子振动模式、能级简并.新模型将气动声学声传播问题与分子振动关联起来。由于发展高效的薛定谔方程的数值计算方法,有利于联系分子的性质来解释声的传播.本文从此出发,用二阶有限差分格式和生成函数法构造的二阶辛格式分别计算一维定态谐振子势场和含时谐振子势场的薛定谔方程,分析了数值解的误差以及传播能量误差.结果表明辛算法具有明显的优势.     

Julia sets for the super-Newton method,Cauchy's method,and Halley's method

We study numerically and dynamically three cubically convergent iterative root-finding algorithms, namely Cauchy's method, the super-Newton method, and Halley's method. Using the concept of a universal Julia set (motivated by the results of McMullen), we establish that these algorithms converge when applied to any quadratic with distinct roots. We give examples showing the existence of attracting periodic orbits not associated to a root for the super-Newton method and Halley's method applied to cubic polynomials. We include computer plots showing the dynamic structure for each algorithm applied to a variety of polynomials. (c) 2001 American Institute of Physics.     

基于单曲面迭代计算的曲面透镜设计方法

为在平面上实现所需的照明,满足照明系统的要求,需要对光学系统进行二次设计。传统的设计方法往往用规则曲面指定透镜的一个表面,并以此为基础来设计另个一表面,这样会导致其表面形状复杂,不方便加工或装配。对此,提出了一种基于单曲面迭代计算的透镜曲面设计方法,即适当设计指定光线从透镜的一个表面到另一个表面的光路分布,再以此分别迭代计算透镜的各个表面。该设计方法采用两个自由曲面配合成曲面透镜,较以往的设计方法更加灵活、方便,设计得到的曲面镜头较以往更加简单光滑,便于加工和装配。结合一陈列灯镜头设计,给出了基于单曲面迭代计算的曲面透镜设计计算结果。     

Relation between heat kernel method and scattering spectral method

Taking into account the available accelerator and astrophysical constraints, the mass of the lightest neutral Higgs boson h in the minimal supersymmetric extension of the Standard Model with universal soft supersymmetry-breaking masses (CMSSM) has been estimated to lie between 114 and ??130?GeV. Recent data from ATLAS and CMS hint that m _h ??125?GeV, though m _h ??119?GeV may still be a possibility. Here we study the consequences for the parameters of the CMSSM and direct dark matter detection if the Higgs hint is confirmed, focusing on the strips in the (m _1/2,m ₀) planes for different tan?? and A ₀ where the relic density of the lightest neutralino ?? falls within the range of the cosmological cold dark matter density allowed by WMAP and other experiments. We find that if m _h ??125?GeV focus-point strips would be disfavoured, as would the low-tan?? ${\tilde{\tau}}$ ?C?? and ${\tilde{t}}_{1} $ ?C?? coannihilation strips, whereas the ${\tilde{\tau}}$ ?C?? coannihilation strip at large tan?? and A ₀>0 would be favoured, together with its extension to a funnel where rapid annihilation via direct-channel H/A poles dominates. On the other hand, if m _h ??119?GeV more options would be open. We give parameterisations of WMAP strips with large tan?? and fixed A ₀/m ₀>0 that include portions compatible with m _h =125?GeV, and present predictions for spin-independent elastic dark matter scattering along these strips. These are generally low for models compatible with m _h =125?GeV, whereas the XENON100 experiment already excludes some portions of strips where m _h is smaller.     

SQUID法和Campbell法测量超导材料的研究

本文对比研究了超导材料磁测量中的SQUID法和Campbell法; 并用高压PIT法制备的超导材料MgB₂作为测量样品,用两种方法,测量了超导样品的临界电流密度, 分别得到了样品的J_c-B关系曲线; SQUID法测量样品的外磁场可以达到6 T, 此时材料已经处于失超状态,此方法测得的结果是样品各个小区域结果的平均值, SQUID还可以用来进一步标度材料的钉扎力行为,研究材料磁特性. Campbell法测量只能测量到外磁场强度为0.4 T,外磁场的交流部分的频率可以达到800 Hz, 用这种测量方法得到的是整块样品的电流,由于测量计及材料内部微观结构缺陷等影响电流传输因素, 所测结果小于直流磁化法,但更切近材料实际电流,能用来深入研究材料内部结构差别对材料电性能的影响.     

“0.618”法、Fibonacci法、抛物线法搜寻复摆周期极值点

在实验室条件下,用"0.618"法、Fibonacci法和抛物线法来搜寻钟摆复摆周期极值点位置.通过实验发现,Fibonacci法在搜索精度上比"0.618"法高,但在搜寻速度上不占优势,而抛物线法在搜寻速度和精度上比"0.618"法和Fibonacci法都好.     

Hybrid encoding method by assembling the magic-matrix scrambling method and the binary encoding method in image hiding

The magic-matrix scrambling method and the binary encoding method are combined to form a hybrid encoding method for hiding digital covert images. For this hybrid encoding method, a covert image is encoded into a host image to form an overt image. First, the magic-matrix scrambling method is used to rearrange all the pixels of the covert image by using a specified magic matrix modified from a magic square to form a scrambled matrix. Then, all the pixels of the scrambled matrix are denoted by binary data. Finally, the binary data are encoded into the host image to form the overt image. The pixels of the overt image contain nine groups of codes used for decoding the covert image, i.e. identification codes, covert-image dimension codes, scrambling-time codes, magic-square dimension codes, corner codes, shifting codes, arrangement codes, graylevel codes, and information codes. The overt image and the host image look almost the same for eyes. Furthermore, the covert image can be decoded directly from the overt image without using the host image. The most important feature is that the decoded covert image is identical to the original covert image, i.e. there is no distortion in the decoding work.     

A new method for orbit determination: Unit vector method

In this paper, a method of orbit determination is presented according to the principle of unit vector method (UVM). The model and arithmetic are improved and it not only suits initial orbit determination with short arc data, it also suits orbit improvement with data longer. It is also suitable for orbit of any eccentricity and any inclination. It omits most partial derivatives of all the elements which must be calculated in classical differential orbit improvement (DOI), so, it is more efficient than DOI, and the accuracy of orbit determination and convergence of algorithm are also improved appreciably.     

Divergence-free WKB method

A new semiclassical approach to the linear and nonlinear one-dimensional Schr?dinger equation is presented. For both equations our zeroth-order solutions include nonperturbative quantum corrections to the WKB solution and the Thomas-Fermi solution, thereby allowing us to make uniformly converging perturbative expansions of the wave functions. Our method leads to a new quantization condition that yields exact eigenenergies for the harmonic-oscillator and Morse potentials.