内陷在C60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。     

氢原子Rydberg态抗磁谱的高阶B-spline基组计算

在球坐标下采用基组展开方法计算了均匀磁场中的氢原子高Rydberg态能谱和振子强度谱.径向和角向均采用高阶B样条基组. 径向采用B样条基组能很好地描述束缚态与连续态的耦合；角向采用B样条基组有效地减少了基组维数，计算效率得到大幅度提高. 用上述方法计算了磁场中氢原子Rydberg态-40cm^-1到零场电离阈的高精度抗磁谱并与已有理论和实验结果作了比较. 该方法适用于低于离化阈的所有能区的精确谱计算并易于推广到非氢原子、交叉场中的原子以及高于离化阈的正能区光谱的计算. 关键词： 氢原子 B样条基组 能谱 振子强度谱     

椭球坐标下求解强磁场中的氢原子

在椭球坐标系下,采用B样条基组方法计算了磁场范围在0-1000 a.u.下氢原子低能态能量以及实验室磁场下(几个特斯拉)氢原子里德堡态的能级,得到了至少9位有效数值的高精度能谱并与文献中的精确结果进行了比较.本文方法为精确计算强磁场下原子能谱提供了一个新的选择方案.     

椭球坐标下求解强磁场中的氢原子

在椭球坐标系下，采用B样条基组方法计算了磁场范围在0—1000 a．u．下氢原子低能态能量以及实验室磁场下（几个特斯拉）氢原子里德堡态的能级，得到了至少9住有效数值的高精度能谱并与文献中的精确结果进行了比较。本文方法为精确计算强磁场下原子能谱提供了一个新的选择方案。     

基于变分法求解氢原子的径向波函数和能级

基于变分法求解量子力学中氢原子模型并给出相应的推导,运用Mathematica软件辅助计算最优的试探波函数和相应的能级,并与由合流超几何函数(Kummer函数)所给出的氢原子能级分布与径向波函数进行比较.     

Monte Carlo方法在B样条函数分频理论中的应用

针对弹道参数的B样条表示问题,运用Monte Carlo方法对B样条函数分频理论进行仿真论证,得到B样条延拓节点的补充方法,并验证B样条函数逼近空间相容性定理的正确性.比较Monte Carlo方法和B样条分频算法的计算结果,说明分频算法合理.将该算法应用于外弹道跟踪测量数据的处理中,可以确定出表示弹道所需要的样条节点个数及样条节点序列的排布,有效减少待估参数个数.     

用玻尔理论统一处理氢原子、电子偶素和氦原子基态能级

用玻尔氢原子理论处理氢原子和电子偶素基态的方法,在假定了氦原子基态的经典模型后,给出了氦原子基态能级和半径,并与实验和量子力学变分法计算的结果作比较,说明玻尔氢原子理论对氦原子基态能级的计算有一定的意义.     

用玻尔理论统-处理氢原子、电子偶素和氦原子基态能级

用玻尔氢原子理论处理氢原子和电子偶素基态的方法，在假定了氦原子基态的经典模型后，给出了氦原子基态能级和半径，并与实验和量子力学变分法计算的结果作比较，说明玻尔氢原子理论对氦原子基态能级的计算有一定的意义．     

平行电磁场中的Rydberg锂原子吸收谱的模型势计算

用B样条基组展开方法结合模型势计算了Rydberg锂原子在平行电磁场下的振子强度谱. 径向和角向均采用高阶Ｂ样条基组.计算结果与已有的实验结果符合得很好.利用分波分析法,对部分谱线的振子强度的强弱进行了分析. 本文方法简单有效，易于推广到交叉电磁场中Rydberg原子的精确谱的计算. 关键词： B样条 能谱 振子强度 平行电磁场 Rydberg原子     

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.     

Polaronic exciton in quantum wells wires and nanotubes

We investigate the effect of the longitudinal-optical phonon field on the binding energies of excitons in quantum wells, well-wires and nanotubes based on ionic semiconductors. We take into account the exciton-phonon interaction by using the Aldrich-Bajaj effective potential for Wannier excitons in a polarizable medium. We extend the fractional-dimensional method developed previously for neutral and negatively charged donors to calculate the exciton binding energies in these heterostructures. In this method, the exciton wave function is taken as a product of the ground state functions of the electron polaron and hole polaron with a correlation function that depends only on the electron-hole separation. Starting from the variational principle we derive a one-dimensional differential equation, which is solved numerically by using the trigonometric sweep method. We find that the potential that takes into account polaronic effects always give rise to larger exciton binding energies than those obtained using a Coulomb potential screened by a static dielectric constant. This enhancement of the binding energy is more considerable in quantum wires and nanotubes than in quantum wells. Our results for quantum wells are in a good agreement with previous variational calculations. Also, we present novel curves of the exciton binding energies as a function of the wire and nanotubes radii for different models of the confinement potential.     

一维和二维多势阱能谱的Bsplines计算

用Bsplines函数基计算了一维多势阱和二维Henon Heiles势的能谱,得到了精度较高的结果.将这一结果与采用高斯基函数计算的结果进行比较,结果表明:Bsplines函数基用于研究一维束缚态问题比高斯函数基方法更方便,具有灵活、可塑性强、效率高等优点,适用于不同形式势作用下的系统的变分求解.     

Laser field-driven potential profiles of double quantum wells

We study the potential profiles of double quantum wells with different geometries. The binding energy of an impurity under a laser field and its simultaneous application with a magnetic field is calculated by means of variational techniques. It is shown that the total potential of the structure suggests a strong control mechanism on the binding energy.     

抛物量子点中强耦合束缚磁极化子的声子平均数

采用线性组合算符和幺正变换方法导出了强耦合束缚磁极化子的振动频率和声子平均数。讨论了量子点的有效受限长度、磁场、库仑场和电子-LO声子耦合强度对抛物量子点中强耦合束缚磁极化子振动频率和声子平均数的影响。数值计算结果表明:强耦合束缚磁极化子的振动频率和声子平均数均随量子点的有效受限长度、回旋共振频率的增加而减小,随库仑束缚势的增加而增加,声子平均数随电子-LO声子耦合强度增加而减小。     

Use of ab initio methods to classify four existing energy density functionals according to their possible variational validity

Density functional theory is, of course, fundamentally a variational method. Therefore, in this Letter we suggest a classification of available energy density functionals into two groups, which we term (i) heuristic (H) and (ii) possibly variationally valid (PV). Quantum-chemical ab initio methods are employed on some selected neutral and anionic atomic systems and the molecules H₂O and LiOB to make this separation into H and PV groups in the case of the exchange-correlation functionals LDA, PBE, PW91 and B3LYP. This study shows that while the PBE is a potential candidate for being variationally valid, the B3LYP, today's other most widely used density functional, shows its strongly heuristic character. The investigation of variational validity can be an important part of systematic functional development, which is today's biggest challenge in DFT.     

Binding energy of a polaron in asymmetric polar semiconductor heterostructures

By using a modified Lee-Low-Pines variational method, we have investigated the ground-state binding energy of a polaron confined in asymmetric single and step quantum wells (QWs) due to interface phonons, confined bulk-like LO phonons, and half-space LO phonons. The relative importance of the different phonon modes is analysed in detail. Our results show that the asymmetry and the well width of the QWs have a significant influence on the polaron energy. The polaron binding energy has an intimate relation to the potential parameters of QWs. The subband nonparabolicity has a little influence to the polaron binding energy. Comparing with the results calculated with perturbation theory, a good agreement is found.     

The Binding Energy of an Exciton in Type-Ⅱ Quantum Wells with a Dielectric Mismatch

From a general viewpoint, the binding energy of the excitons in type-Ⅱ hetero-quantum- wells with the presence of a dielectric mismatch is discussed by making use of image potentials, variational method and infinite-potential-barrier model. The calculation is performed for various parameters including the electron-hole mass ratio σ, dielectric constant ratio δ and well width d. A static Gabovish-type potential is engaged to describe the image potential inside the well. It is found that the image potential may play an important role in the formation of the excitons. The contribution of image potentials to the binding energy is compared with binding energy for two kinds of type-I1 hetero-QWs, GaSb-InAs-GaSb and AlAs-GaAs-AlAs. In these two cases, the image potentials are above 10% of the corresponding binding energies.     

Variational calculation of low-lying and excited vibrational levels of the water molecule

The variational method of calculating vibrational energy levels for triatomic molecules has been extended to determine the lowest 22 levels for H₂O, using an analytic form for the potential surface developed by Sorbie and Murrell. In addition, complete ab initio calculations of the fundamental frequencies for H₂O have been carried out using extensive configuration interaction forms for the potential. They are predicted to be 3720, 1629, and 3807 cm^?1, to be compared with experimental values of 3656, 1597, and 3754 cm^?1. Also discussed is how the variational method may be extended to allow the calculation of vibrational energy levels for larger molecules.     

The binding energy of a shallow donor in type-II quantum wells

The binding energy of a shallow donor in type-II quantum wells was calculated by a variational method, using a single parameter. A type-II AlAs/GaAs single quantum well was chosen to calculate the binding energy of a shallow donor as a function of the donor position and the barrier width.