一维、二维、三维氢原子能级和电子分布概率

通过一维、二维氢原子定态薛定谔方程的严格解得出的能级公式和波函数，分析了一维、二维氢原子能级特点、简并度和电子分布概率，并将它们与三维氢原子进行比较，发现一维、二维、三维氢原子能级和电子分布概率有许多不同之处。     

氢原子电子云的蒙特卡罗模拟

根据量子力学原理,氢原子中电子的几率分布由电子的定态波函数可以唯一地确定.在大多数教科书中,通常是将电子沿径向和角度方向的几率分布分别进行讨论,因此很难给出电子在整个空间几率分布的一个完整图象.我们使用蒙特卡罗随机抽样的方法,通过计算机作图形象而逼真地绘制了氢原子中电子的几率分布图,即所谓的电子云.下面介绍所使用的方法.     

圆柱形人造原子的能级结构及电子几率密度分布

通过求解定态薛定格方程得到了园柱形人造原子的能级结构,进而求出了电子几率密度的分布。计算结果表明,电子被束缚在园柱内的条件与位阱深度Ｖ０及园柱的园柱的结构参数有关。当园柱的高ｈ＝４．００ｎｍ,半径α＝２．７５ｎｍ时,要求Ｖ０≥４．７４ｍｅＶ。在ｚ－轴方向上的电子几率密度分布是以ｈ／２为对称中心周期震荡,并且柱体内外的电子几率的大小是可比较的;而在ｘ－ｙ平面上的电子几率密度分布类似于氢原子,并且柱外     

二维Sinai台球系统的量子混沌研究

研究了二维Sinai台球系统的经典与量子的对应关系,运用定态展开法和Gutzwiller的周期轨道理论对Sinai台球系统的态密度经傅里叶变换得到的量子长度谱进行分析,并把量子长度谱中峰的位置与其所对应的经典体系的周期轨道长度做对比,发现两者之间存在很好的对应关系.观察到了一些量子态局域在短周期轨道附近形成量子scarred态或量子superscarred态.还研究了同心与非同心Sinai台球系统的能级最近邻间距分布,发现同心Sinai台球系统是近可积的,非同心Sinai台球系统在θ=3π/8下,随两中心间距离的增加,能级最近邻间距分布将由近可积向维格那分布过渡.     

氢原子两种能级跃迁形式的比较

根据玻尔原子模型理论，氢原子只能处于某些不连续的特定能量的定态，在不同定态之间可以通过辐射或吸收一定的能量跃迁．为氢原子发生跃迁提供能量的粒子可以是光子，也可以是电子，但光子和电子使氢原子发生跃迁的条件有所不同。     

A^z^＋—H（1s）碰撞中的电荷交换和电离

本文采用与经典轨道蒙特卡罗方法（ＣＴＭＣ）不同的方法，利用精确的量子力学氢原子的波函数，抽样氢原子中电子的位置及动量分布，而不是用经典轨道抽样的办法。仔细计算了Ｈ＾＋，Ｈｅ＾２＾＋，Ｌｉ＾３＾＋，Ｃ＾６＾＋，Ｏ＾８＾＋，Ｎｅ＾１＾０＾＋，Ｓｉ＾１＾４＾＋等全裸离子与氢原子碰撞过程中的电子俘获及电离截面，并给出被俘获后的电子在入射裸离子中的壳层分布图象，实际计算表明，其结果是令人满意的，特别是俘获截     

类氢原子核质量对电子状态的影响

在孤立的两体复合系统中,讨论其中一体的变化如何影响另一体的状态,有助于了解单粒子混合态与纯态的关系.本文讨论5个孤立的一维类氢原子模型系统,原子核的质量互不相同.这5个两体(电子与原子核)复合系统的相对运动状态都处于纠缠态,其中电子状态都用约化密度矩阵表示的混合态描述.在原子核质量趋近无穷大的一维氢原子模型中,电子处于纯态.为比较这里的纯态和混合态,在位置表象中计算了这些混合态的纯度、它们分别与纯态的保真度、以及所有这些态的相干性.研究表明,原子核的质量越大,纯度和保真度越接近1,混合态的相干性与纯态的也越接近.这样的纯态及其相干性可以是这种混合态及其相干性的近似,并与原子核及库仑相互作用有关.     

二维椭圆量子台球中的谱分析

研究了二维椭圆台球中的量子谱和经典轨道之间的对应关系.为尝试求解没有解析波函数和本征能量又不能分离变量的体系，采用了定态展开方法(expansion method for stationary states，简称EMSS)得到尽可能精确的数值解，这是闭合轨道理论被推广到计算开轨道的情况.比较了傅里叶变换谱和经典轨道，发现量子谱的峰位置与经典轨道的长度在可分辨的范围内符合得很好，这是半经典理论为经典与量子力学的联系提供桥梁作用的又一个例子. 关键词： 椭圆量子台球 定态展开方法 闭合轨道理论 量子谱     

原子的壳层填充次序与电离次序

关于过渡族元素壳层填充和电离次序,现行的某些原子物理书籍介绍得不够准确。本文在回顾轨道贯穿的物理实质之后,作简要讨论。 核外电子空间几率分布是电子真实运动的反映。有时也可以从某一方面来研究它的分布规律,如讨论它的径向几率分布。轨道贯穿效应实质是 S、P、d、f态电子径向几率分布不同而引起的能量效应。图1是氢原子的3d态与4.s态径向分布。其特点是每个曲线有(n-l)个峰,4s态有四个峰,3d态有一个峰。可以藉此图对多电子原子的贯穿效应给以形象说明。值得注意的是,多电子原子中各态电子由于几率分布的特点,电子间既有屏蔽共它电…     

氢原子相干态

由Kustannheimo-Stiefel变换,可将量子力学中的氢原子问题化为带有约束条件的四维各向同性谐振子。在此基础上定义相干态,并证明力学量坐标和动量对相干态的平均,给出经典开普勒运动轨道。同时也讨论该相干态中的测不准关系式。 关键词：     

居民出行分布中的电子云现象

研究发现，居民出行分布的概率密度曲线与氢原子基态电子在核外出现的概率密度曲线极为相似，运用量子力学中的电子云分布模型可以很好地解释居民出行分布特性，根据氢原子中电子的径向概率密度函数建立了模拟电子云居民出行分布模型.利用长春市和旧金山地区的抽样调查数据对模型进行了验证.在此基础上，进一步建立了实用模型，并结合实例给出了模型标定方法和过程.该模型可在城市规划和城市交通规划中定量描述居民出行分布状态. 关键词： 科学与社会 自组织系统 电子云 出行分布     

Quantum mechanics in theK-field formalism: The kepler problem (without spin)

The primary goal of this work is to use a very well-known problem (the Kepler problem) to demonstrate the procedure for the construction in theK-field formalism of the nonrelativistic approximation of the quantum mechanical model of the stationary states of the hydrogen atom neglecting the spin properties of the electron. It is shown that the standard stationary states of the hydrogen atom correspond to Lyapunov-stable trajectories of theK particle (point test particle, the classical model of the electron in the atom). In spite of the electron being considered initially as a point particle without angular momentum, the internal logic of quantum mechanics in theK-field formalism requires the existence of the spin characteristics for the quantum mechanical model of the electron in the Kepler problem, even in the nonrelativistic approximation. Tomsk Polytechnic Institute. Translated fromIzvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 59–64, July, 1998.     

Ionization of atoms in strong low-frequency electromagnetic field

The ionization of atoms in a low-frequency linearly polarized electromagnetic field (the photon energy is much lower than the ionization potential of an atom) is considered under new conditions, in which the Coulomb interaction of an electron with the atomic core in the final state of the continuum cannot be considered in perturbation theory in the interaction of the electron with the electromagnetic field. The field is assumed to be much weaker that the atomic field. In these conditions, the classical motion of the electron in the final state of the continuum becomes chaotic (so-called dynamic chaos). Using the well-known Chirikov method of averaging over chaotic variations of the phase of motion, the problem can be reduced to non-linear diffusion on the energy scale. We calculate the classical electron energy in the final state, which is averaged over fast chaotic oscillations and takes into account both the Coulomb field and the electromagnetic field. This energy is used to calculate the probability of ionization from the ground state of the atom to a lower-lying state in the continuum using the Landau-Dykhne approximation (to exponential accuracy). This ionization probability noticeably depends on the field frequency. Upon a decrease in frequency, a transition to the well-known tunnel ionization limit with a probability independent of the field frequency is considered.     

Fractal Motion of Electrons with Variable Weak Memory and Nonlocality

Equations of fractal motion of electrons with variable weak memory and nonlocality are investigated. It is demonstrated that the fractal dimension of time changes by a harmonic law for stationary electron motion. The fractal nonlocality has been established for the free electron; it also changes by a harmonic law. The fractal nonlocality of the electron bound with the hydrogen atom nucleus differs radically. In this case, the fractal dimension of radial electron motion is everywhere less than unity. It can be greater than unity in regions well away from the nucleus. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 52–57, September, 2005.     

Periodicity and chaos in strongly perturbed classical orbitals for Coulomb interactions

Within the framework of classical mechanics two prototypes of strongly perturbed orbitals, the diamagnetism in hydrogen and electronic double excitation, are analyzed near critical phase space points (fixed points). The motion of the hydrogen electron under the joint influence of the Coulomb field and the magnetic field is periodic for any field strengths. For a two-electron atom however we find a chaotic time evolution of the electron pair correlation, causing presumably irregular spectral patterns.     

单轴应变对H在α-Fe中占位及扩散的影响

采用基于密度泛函理论的第一性原理方法,研究了H在不同单轴应变下α-Fe中的间隙占位,计算了H原子的溶解能、态密度、电荷差分密度和电荷布居.结果表明:不同单轴拉压应变作用下,H原子优先占据四面体间隙(Ts)位,且随着压应变减小、拉应变增加,H原子越易溶于α-Fe.压应变使得Ts位的H获得更多的电子,而拉应变减少了这种电荷转移.应用LST/QST过渡态搜索计算垂直应变方向的扩散.八面体间隙位是邻近Ts位H的扩散过渡态.扩散激活能与应变呈线性关系,且随着压应变的增加,扩散激活能降低,扩散更容易.     

单个钛原子储氢能力和储氢机制的第一性原理研究

采用基于密度泛函理论的第一性原理方法研究了单个过渡金属钛原子吸附氢分子的物理机制. 研究表明,单个钛原子最多能吸附8对氢分子,吸附结构为对称的两个类金字塔型结构, 其平均吸附能为- 0.28 eV.通过计算轨道能级和差分电荷密度分布,分析决定吸附结构、 吸附能大小以及吸附氢分子数目的内在物理机制.研究表明,钛原子的4s电子转移到3d轨道上, 从而产生较强的极化电场,导致氢分子极化,钛原子通过静电极化作用吸附氢分子. 本文的研究将对设计高密度储氢材料有一定的指导作用.     

Zero field isotropic Muonium Kubo — Toyabe relaxation functions

Static zero field Gaussian Kubo — Toyabe relaxation functions for muons in isotropic muonium atoms are presented. That is, as with diamagnetic muons, an average of the spin dynamics of a muon in an isolated isotropic ground state muonium atom is taken over an isotropic Gaussian continuous classical local random magnetic field distribution. This motion approximates the exact quantal spin dynamics generated by the dipole-dipole interactions between the muonium atom and the surrounding nuclear spins associated with the site at which the muonium atom has stopped. Expressions are derived for triplet muonium only since, in general, singlet muonium is not observed. For normal nuclear spins and ground state muonium, the resulting relaxation functions are identical to the standard diamagnetic function (except for a shift in the time scale).     

Cross sections of electron capture and electron capture ionization versus the impact parameter in collisions of a proton with multielectron atoms

The absolute differential cross sections of scattering of hydrogen atoms resulting from an electron capture and an electron capture ionization are measured for collisions of 4.5- and 11-keV protons with argon and xenon atoms. The range of scattering angles is 0°–2°. From the scattering differential cross section found experimentally, the probabilities of single-electron capture and electron capture ionization as a function of the impact parameter are calculated. The dependences of the incident particle scattering angle on the impact parameter (deviation function) for interactions with Ar and Xe atoms are calculated in terms of classical mechanics using the Moliére—Yukawa potential to describe the interaction of atomic particles. Analysis is given to the probabilities of electron capture and electron capture ionization versus the impact parameter and to the distribution of the electron density on different electron shells in a target atom versus a distance to the core. It is concluded that only electrons from the outer shell of the target atom are involved in the process of electron capture ionization. The cross section of electron capture ionization is calculated in the proton energy range 5–20 keV.     

氢原子的总电流及其经典对应

定态下氢原子平均电流密度只有一个沿纬线的分量非零,本文在这一结果的基础上计算了氢原子的总电流,发现它与经典力学中行星运动的开普勒定律之间有明确的对应关系．