B样条基组在原子物理及人工受限结构中的若干应用

发布时间：2018-01-05 13:08

  本文关键词：B样条基组在原子物理及人工受限结构中的若干应用　出处：《中国科学院研究生院(武汉物理与数学研究所)》2016年博士论文　论文类型：学位论文

  更多相关文章： B样条基组 氢原子 碱土离子 超极化率 量子环

【摘要】：B样条函数基组是定义在有限空间的由分段多项式构成的基组,具有高局域性、近似完备性、和高可塑性等特点。这些独有的特征使得其能够很好地描述原子、分子的束缚态和连续态,因而在原子结构计算、碰撞动力学以及原子与分子外场效应研究中得到广泛的应用。本文把B-样条基组方法应用到简单原子体系的精密能谱计算与外场效应的研究中；同时构建了满足周期性边界条件的新的基组,并应用于量子环体系的能谱、磁场和杂质效应的研究中。论文主要内容包括：(1)采用B样条基组方法得到了氢原子精确的非相对论和相对论能级、波函数以及电偶极极化率和超极化率,精确确定了氢原子1s→2s和1s→3s跃迁的系列幻波长；针对1s→3s跃迁光谱测量,提出利用1371nm幻波长适用于氢原子的光囚禁方案以提高该跃迁光谱测量的精度。(2)发展了基于B样条基组的有限场方法,利用模型势计算得到了碱土离子Be+、Mg+、Ca+和Sr+离子低能态的极化率和超极化率理论值,为跃迁频移的高阶极化效应的理论评估提供了参考数值；利用准静态近似给出了超极化效应对光阱囚禁Ca+离子钟跃迁频移的影响。(3)氢原子QED修正领头项涉及贝特对数项计算,本文采用B样条基组在三种不同的规范下计算了氢原子的贝特对数项,给出了不依赖前人结果的自洽验证；发展了有外电场存在时的贝特对数项的高效计算方法,为极化率的QED修正计算打下了基础。(4)设计构造了一种环形B样条基组用于计算量子环中的电子波函数,这种构造的B样条基组避免了传统B样条基组在定义区间两端处存在导数不连续问题,满足周期性边界条件,并成功应用于等人工受限结构(量子环)的能谱、磁场和杂质效应的研究中。
[Abstract]:The basis set of B-spline function is defined in finite space, which is composed of piecewise polynomials. It has the characteristics of high locality, approximate completeness, and high plasticity. These unique characteristics enable it to describe atoms well. The bound state and continuous state of the molecule are thus calculated in atomic structure. The collision dynamics and the field effect of atoms and molecules have been widely used. In this paper, the B-Spline basis set method has been applied to the precise energy spectrum calculation of simple atomic systems and to the study of external field effects. At the same time, a new basis group satisfying periodic boundary condition is constructed and applied to the energy spectrum of quantum ring system. In the study of magnetic field and impurity effect, the main contents of this paper include: 1) the exact nonrelativistic and relativistic energy levels, wave functions, electric dipole polarizabilities and hyperpolarizabilities of hydrogen atoms are obtained by using B-spline basis set method. The hydrogen atom was accurately determined by 1s. 鈫，

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