在均匀强磁场中氢原子塞曼效应久期方程的简化公式

在均匀强磁场中,当氢原子的哈密顿量中B2项不能忽略时,氢原子的库仑场对称性遭到破坏,能级简并被全部解除.在应用变分法和数值法计算氢原子的能级过程中,计算十分复杂,而应用微扰法求解氢原子的能级,存在解久期方程的n2高阶行列式的困难.本文应用简并态微扰理论和球谐函数的性质,得到久期方程中非零微扰矩阵元普遍表达式.根据非零微扰矩阵元普遍表达式的性质,可以将氢原子塞曼效应久期方程的n2高阶行列式分解成1阶到n阶共n个低阶行列式的乘积,得到氢原子塞曼效应久期方程的简化公式,使得求解均匀强磁场中氢原子塞曼效应能级过程简化.而且由该公式可以得到氢原子在低能态时塞曼效应能级的解析解.根据该久期方程的简化公式计算了n=3氢原子塞曼效应一级近似能级.     

利用量子力学解释原子物理学中问题的一个简单例子

在原子物理学中,碱金属原子的光谱可以用与描述氢原子光谱的相仿的公式来表示,其光谱项可以表示为当n较大时,咸金属原子的能级很接近氢原子的能级;当n较小时,和氢原子能级差别较显著,这里n是主量子数.同时,当角量子数1较大时,咸金属能级很接近氢原子能级;当1较小时,差别较大.以上这些规律很容易从下面这张锂原子的能级图中看出. 在学习原子物理学时,咸金属原子能级和氢原子能级的差别一般都用原子实的极化和轨道的贯穿作了很好的解释.不过多数大都只是定性地说明.关于这一问题的较完满的量子力学分析方法,如 Thomas-Fermi方法,Hartree自洽…     

类氢原子能级与轨道半径的计算

从氢原子的基本模型出发,归纳分析了几种类氢原子能级和轨道半径的计算方法.     

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。     

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.     

强激光短脉冲的引力效应

研究了强激光短脉冲产生的引力场中氢原子能级的移动.指出在目前高功率激光脉冲条件下，高激发态氢原子的能级移动大小将达到可观察值. 关键词：     

氢原子一级Stark效应能级的解析式

根据简并态微扰论、球坐标系中氢原子波函数的性质,得到任意能级下氢原子一级Stark效应能级计算的简单方法,并计算了n=5的能级修正值,由此得到了氢原子一级Stark能级的解析式。     

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.     

微扰法计算中等强磁场中氢原子的能级

本文在考虑氢原子轨道运动磁矩与磁场之间、自旋磁矩与磁场之间和感生磁矩与外磁场之间的相互作用的基础上,根据角动量和球谐函数的性质,应用简并态微扰方法研究了在中等强磁场中氢原子的能级,给出了计算中等强磁场中氢原子的一级近似能级的方法,具体计算了23.5126≤B≤1.881728×10~4T范围内氢原子n=2的各能级的数值,结果与有关文献给出的理论计算值是相近的,表明本文所给出的方法是简单的、计算结果是正确的.     

氢原子的一级斯塔克效应的能级分裂和简并度

我们以表格的形式给出了氢原子的一级斯塔克效应的能级分裂及简并度的情况,并通过与以往文献中的理论计算比较得到了验证.最后在抛物坐标下,通过对氢原子一级斯塔克效应能级分裂一般表达式的分析,给出了相邻两条能级间距满足1.5neεa的理论支持.     

Photoionization microscopy of Rydberg hydrogen atom in a non-uniform electrical field

In this paper,we investigate the photoionization microscopy of the Rydberg hydrogen atom in a gradient electric field for the first time.The observed oscillatory patterns in the photoionization microscopy are explained within the framework of the semiclassical theory,which can be considered as a manifestation of interference between various electron trajectories arriving at a given point on the detector plane.In contrast with the photoionization microscopy in the uniform electric field,the trajectories of the ionized electron in the gradient electric field will become chaotic.An infinite set of different electron trajectories can arrive at a given point on the detector plane,which makes the interference pattern of the electron probability density distribution extremely complicated.Our calculation results suggest that the oscillatory pattern in the electron probability density distribution depends sensitively on the electric field gradient,the scaled energy and the position of the detector plane.Through our research,we predict that the interference pattern in the electron probability density distribution can be observed in an actual photoionization microscopy experiment once the external electric field strength and the position of the electron detector plane are reasonable.This study provides some references for the future experimental research on the photoionization microscopy of the Rydberg atom in the non-uniform external fields.     

外电场中金属表面附近里德堡氢原子的动力学行为

利用相空间分析方法研究了外电场中金属表面附近里德堡氢原子的动力学性质. 结果表明, 体系的动力学性质敏感地依赖于原子与金属表面间的距离和电场强度.通过固定原子与金属表面间的距离, 分析了外加电场作用下里德堡电子的Poincaré 截面和运动轨迹的演化过程. 研究表明: 电场的出现加速了金属表面对电子的吸附, 随着电场强度的增加,体系的动力学性质由原子与金 属表面间的距离控制逐渐变为由电场起主导作用,体系逐渐由不可积变为可积, 电子的运动轨道最终全部变为振动型轨道. 关键词： Poincaré截面 相空间分析方法 里德堡氢原子     

Effects of an electric field on the confined hydrogen atom in a parabolic potential well

Using the perturbation method, the confined hydrogen atom by a parabolic potential well is investigated. The binding energy of the confined hydrogen atom in a parabolic potential well is calculated as a function of the confined potential radius and as a function of the intensity of an applied electric field. It is shown that the binding energy of the confined hydrogen atom is highly dependent on the confined potential radius and the intensity of an applied electric field.     

超强激光场中氢原子辐射高次谐波蒙特卡罗模拟

运用蒙特卡罗方法，模拟和计算出在超强激光场中，氢原子在相对论领域的电离几率和辐射出的高次谐波，并且讨论了氢原子的电离几率和辐射出的高次谐波与激光场的电场和磁场的关系。     

Resonances of a hydrogen atom in strong parallel electric and magnetic fields using B-spline basis sets

The B-spline basis set plus complex scaling method is applied to the numerical calculation of the exact resonance parameters $E_r}$ and $\Ga/2$ of a hydrogen atom in parallel electric and magnetic fields. The method can calculate the ground and higher excited resonances accurately and efficiently. The resonance parameters with accuracies of $10^{-9}-10^{-12}$ for hydrogen atom in parallel fields with different field strengths and symmetries are presented and compared with previous ones. Extension to the calculation of Rydberg atom in crossed electric and magnetic fields and of atomic double excited states in external electric fields is discussed.     

Nuclear magnetic shielding of a hydrogen atom in an electric field

The nuclear magnetic screening constant of a hydrogen atom in a uniform electric field is calculated, neglecting any effect of electron spin. The screening is found to be reduced by the electric field for all directions of the applied magnetic field, the reduction being greatest if the two fields are perpendicular.     

Resonances of a hydrogen atom in strong parallel electric and magnetic fields using B-spline basis sets

The B-spline basis set plus complex scaling method is applied to the numerical calculation of the exact resonance parameters Er and Г/2 of a hydrogen atom in parallel electric and magnetic fields. The method can calculate the ground and higher excited resonances accurately and efficiently. The resonance parameters with accuracies of 10^-9 - 10^-12 for hydrogen atom in parallel fields with different field strengths and symmetries are presented and compared with previous ones. Extension to the calculation of Rydberg atom in crossed electric and magnetic fields and of atomic double excited states in external electric fields is discussed.     

Semiclassical calculation of ionization rate for Rydberg hydrogen atoms near a metal surface

The ionization of Rydberg hydrogen atoms near a metal surface at different scaled energies above the classical saddle point energy has been discussed by using the semiclassical method. The results show that the atoms ionize by emitting a train of electron pulses. In order to reveal the chaotic and escape dynamical properties of this system in detail, the sensitive dependence of the ionization rate upon the scaled energy is discussed. As the scaled energy is close to the saddle point energy, the ionization process of the hydrogen atom is nearly the same as the case of hydrogen atom in an electric field. There is only a single pulse of electrons, with an exponentially decaying tail. With the increase of the scaled energy, the ionization rates are similar to the case of the hydrogen atom in parallel electric and magnetic field, a series of electron pulses appear in the ionization process. This is caused by classical chaos, which occurs for the metal surface. Our studies also suggest that the metal surface can play the role of both the electric and the magnetic fields. Our theoretical analysis will be useful for guiding experimental studies of the ionization of atoms near the metal surface.     

ELECTRON DIFFUSION IN A NON-UNIFORM ELECTRIC FIELD AND A UNIFORM MAGNETIC FIELD

A Monte Carlo simulation technique has been used to model the electron transport beharlot, especially the electron diffusion motion, in the cathode fall region of a glow discharge under the influence of a non-uniform electric field and a transverse magnetic field perpen-dicular to the cathode sheath electric field. Three types of collisions (elastic, excitation and ionization) are taken into account in our model. The electron free flying time is determined by the electron-neutral atom collision frequency. We focus attention on the electron diffusion distance and velocity. The electron-neutral atom collision processes and the electron drift velocity are also studied. The results indicate that with the increase of the magnetic field the electron diffusion distance increases and the electron diffusion velocity decreases. The results Mso show that the collision processes are enhanced by the magnetic field, this is in agreement with the experimental result. However, the axial magnetic field does not affect the electron transport behavior.     

光电子离开氢术核的方向

基态氢原子在电磁波的作用下发生电离，这主不是氢原子的光电效应，本文讨论氢原子的电子离开氢核的方向与电磁波的电场强度Ｅ的方向之间的关系。