一维δ势阱中的相对论粒子

求解一维相对粒子的Dirac方程。对一维δ势阱，计算了束缚态能级与波函数；对一维双δ势阱，给出了束缚态能级所满足的超越方程，并确定了束缚态的数目，简单讨论了散射问题。     

方势阱中束缚态粒子能级的数值方法和波函数的图示

用数值方法求出了一维有限深不对称方势阱中束缚态粒子的能级和归一化波函数及其图示,所得结果在势阱深度趋于无穷大时与无限深势阱的结果一致.     

Ne-Xe体系势能曲线和光谱研究

本论文对Ne-Xe体系的势能曲线和束缚态能级作了系统的研究.采用耦合簇CCSD(T)方法和超分子近似,以及aug-cc-PVXZ(X=T,Q,5)基组,计算了Ne-Xe体系的相互作用势,并采用三种方案外推得到基底限值,给出了不同基底和外推方法下的势能曲线平衡位置和势阱深度.计算了Ne-Xe体系振转能级和各同位素基振动态的纯转动跃迁频率,及相应的光谱常数,并与实验结果进行了比较.     

一维有限深方势阱中的束缚态

主要对量子力学一维有限深方势阱中运动粒子的束缚态存在条件进行讨论.通过求解定态薛定谔方程,得到粒子运动满足的超越方程,借助于Mathematica软件求解该超越方程得到粒子的能级结构,对粒子束缚态存在条件进行分析.结果表明,对于在一维有限深对称方势阱中运动的粒子,总会有束缚态的存在,和势阱的宽度、深度及粒子的质量无关.而在半壁有限深势阱中运动的粒子,出现束缚态是有条件的.并且分别给出了在两种势阱中粒子存在多个束缚态需要满足的条件.     

在点正则变换下双原子分子的广义Hulthén势映射至P(o)schl-Teller Ⅰ势

利用在点正则变换下形状不变势的映射方法,找出了该问题需要的点正则变换,建立了双原子分子的广义Hulthén势和Pschl-Teller Ⅰ势之间的关系,并由Pschl-Teller Ⅰ势的束缚态能级和波函数,方便地求得了广义Hulthén势的束缚态能级和波函数.     

一维无限深梯形势阱中微观粒子波函数和能级的半解析解

利用特殊函数研究了一个数学形式简单但物理内涵丰富的新势阱——一维无限深梯形势阱,并得到了处于该势阱中微观粒子的波函数和能级的半解析解,其结果可以用来从理论上分析梯形沟道势阱的二维电子气的物理机制.此外指明了它与熟知的一维无限深方势阱和三角势阱的联系与区别,并基于对应原理讨论了该模型下粒子波函数的特征.     

具有一维Coulomb型对称势Dirac方程的精确解

在标量势大于矢量势的情况下,一维Dirac方程的束缚态能级是二重简并的.任意两个不同能量本征值的波函数和同一能量本征值的两个波函数都是相互正交的.对于纯标量场,存在零能量束缚态,存在分数电荷 关键词： Coulomb型对称势 Dirac方程 束缚态 分数电荷     

用点正则变换方法求解双原子分子的双曲型Poschl-Teller势的束缚态

采用在点正则变换下形状不变势的映射方法,给出了将Poschl-Teller Ⅰ势映射至Poschl-Teller Ⅱ势的点正则变换,并从Poschl-TellerI势的束缚态能级和波函数求得了Poschl-Teller Ⅱ势的束缚态能级和波函数.     

用点正则变换方法求解双原子分子的双曲型P?schl-Teller势的束缚态

采用在点正则变换下形状不变势的映射方法,给出了将Poschl-Teller Ⅰ势映射至Poschl-Teller Ⅱ势的点正则变换,并从Poschl-TellerI势的束缚态能级和波函数求得了Poschl-Teller Ⅱ势的束缚态能级和波函数.     

一维双势阱问题的理论研究

利用数值计算的方法求解了一维理想双势阱模型的基态及低激发态能级和相应的波函数,将双势阱之间的间距、双势阱的相对深度和双势阱的宽窄与实际的物理问题建立了联系,并分析了它们对一维双势阱的能级和相应波函数的影响,定性地模拟了双原子分子和原子中的双势阱问题.     

The stereodynamic properties of the F+HO(v,j) → HF+O reaction on~1 A' and ~3A' potential energy surfaces by quasi-classical trajectory calculations:Initial excitation effect(v=1-3, j=0 and v= 0, j=1-3)

The stereodynamic properties of the F ＋ HO （v, j） reaction are explored by quasi-classical trajectory （QCT） calculations performed on the 1At and 3At potential energy surfaces （PESs）. Based on the polarization-dependent differential cross sections （PDDCSs） and the angular distributions of the product angular momentum with the reactant at different values of initial v or j, the results show that the product scattering and product polarization have strong links with initial vibrationalrotational numbers of v and j. The significant manifestation of the normal DCSs is that the forward scattering gradually becomes predominant with the initial vibrational excitation increasing, and the scattering angle of the HF product taking place on the 3At potential energy surface is found to be more sensitive to the initial value of v. The product orientation and alignment are strongly dependent on the initial rovibrational excitation effect. With enhancement in the initial rovibrational excitation effect, there is an overall decrease in the product orientation as well as in the product alignment either perpendicular to the reagent relative velocity vector k or along the direction of the y axis, for which the initial rotational excitation effect is much more noticeable than the vibrational excitation effect. Moreover, the initial rovibrational excitation effect on the product polarization is more pronounced for the 3At potential energy surface than for the 1At potential energy surface.     

The stereodynamic properties of the F + HO (v,j)→HF + O reaction on the 1A' and 3A' potential energy surfaces by quasi-classical trajectory: Initial excitation effect (v =1-3, j = 0 and v = 0, j =1-3)

The stereodynamic properties of the F + HO (v, j) reaction are explored by quasi-classical trajectory (QCT) calculations performed on the ¹A' and ³A' potential energy surfaces (PESs). Based on the polarization-dependent differential cross sections (PDDCSs) and the angular distributions of the product angular momentum with the reactant at different values of initial v or j, the results show that the product scattering and product polarization have strong links with initial vibrational-rotational numbers of v and j. The significant manifestation of the normal DCSs is that the forward scattering gradually becomes predominant with the initial vibrational excitation increasing, and the scattering angle of the HF product taking place on the ³A' potential energy surface is found to be more sensitive to the initial value of v. The product orientation and alignment are strongly dependent on the initial rovibrational excitation effect. With enhancement in the initial rovibrational excitation effect, there is an overall decrease in the product orientation as well as in the product alignment either perpendicular to the reagent relative velocity vector k or along the direction of the y axis, for which the initial rotational excitation effect is much more noticeable than the vibrational excitation effect. Moreover, the initial rovibrational excitation effect on the product polarization is more pronounced for the ³A' potential energy surface than for the ¹A' potential energy surface.     

Ne-BeH体系的相互作用势和能级结构的理论研究

本文对Ne-BeH体系采用单双迭代(包括非迭代三重激发)耦合簇理论CCSD(T)方法,对Be , H 和 Ne原子采用aug-cc-pVQZ基组和3s3p2d1f1g中心键函数.利用非线性最小二乘法拟合该理论水平下的相互作用能,得到了Ne-BeH弱相互作用体系在冻结BeH键长情况下的二维的全程势能面,在 和 处存在一全局最小值-34.43607 .利用该势能面,计算了Ne-BeH体系的J=0-9的能级结构.以期对Ne-BeH的相关的实验和理论研究提供必要的参考和借鉴.     

Ne-BeH体系的相互作用势和能级结构的理论研究

本文对Ne-BeH体系采用单双迭代(包括非迭代三重激发)耦合簇理论CCSD(T)方法,对Be , H 和 Ne原子采用aug-cc-pVQZ基组和3s3p2d1f1g中心键函数.利用非线性最小二乘法拟合该理论水平下的相互作用能,得到了Ne-BeH弱相互作用体系在冻结BeH键长情况下的二维的全程势能面,在 和 处存在一全局最小值-34.43607 .利用该势能面,计算了Ne-BeH体系的J=0-9的能级结构.以期对Ne-BeH的相关的实验和理论研究提供必要的参考和借鉴.     

Variational Calculation of Energies of Highly Excited Rovibrational States of CO2

Accurate variational calculations of energies of highly excited rovibrational states of ¹²C¹⁶O₂ using a Lanczos recursion are presented. In a first step, we use experimental rovibrational transition frequencies to determine by a least-square fitting procedure a potential energy surface for the CO₂ molecule. This potential energy surface is expressed as a multidimensional power series expansion in the normal coordinates. It is then used to determine all the rovibrational energies for symmetry e levels up to a rotational number J=200, a vibrational energy of 13 000 cm⁻¹, and a vibrational angular momentum l=13.     

Mg-CO体系的相互作用势和光谱预测

采用单双迭代包括非迭代三重激发微扰处理的耦合簇CCSD (T)理论和大的基组, 计算了Mg-CO体系的相互作用势, 首次得到了该体系解析表达的势能面,发现势能面呈现较弱的各向异性, 全域极小势阱深-72.21 cm^-1, 位于R_e=8.98a₀和θ=119.09°. 利用该势能面, 计算了体系的束缚态能级, 理论上对光谱常数和微波谱作出了预测. 关键词： Mg-CO体系 势能面 光谱     

Collective and independent-particle motion in two-electron artificial atoms

Investigations of the exactly solvable excitation spectra of two-electron quantum dots with a parabolic confinement, for different values of the parameter R(W) expressing the relative magnitudes of the interelectron repulsion and the zero-point kinetic energy, reveal for large R(W) a rovibrational spectrum associated with a linear trimeric rigid molecule composed of the two electrons and the infinitely heavy confining dot. This spectrum transforms to that of a "floppy" molecule for smaller R(W). The conditional probability distribution calculated for the exact two-electron wave functions allows identification of the rovibrational excitations as rotations and stretching/bending vibrations.     

Vibronic spectra of aluminium monochloride relevant to circumstellar molecule

The A^1Π→ X^1Σ^+ transition system of aluminium monochloride is determined by using ab initio quantum chemistry.Based on the multi-reference configuration interaction method in conjugate to the Davidson correction(MRCI + Q), the potential energy curves(PECs) of the three electronic states are obtained. Transition dipole moments(TDMs) and the vibrational energy levels are studied by employing the aug-cc-pwCV5Z-DK basis set with 4220-active space. The rovibrational constants are first determined from the analytic potential by solving the rovibrational Schr ¨odinger equation, and then the spectroscopic constants are determined by fitting the vibrational levels, and these values are well consistent with the experimental data. The effect of spin–orbit coupling(SOC) on the spectra and vibrational properties are evaluated.The results show that the SOC effect has almost no influence on the spectroscopic constants of AlCl molecules. For the A^1Π→ X^1Σ^+transition, the highly diagonalized Frank–Condon factor(FCF) is f(00)=0.9988. Additionally, Einstein coefficients and radiative lifetimes are studied, where the vibrational bands include ν'= 0–19→ν'=0–9. The ro-vibrational intensity is calculated at a temperature of 296 K, which can have certain astrophysical applications. At present, there is no report on the calculation of Al Cl ro-vibrational intensity, so we hope that our results will be useful in analyzing the interstellar Al Cl based on the absorption from A^1Π→ X^1Σ^+.     

Semiempirical study of perturbations of the Landé g factors of the electronic-vibrational-rotational levels of hydrogen: I. Theory

Theoretical analysis of perturbations of the Landé g factors of the electronic-vibrational-rotational levels of a diatomic molecule is performed for the case of interactions between electronic states whose number is arbitrary finite and that are not limited by the smallness of the parameter describing these interactions, with regard for the interaction of rovibrational states with an arbitrary finite number of vibrational-rotational levels of individual perturbing electronic states. The spin-multiplet interaction between rovibrational states was disregarded. As a result of general consideration, formulas are obtained for the g factors of rovibrational levels for the following cases: (i) mutual perturbation of a pair of levels; (ii) an nl complex of terms; and (iii) the interaction between an arbitrary number of vibrational-rotational levels of electronic states (whose number is also not limited) considered in the first order of the perturbation theory. The formulas obtained are given in the form of dependences on differences in observed (perturbed) values of rovibrational terms and matrix elements of vibrational wave functions dependent on the internuclear distance, which, in turn, are matrix elements of the electron wave functions of different operators that take into account the interaction between the electrons and nuclei of a molecule. The possibilities of using the obtained expressions in semiempirical study of perturbations and of determining the absolute dependences of the g factors of rovibrational levels of the electronic states of diatomic molecules (in particular, the hydrogen molecule) on the vibrational and rotational quantum numbers are analyzed.