N维势箱函数量子特性的可视化研究

运用量子理论推导和数值计算相结合的方法,本文首先得到了一维势箱函数的示意图及其模型.接着,全面、系统地研究了量子理论中N维势箱函数的波函数、能级和概率密度.最后,运用MATLAB软件对势箱函数的所有特性进行了仿真模拟.我们发现:N维势箱中粒子的能量是量子化的、不连续;量子数n不能为零,且n越大对应的能级越高,而质量m越大,对应的能级越低.一般条件下,一维势箱长度a越大(粒子运动范围越大),对应的能级越低;节点数为n-1,节点越多,波长越短,频率越高,能级越高.二维势箱函数波函数的峰值个数为n x 0x0E?SymboltB@0x0Fn y,且与Ψ=0平面的交线数也为n x 0x0E?SymboltB@0x0Fn y;概率密度分布的极大值个数也为n x 0x0E?SymboltB@0x0Fn y.对于简并度,一般情况下,二维势箱模型下的粒子的简并度是不确定的;但对于二维正方势箱函数模型,其箱内微观粒子的能级简并度分为特殊和一般两种情况.三维势箱函数的简并度为n x+n y+n z.最后,首次借助MATLAB软件的色彩实现了四维表现,得到了三维势箱函数的四维空间切片图.这种可视化的结果与理论结果完全一致,这对于抽象性概念的理解具有重要意义.     

势问题的径向基函数——局部边界积分方程方法

将基于径向基函数构造的具有插值特性的近似函数和局部边界积分方程方法相结合，建立了求解势问题的径向基函数——局部边界积分方程方法，推导了相应离散方程.与其他边界积分方程的无网格方法相比，本文方法具有数值实现过程简单、计算量小、精度高的优点，并可直接施加边界条件.最后通过算例说明了该方法的有效性. 关键词： 径向基函数 无网格方法 局部边界积分方程 势问题     

PuN基态分子势能函数与热力学函数的理论计算

在Pu的相对论有效原子实势近似和N原子 6 - 311G 全电子基函数下 ,用密度泛函B3LYP方法计算得到PuN分子基态X6Σ+ 的结构与势能函数、力常数与光谱数据 .同时计算得到PuN(g)分子在 2 98K时的标准生成热力学函数ΔfH0 、ΔS0 和ΔfG0 ,分别为 - 4 87.2 39kJ/mol、95 .345J/molK和 - 5 15 .6 6 6 1kJ/mol.     

线性变分法研究一维无限深势阱中粒子的能级和波函数

采用满足连续性条件的多项式独立基函数,应用线性变分法通过求解广义本征值方程研究了一维无限深势阱中粒子的能级和波函数.计算表明,随着试验基函数个数的增大,线性变分法的结果趋近于精确的解析结果.     

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.     

重金属钋化物分子MPo(2∏),(M=Cu,Ag,Au)的结构和势能函数

利用相对论小核赝势研究了重金属钋化物分子MPo(X2∏),(M=Cu,Ag,Au).用群论方法结合原子分子反应静力学原理导出了分子的基电子状态和相应的离解极限,并在各种电子相关理论水平上计算了它们的平衡几何和振动频率.在此基础上用Murrell-Sorbie函数形式拟和势能曲线,得到了总的解析势能函数,并计算出了光谱数据和力常数.     

紧束缚势和修正的嵌入原子势计算液态Sn双体相关函数差异

对500个Sn原子分别用两种模型(紧束缚势和修正的嵌入原子势)计算了400℃～1700℃温度范围内纯Sn的双体相关函数g(r).将计算结果与实验数据进行了对比分析,发现两种计算结果都能基本上反映液态Sn的结构及其随温度的变化情况:原子最近邻距离与实验结果相近;随着温度降低,双体相关函数第一峰变得尖锐,第二峰变得明朗.修正的嵌入原子势模型得到的双体相关函数的第一峰右侧有个突起的肩膀,这在实验结果中也被发现,而紧束缚势模型得到的双体分布函数肩膀不明显.     

电子关联与二维晶格的不稳定性

本文从电子相互作用的屏蔽库仑势出发,构造了Wannier函数来计算二维不稳定晶格的能带及电子波函数,用相关基函数理论计算了二维非均匀体系的电子关联函数,由此研究了电子关联对二维晶格不稳定性的影响。结果表明,二维体系与一维体系不同,电子相互作用使晶格二聚化减弱。 关键词：     

散射相函数对一维介质内辐射传递的影响规律

采用有限体积法研究了一维线性各向异性散射介质内散射相函数对辐射传递的影响规律.经与理论解、辐射元法、蒙特卡洛法计算结果比较表明,有限体积法的计算结果更可靠,且不同散射相函数的辐射换热系统中,其无因次热流之比与光学厚度之间存在某种单调变化的函数关系,利用该函数关系可以检验模型的准确度.     

耦合径向基函数与多项式基函数的无网格方法

耦合径向基函数和多项式基函数,形成一种新的近似函数.该近似函数对散乱分布的离散数据点进行逼近时,只需节点信息,不需要划分网格.详细描述了耦合近似函数的建立、属性、插值行为及其形函数和形函数导数的性质.最后引入修正变分原理和单位分解积分技术求解边值问题,并给出了计算实例,表明耦合径向基函数和多项式基函数是一种非常有效的方法.     

Inner‐shell chemical shift of DNA/RNA bases and inheritance from their parent purine and pyrimidine

Inner‐shell electronic structures, properties and ionization spectra of DNA/RNA bases are studied with respect to their parent pyrimidine and purine species. Density functional theory B3LYP/aug‐cc‐pVTZ has been employed to produce the geometries of the bases, whereas LB94/et‐pVQZ//B3LYP/aug‐cc‐pVTZ is used to calculate site‐related Hirshfeld charges and core (vertical) ionization energies, as well as inner‐shell spectra of C1s, N1s and O1s for DNA/RNA bases and their parent pyrimidine and purine species. The site‐dependent variations of properties indicate the changes and inheritance of chemical environment when pyrimidine and purine become substituted. In general, although the changes are site‐dependent, they are also ring‐dependent. Pyrimidine bases change less significantly with respect to their parent pyrimidine than the purine bases with respect to their parent purine. Pyrimidine bases such as uracil, thymine and cytosine inherit certain properties from their parent pyrimidine, such as the Hirshfeld charge distributions and the order of core ionization energy level etc. No particular sites in the pyrimidine derivatives are engaged with a dramatic chemical shift nor with energy crossings to other sites. For the core shell spectra, the purine bases inherit very little from their parent purine, and guanine exhibits the least similarities to the parent among all the DNA/RNA bases.     

内陷在C_(60)中的氢原子的性质

在短程球形势阱的模型下 ,运用线性变分法并采用B 样条作为展开基函数计算了内陷于C60 几何中心的氢原子能谱和波函数 ,并计算了势阱深度对能谱的影响 ,详细讨论了内陷氢原子表现出的一系列特殊性质 ,从而对低维半导体材料性能的研究提供了有效的数据 ;同时这一工作也表明 ,用线性变分法结合B 样条函数在处理这类问题时是非常有效的。     

Fisher information for endohedrally confined hydrogen atom

Electron localization and delocalization of endohedrally confined hydrogen atom has been investigated employing Fisher information theory. Confinement has been modeled using a spherical Gaussian-type potential. B-spline bases expansion method was used to solve the Schrödinger equation to obtain the required energy eigenvalues and the corresponding wave functions. Changes in energies with depths of potential are explained using Hellmann-Feynman theorem. The behavior of Fisher information against the confining potential depths and positions are demonstrated. Moreover, our results show that Fisher information is an effective way to measure the localization of valence electrons.     

三种非对称Schiff碱的1H NMR谱

讨论了三种新型非对称Schiff碱3,4-二羟基苯甲叉单草酰胺肟,2-羟基苯甲叉单草酰胺肟和苯甲叉单草酰胺肟的¹H NMR谱,并给出这三种化合物的活泼氢的归属.     

三种Schiff碱的Raman振动特性及其归属

本文研究了三种反对称Schiff碱的Raman振动特性,分析了三种Schiff碱的拉曼振动模式,给出了所观察到的Raman振动的归属。     

Theoretical analysis of the experimental UV-Vis absorption spectra of some phenolic Schiff bases

The time-dependent density functional theory (TDDFT) was applied in conjunction with the natural bond orbital analysis to examine the UV-Vis properties of 10 phenolic Schiff bases. The calculations were performed with different functionals, but main discussion refers to results obtained at the B3LYP/6-311+G(d,p) level of theory. The approach based on the natural localised molecular orbital clusters indicates similar behaviour for majority of examined compounds. The HOMO (“highest occupied molecular orbital”) cluster is delocalised over the ring which is electron richer, the HOMO-1 cluster is spread over the other ring, whereas the LUMO (“lowest unoccupied molecular orbital”) cluster is situated on the imino group. The two bands at long wavelengths correspond to the HOMO → LUMO and HOMO-1 → LUMO transitions, i.e. from both A and B rings to the imino group. The next band originates from a transition from the imino group to the imino group. The band at the smallest wavelengths originates from a transition from the A ring to the A ring, or from the B ring to the B ring. Our findings are in very good agreement with the existing literature data.     

强激光等离子体的光学度规描述

利用一维等温膨胀激光等离子体的自洽密度分布和有质动力势,得到了强激光等离子体的光学度规,阐述了它的物理意义。 关键词：     

A multinuclear magnetic resonance study of intramolecular hydrogen bonding in some Schiff and Schiff-Mannich bases in solution and in the solid state

Two Schiff bases; N, N′-bis(5-bromosalicylidene)-1,2-diaminoethane, BS, and 7-[(1-{5-bromo-2-hydroxyphenyl} methylidene)amino]-4-methylcoumarin, Sc, and two appropriate Schiff–Mannich bases, N, N′-bis{5-bromo-3-[(diethylamino)methyl]salicylidene}-1,2-diaminoethane, BSM, and 7-[(1-{5-bromo-3-[(diethylamino)methyl]-2-hydroxyphenyl} methylidene)amino]-4-methylcoumarin, SMc, capable of intramolecular hydrogen bonding have been investigated by multinuclear magnetic resonance methods in both solid and liquid phases. In all of the compounds under investigation tautomeric equilibrium involving an intramolecular hydrogen bond has been found. The Schiff–Mannich bases, which can form two different kinds of H bonds at room temperature, form relatively weak H bonds with the imino nitrogen atoms. At low temperatures the tautomeric proton exchange becomes slow on the NMR time scale and both hydrogen-bonded forms can be observed by ¹H, ¹³C, and ¹⁵N NMR methods. In the solid state the tautomeric process is frozen and only one H-bonded form is present. On the basis of 13C and ¹⁵N CPMAS NMR spectra this is identified as the form with hydrogen bonds involving the imino groups. This conclusion is in good agreement with previous results obtained by X-ray diffraction methods.

The investigated Schiff bases (BS and Sc) form relatively weak H bonds. The proton position in the hydrogen bridge, estimated from ¹⁵N and ¹³C chemical shifts, is very similar in both the solution and solid phases. In chloroform solution the observed tautomeric equilibria are almost insensitive to a temperature change within the range 223 to 303 K.     

对“有限空间里可不可以有量子力学?”的回答

本文回答了文献《光子学报》1999,28(2):118～119对我们的论文(《光子学报》1998,27(8):734～738)所作的评论,强调指出,量子力学的整体性概念具有深刻的物理基础,Lan-dau和Lifshitz所讨论的一维无限深势阱中粒子的动量概率分布的出发点和结论是完全正确的。     

Quantum Standard Teleportation Based on the Generic Measurement Bases

We study the quantum standard teleportation based on the generic measurement bases. It is shown that the quantum standard teleportation does not depend on the explicit expression of the measurement bases. We have giventhe correspondence relation between the measurement performed by Alice and the unitary transformation performed byBob. We also prove that the single particle unknown states and the two-particle unknown cat-like states can be exactlytransmitted by means of the generic measurement bases and the correspondence unitary transformations.