解题比较

牛顿运动定律是解经典力学题目的主要手段.能量守恒定律则是自然界普遍适用的定律.经典力学中只要涉及到与能量或做功有关的问题,同样也可用能量守恒定律来解.下面举一具体的例子进行比较、说明. 如图所示,质量m=4×103kg的汽车以v1=10m/s的速度开上倾角θ=30°的斜坡,已知坡长s=     

HNO分子基态的结构与解析势能函数研究

应用群论及原子分子反应静力学的方法, 导出了HNO分子基态电子态和合理的离解极限.利用优选出的密度泛函理论B3LYP方法结合6-311G **优化计算了HNO分子基态的平衡结构和谐振频率.计算结果表明基态HNO分子稳定态为C_S构型,电子组态为X¹A',平衡核间距分别为R_H-N=0.1065 nm,R_N-O=0.1200 nm,键角∠H-N-O=108.60°,离解能D_e=15.379 eV.基态简正振动频率分别为:弯曲振动频率ν₁=1575.6351 cm^-1,对称伸缩振动频率ν₂=1673.2890 cm^-1,反对称伸缩振动频率ν₃=2837.7856 cm^-1.在此基础上,应用多体项展式理论导出了基态HNO分子的全空间解析势能函数,该势能函数等值势能图准确再现了HNO分子平衡结构和离解能. 关键词： 势能函数 光谱常数 密度泛函方法     

N II离子禁戒跃迁几率的理论计算

用多组态Dirac Fock方法 ,系统考虑了相对论效应、电子关联、延迟效应等重要贡献 ,计算了NII离子 2p3d— 2p2 以及 2p3d— 2p3p (ΔL =± 2 ,ΔS =± 1)禁戒跃迁的几率 .与已有的理论相比 ,目前计算的精度有了明显提高. The forbidden transition probabilities have been calculated for the 2p3d -2p 2 and 2p3d-2p3p(ΔL=±2, ΔS=±1) spectra of N II by using a large-scale multiconfiguration Dirac-Fock (MCDF) method. The most important effects of relativity, correlation, and relaxation are considered in the calculation Comparing with other calculations, a remarkable improvement is achieved.     

一道RC电路题解的商榷

在一辅导练习上,有电路如图1所示一题的解法,电源 =I0V,Rl=30Ω,R2=20Ω,R3=50Ω,Cl=lμF,C2=2μF,问C1,C2的带电量为多少. 原解:因为R3中无电流,故拿走,此时C1与C2串联与R1并联     

Invariant Sets and Exact Solutions to Higher-Dimensional Wave Equations

The invariant sets and exact solutions of the （1 ＋ 2）-dimensional wave equations are discussed. It is shown that there exist a class of solutions to the equations which belong to the invariant set E0 = {u ： ux = vxF（u）,uy = vyF（u） }. This approach is also developed to solve （1 ＋ N）-dimensional wave equations.     

164Lu的三轴超形变核态的理论计算

用三维TRS(totalrouthiansurface)自洽理论对奇奇核164Lu的位能面进行了计算,计算结果与实验上得到的ε2=0.38基本一致,从而从理论上确认了164Lu是三轴超形变核,并且指出了存在三轴超形变带的两个组态. Total routhian surface in~(164)Lu nuclei is calculated according to the three dimensional Total Routhian Surface (TRS) theory. The result of the calculation is in agreement with the experiment. At the same time, two TSD bands could be assigned to the configuration(π\(1/2), α=1/2)(ν\(5/2), α=1/2), (π\(1/2), α=1/2)(ν\(3/2), α=-1/2).     

里德伯钠原子经绝热快速通道的布居数跃迁相干控制

运用含时多态展开方法和B-样条函数研究了啁啾频率微波场中里德伯钠原子的量子态之间的布居数迁移.计算了里德伯钠原子n=70-77的开普勒频率.计算了在不同的微波场中六个态的布居数从n=70到n=77随时间的迁移,布居数跃迁到最终态n=77达到了98%,这可以通过连续的单光子跃迁来实现.结果表明,通过优化微波脉冲参数可以实现从低态到较高态的布居跃迁的相干控制.     

Analytical and Numerical Studies of Quantum Plateau State in One Alternating Heisenberg Chain

By using the coupled duster method and the numerical density matrix renormalization group method, we investigate the properties of the quantum plateau state in an alternating Heisenberg spin chain. In the absence of a magnetic field, the results obtained from the coupled cluster method and density matrix renormalization group method both show that the ground state of the aiternating chain is a gapped dimerized state when the parameter a exceeds a critical point ac. The value of the critical points can be determined precisely by a detailed investigation of the behavior of the spin gap. The system therefore possesses an m = 0 plateau state in the presence of a magnetic field When a 〉 ac. In addition to the m = 0 plateau state, the results of density matrix renormaiization group indicate that there is an m = 1/4 plateau state that occurs between two critical fields in the alternating chain if a 〉 1. The mechanism for the m = 1/4 plateau state and the critical behavior of the magnetization as one approaches this plateau state are also discussed.     

Octupole deformation for Ba isotopes in a reflection-asymmetric relativistic mean-field approach

The potential energy surfaces of even-even 142-156Ba are investigated in the constrained reflectionasymmetric relativistic mean-field approach with parameter set PK1. It is shown that for the ground states, 142Ba is near spherical,156Ba well quadrupole-deformed, and in between 144-154Ba octupole deformed. In particular, the nuclei 148,150Ba with N=92, 94 have the largest octupole deformations. By including the octupole degree of freedom, energy gaps N = 88, N = 94 and Z = 56 near Fermi surfaces for the singleparticle levels in 148Ba with β2 ～ 0.26 and β3 ～ 0.17 are found. Furthermore, the performance of the octupole deformation driving pairs （ν2f7/2, ν1i13/2） and （π2d5/2, π1h11/2） is demonstrated by analyzing the singleparticle levels near Fermi surfaces in 148Ba.     

分子拓扑学方法估算多环芳香烃类化合物的电离能

在构建多环芳烃类化合物分子的邻接矩阵主对角元时,结合烷基极化效应指数考虑分子图顶点的性质,以分子碎片C、CH、CH2、CH3等的相对能量作主元,用分子拓扑学方法构建了多环芳香烃类化合物新的邻接矩阵.研究结果发现,新的邻接矩阵特征根与多环芳香烃类化合物的电离能有良好的相关性Ipi=4.756+2.870OMOi,R=0.9853,s=0.1765,n=446.用这种新方法估算多环芳香烃类化合物的电离能,所用参数少且为分子结构性参数,稳定可靠,计算简便,结果较满意.     

单晶变角EPR谱的解释——I.掺Cr~(3 )铝铵矾单晶的EPR

对本征场的计算方法作了新的分析,提出了新的计算方案,根据这方案编写了程序,并应用这一程序对掺Cr~3 铝铵矾单晶变角的EPR谱作了解析,得到了更加可靠更为准确的自旋-Hamilton参数;D=0.04845cm~(-1),g_x=g_y=1.9761,g_x=1.9752.用上述参数,对各个离子不同角度下的广义本征场计算的共振磁场与实验数据拟合很好.充分说明采用此法处理EPR的优越性。     

单晶变角EPR谱的解释I.掺Cr3+铝铵矾单晶的EPR

对本征场的计算方法作了新的分析,提出了新的计算方案,根据这方案编写了程序,并应用这一程序对掺Cr³⁺铝铵矾单晶变角的EPR谱作了解析,得到了更加可靠更为准确的自旋-Hamilton参数;D=0.04845cm^-1,g_x=g_y=1.9761,g₂=1.9752.用上述参数,对各个离子不同角度下的广义本征场计算的共振磁场与实验数据拟合很好.充分说明采用此法处理EPR的优越性.     

碰撞能对O++DH (v=0, j=0)→OD++H的准经典轨线

运用准经典轨线的方法,基于RODRIGO势能面,研究反应体系O⁺+DH (v=0, j=0)→OD⁺+H的立体动力学性质. 对描述k-j′两矢量相关和k-k′-j′三矢量相关的分布函数P(θr)和P(φr)以及产物转动取向参数进行了详细的讨论,发现极化微分反应截面呈现有趣的现象. 计算了反应几率与反应截面. O⁺+DH (v=0, j=0)→OD⁺+H反应的立体动力学性质对体系的碰撞能非常敏感.     

对"吹肥皂泡过程中做功问题"的再讨论

"将压强p0=1.0 atm的空气等温地压缩进肥皂泡内,最后吹成R=2.5 cm的肥皂泡.设肥皂泡的胀大过程是等温的,求吹成这个肥皂泡所需的功,设肥皂水的表面张力系数为σ=4.5×10-2N/m".这是普通物理热学教学中少数极为精彩的习题之一,因而为国内许多通行的教材或选为习题,或采用为例题.用为例题的诸多教材中,一般都对求解过程描述得过于简捷[2],因而引起文[1]的讨论,并提出了自己的解题过程,得到异于通常教材的解答.实际上,文[1]的这种解法是错误的.     

He和D2分子相互作用转动激发研究

用T.T(K.T.TangandJ.Peter.Toennies)势模型和公认精密度较高的密耦(Close-Coupling)近似方法计算了E=0.1eV和E=0.2eV时,00-00弹性碰撞及00-02、00-04、00-06非弹性碰撞,得出D2分子转动激发分波截面,并得到了原子与分子碰撞弹性分波截面和非弹性激发截面随量子数增加的变化规律.     

AunPd(n=1～5)团簇的第一原理研究

用基于密度泛函理论的第一原理方法研究二元混合团簇AunPd(n=1~5)的稳定结构,得到团簇各种稳定结构的几何构形和对应的电子态,与纯Aun团簇比较研究了混合团簇AunPd(n=1~5)的稳定性.结果表明:AunPd(n=1~5)混合团簇具有多种稳定的异构体,部分异构体具有较高的自旋多重性.在Aun团簇中掺入Pd原子后,Au-Pd间的强相互作用改变了团簇的稳定结构,这种变化随团簇体积的增大而减小.     

Anisotropic electrical conductivity,phase transition and thermal hysteresis of a charge-transfer salt dibutylammonium bis-7,7,8,8-tetracyanoquinodimethane DBA（TCNQ）2

This paper reports that a charge-transfer salt dibutylammonium bis-7,7,8,8-tetraeyanoquinodimethane [DBA （TCNQ）2] has been prepared. The temperature dependences of the DC electrical conductivity of the DBA （TCNQ）2 single crystal measured along the crystallographic a, b, and c axes are reported. The crystal shows semicondueting behaviour and the room-temperature conductivities are highly anisotropic （σa = 3.63× 10^-4S/cm, σb = 2.84× 10^-6S/cm, and （σe = 1.82 × 10^-5S/cm）. Particularly, a sharp semiconductor to semiconductor transition has been observed around 270 K on the resistivity curves measured under cooling and heating. In addition, thermal hysteresis phenomena on conductivity and differential scanning calorimetry curves are also reported.     

隐性力矩问题与力矩概念教学——2003全国高考理综19题引发的思考

物体在共点力(力的作用点在同一点或力的作用线相交于一点)作用下的平衡条件为F合=0以及M合=0.在静力学问题中,学生往往善用F合=0这个平衡方程去解决,其实,将M合=0应用于静力学问题有时会更简洁、方便.这样,就要求学生善于在习题中看出隐性的力矩来.下面先以2003年高考理综19题为例,说明这种方法,同时谈一点对力矩教学的拙见.     

Supersymmetric Sawada-Kotera-Ramani Equation： Bilinear Approach

In this paper, using the Hirota＇s bilineax method, we consider the N = 1 supersymmetric Sawada-Kotera- Ramani equation and obtain the Bazcklund transformation of it. Its one- and two-supersoliton solutions axe obtained and N-supersoliton solutions for N ≥ 3 are given under the condition kiξj = kjξi.     

高离化态金离子的辐射复合及其退激发过程的理论研究

利用基于多组态Dirac-Fock方法的程序包GRASP92和RATIP以及最新发展的RERR06程序,详细计算了高离化态金离子(类镍Au51+、类铜Au50+和类锌Au49+)俘获一个自由电子到nl(n=4—8,l=0—3)壳层的辐射复合谱以及相应的辐射退激发谱.理论计算的辐射复合谱很好地重现了实验谱.研究结果表明:对类镍Au51+、类铜Au50+和类锌Au49+而言,将一个自由电子俘获到n=4壳层的概率最大;在辐射复合过程之后,处在n=4壳层的俘获电子的辐射退激发谱线最强,并且体现了整个辐射退激发谱的主要特征.