确定原子基态的具体方法

确定原子基态的定则是洪德(Hund)定则。洪德定则认为,自由原子(或离子)的基态的总自旋角动量、总轨道角动量和总角动量(其量子数)满足下列关系: (1)总自旋角动量 S取泡利原理所能允许的最大值; (2)总轨道角动量L取按(1)确定的S后,泡利原理所能允许的最大值; (3)当支壳层不满时,若不到丰满,总角动量取值J=L-S(正序);若达到或超过半满, 则J=L S(倒序)。 但是,如何根据洪德定则来具体确定原子的基态,在一般教科书中并未提供较为方便的方法。我们在教学中采用了下述的具体方法,感到还较方便。 1.根据L—S耦合和泡利原理,由于同科电子的n、 …     

弗兰克-赫芝实验曲线的峰间距

弗兰克-赫芝实验的装置原理如图1所示,图2是实验记录汞蒸汽的I_A-U_(CK)曲线,测出的蜂间距为4.9V,那么汞的最低激发态能量是否是4.9eV呢? 一、汞的最低激发态能量是4.67eV 汞在第一激发态的电子组态是6s6p,由于两个电子的相互作用(LS耦合)可以形成不同的原子态。汞的两个价电子分别为s电子和p电子,则s_1=s_2=1/2。l_1=0,l_2=1。则合成的自旋总角动量量子数S=0,1。合成的轨道总角动量量子数L=0,1。这两个L值的原子态分别记作S和P态。然后自旋总角动量和轨道总角动量合成原子的     

Paul阱中共面构型三费米子的量子力学运动

求解了Paul阱中总自旋为S=1/2,3/2的三全同费米子体系在共面情形下的Schrdinger方程.根据其波函数节线结构和形状密度分布,研究了系统的结构和量子力学运动模式,并与玻色子体系和经典情形进行了比较.     

Paul阱中共面构型三费米子的量子力学运动

求解了Paul阱中总自旋为S=1/2,3/2的三全同费米子体系在共面情形下的Schr?dinger方程.根据其波函数节线结构和形状密度分布,研究了系统的结构和量子力学运动模式,并与玻色子体系和经典情形进行了比较.     

从空间转动的几何性质推导角动量对易式

经典力学中把L=r×P叫做角动量.量子力学将r和P看作算符后得到算符(1)(V是微分算符),称L为角动量算符.由定义式(1)出发,经过微分运算可得到角动量算符不同分量间的对易关系(2a) (2b) (2c)这种关于角动量的定义和对易关系的推导方法,不具有普遍意义,它只适用于轨道角动量.而角动量这个量跟系统在转动下的变换性质有本质联系.角动量的对易关系,与体系在转动下的特性密切相关.笔者认为,在量子力学的教学中,如果在利用经典概念建立了量子力学的轨道角动量算符后,能再进一步从体系的转动变换性质推导角动量算符,并给出角动量的一般定义式,对提…     

一个验证电磁系统角动量守恒的实例

本文从一个实验出发，就电磁角动量、电磁场角动量流密度张量和机械角动量进行讨论，给出带电体系角动量与场角动量守恒的条件．     

L-S耦合中原子基态诸量子数的计算

由原子基态的电子组态所形成的可能状态中,能级最低的为原子的基态.在LS耦合中,利用原子中电子的壳层分布,应用洪特定则,可以推导出几个公式计算各种原子基态的总轨道角动量量子数L、总自旋角动量量子数S和总角动量量子数J.一、原子基态(L,S,J)的计算 大多数元素的原子中只有一个次壳层未被电子占满,计算时只需计及这一个次壳层中的电子,其他已占满的次壳层无需考虑.下面先讨论这种情形. 根据洪特定则,由同一电子组态所形成的原子状态中,S最大的态能级最低;具有相同S的态中,L最大的态能级最低.所以,由原子基态电子组态所形成的状态中,S…     

洪德定则的理论解释

引言 1925年,洪德(Hund)发现了一个对给定的原子组态确定最低能级的经验规则[1]它就是我们今天所熟悉的洪德定则.洪德定则可表述为:对一个给定的原子组态,具有最大总自旋角动量的量子数S的能级最低,其中又以最大的总轨道角动量量子数L的能级最低.1927年,洪德描述了只能应用于同科电子的组态的另一个附加的定则[2],这个定则是:凡同科电子的数目N少于或等于一个满支壳层电子数的一半时,由J=｜L一S｜给出最低能级的总角动量量子数J;反之,凡同科电子的数目N大于一个满支充层电子数的一半时,由J=L+S给出最低能级的总角动量量子数J. 洪德定…     

关于电子-磁单极子的经典角动量

电子在磁单极子场中的特殊性质,很早就有所讨论,静止的电子-磁单极子(e-g)体系的电磁场带来的附加角动量,是众所周知的,将此附加角动量叠加到轨道角动量中,给出此体系的总角动量.这里有两点值得进一步探讨,首先,我们知道,体系的角动量守恒是由空间转动不变性所决定的,那么e-g体系的角动量如何由空间转动不变性导出,其次,e-g体系的总角动量,除了计入静态场的附加角动量外,还有否其他的贡献.本文对此作简短讨论. 早先Dirac在讨论磁单极子的电磁场时,电磁势有奇异性,存在奇异弦使体系的拉氏     

轨道角动量分量算符的本征函数间的变换

本文讨论了不同轨道角动量分量算符本征函数间的变换关系,给出了对应的变换系数的计算方法,求解了几个比较常见情形l=1,2,3的变换系数,得到了各个变换系数之间的规律.     

对角动量算符的讨论——对自旋的讨论之三

从算符^／J的构成上证明,所谓的总角动量J实质上是相对论性的轨道动量,自旋是相对论性轨道角动量的一个组成部分。     

Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner

We use a Laguerre-Gaussian laser mode within an optical tweezers arrangement to demonstrate the transfer of the orbital angular momentum of a laser mode to a trapped particle. The particle is optically confined in three dimensions and can be made to rotate; thus the apparatus is an optical spanner. We show that the spin angular momentum of +/-?per photon associated with circularly polarized light can add to, or subtract from, the orbital angular momentum to give a total angular momentum. The observed cancellation of the spin and orbital angular momentum shows that, as predicted, a Laguerre-Gaussian mode with an azimuthal mode index l=1 has a well-defined orbital angular momentum corresponding to ? per photon.     

Regge oscillations in integral cross sections for proton impact on atomic hydrogen

The integral cross sections for elastic scattering and spin exchange for proton impact on atomic hydrogen show several oscillations in the energy range 0.01-1.0 eV that cannot be associated with resonances or the glory effect. A complex angular momentum analysis using computed Regge trajectories shows that each peak of the oscillatory structure is predominantly associated with at most three trajectories. In this way, the peaks are related to the L=0 bound states of H+ 2. The complex angular momentum theory for integral cross sections that we introduce shows that such oscillations are a general feature of potential scattering.     

Electromagnetic energy, momentum, and angular momentum in an inhomogeneous linear dielectric

In a previous work, Optics Communications 284 (2011) 2460-2465, we considered a dielectric medium with an anti-reflection coating and a spatially uniform index of refraction illuminated at normal incidence by a quasimonochromatic field. Using the continuity equations for the electromagnetic energy density and the Gordon momentum density, we constructed a traceless, symmetric energy-momentum tensor for the closed system. In this work, we relax the condition of a uniform index of refraction and consider a dielectric medium with a spatially varying index of refraction that is independent of time, which essentially represents a mechanically rigid dielectric medium due to external constraints. Using continuity equations for energy density and for Gordon momentum density, we construct a symmetric energy-momentum matrix, whose four-divergence is equal to a generalized Helmholtz force density four-vector. Assuming that the energy-momentum matrix has tensor transformation properties under a symmetry group of space-time coordinate transformations, we derive the global conservation laws for the total energy, momentum, and angular momentum.     

Hylleraas-Breit变换在类氦离子Schr(o)dinger方程中的应用

给出了Hylleraas-Breit变换(HBT)的具体形式,并用之将类氦离子不动核问题的六维Schrdinger方程化为三维的形式.给出了求解类氦离子任一能量定态问题的三维能量方程或方程组以及对应的变分形式.     

Orbital and Field Angular Momentum in the Nucleon

The nucleon spin problem raises experimental and theoretical questions regarding the contribution of the orbital angular momentum of the quarks to the total spin of the nucleon. In this article we examine the commutation relationships of various operators that contribute to the total angular momentum of the nucleon. We find that the sum of the orbital plus gluon field angular momenta should satisfy the angular momentum commutators, at least up to the one-loop level. This, requirement on the sum of these operators imposes a non-trivial restriction on the form of the color electric and magnetic fields. This is similar to the magnetic monopole/electric charge system where it is only the sum of the orbital plus field angular momentum that satisfies the correct commutation relationships.     

Magnetic symmetry and dyons

A self-consistent theory of dyons in Abelian and non-Abelian limits has been formulated in terms of an extra magnetic symmetry and topological magnetic charge. It has been shown that the restricted gauge potential describes the fields of dyons in terms of two regular (time-like) potentials only when recourse is made to the duality of topological (magnetic) and isocolour (electric) charges. Choosing a suitable Lagrangian density for the system of dyons in non-Abelian gauge theory, the field equations, energy-momentum tensor, Hamiltonian and momentum densities have also been derived and the conservation of the four-linear momentum and the total angular momentum has been demonstrated.     

用波晶片相位板产生角动量可调的无衍射涡旋空心光束

本文提出了一种用波晶片产生无衍射涡旋空心光束的新方案. 根据晶体双折射的性质, 设计波晶片的厚度, 在一块晶体薄片上对o光和e光分别形成各自的四台阶相位板, 线偏振光入射到该相位板后, o光和e光衍射按强度叠加, 利用准伽利略望远镜系统聚焦, 得到近似无衍射涡旋空心光束. 光路简单, 调节方便. 在近轴条件下, 运用菲涅耳衍射理论和经典电磁场角动量理论, 数值模拟计算了周期数不同的两块波晶片相位板衍射光强和角动量的分布, 结果表明: 两块相位板都能在较长距离内产生近似无衍射涡旋空心光束, 光强和轨道角动量的分布与螺旋相位板产生的涡旋光束基本相同. 在衍射光路中加入相位补偿器, 调节o光和e光的相位差可以调节自旋角动量的大小, 从而可以调节总角动量密度和平均光子角动量的大小. 用这种空心光束导引冷原子或冷分子, 原子在与光子相互作用过程中可获得可调的转动力矩.