如何给工科学生讲波函数（3）

本文介绍作者在华中理工大学给二年级工科学生讲波函数的思路与方法。     

强磁场中碱金属原子原演化和Aharonov—Anandan相因子

利用量子不变量理论研究了任意随变化的强磁场中碱金属原子系统的演化问题，得到了此精确的演化态，并利用此精确的演化态求出了相应的Ａｈａｒｏｎｏｖ－Ａｎａｎｄａｎ相因子和绝热极限下的Ｂｅｒｒｙ相因子。将此系统精确的演化按哈密顿量的瞬音本征态展开，可以得到绝热近似似的任意阶修正。     

力学Berry相因子和相应的经典拓扑相角

最近,有人讨论了"力学Aharonov-Bohm效应",并获得了实验验证.本文则进而研究并计算了"力学Berry相因子"及其相应的经典拓扑相角.     

量子Berry相因子的经典模型

本文考虑了经典演化方程和Schrodinger方程的类似性,指出具有缓变参数的经典演化方程的解会自然给出具有拓扑性质的几何相因子—我们称之为经典Berry相因子.我们给出了绝热条件破坏时非简并情况各级近似方程的通解.作为例子,详尽研究了带电粒子在绝热变化磁场中的运动,明显地得到了一个量子Berry相因子的经典模型.这个相因子在几何上可解释为参数空间中单位球面S²上厄米线丛的和乐.     

强磁场中碱金属原子的演化和Aharonov－Anandan相因子

利用量子不变量理论研究了任意随时间变化的强磁场中碱金属原子系统的演化问题，得到了此系统精确的演化态，并利用此精确的演化态求出了相应的Ａｎａｒｏｎｏｖ－Ａｎａｎｄａｎ相因子和绝热极限下的Ｂｅｒｒｙ相因子。将此系统精确的演化态按哈密顿量的瞬时本征态展开，可以得到绝热近似的任意阶修正。     

动力参照系中的Berry相因子及其可观测物理效应

本文在非相对论情况下,讨论了运动参照系中Schrodinger方程绝热近似解的性质和Berry相因子大坐标变换下的行为,对转动和平动参照系两种具体情况作了较为详尽的分析.这些讨论表明了Berry相因子的出现与参照系的选择有关.对于涉及到平动参照系的Bitter和Dubbers的中子极化问题.我们不仅在零级近似下给出理论和实验相符合的结果,而且还进一步分析了绝热条件破坏时可能出现的高阶效应.     

关于Berry几何位相理论的推广

对于可参数化时间t的周期Hamiltonian系统,由non－adiabatic到adiabatic－limit的“严格”演变以获得Berry几何相γn（C）的问题．结果表明,存在“四种类型”的演变态,它们都可以满足在参数R空间中的同一条闭合曲线C上作这样的“严格演变”,并且还都可以获得同一个Berry几何相γn（C）;而Berry发现这一几何相γn（C）时所考虑和采用的“演变态”,恰好属于本文“四种类型”的“严格”演变态之一的adiabaticapproximation情形．据此,可以把Berry几何位相理论推广到本文所研究的“四种类型”的“严格”演变中．     

关于Berry几何位相理论的推广

对于可参数化时间t的周期Hamiltonian系统,由non–adiabatic到adiabatic–limit的“严格”演变以获得Berry几何相γ_n(C)的问题.结果表明,存在“四种类型”的演变态,它们都可以满足在参数R空间中的同一条闭合曲线C上作这样的“严格演变”,并且还都可以获得同一个Berry几何相γ_n(C);而Berry发现这一几何相γ_n(C)时所考虑和采用的“演变态”,恰好属于本文“四种类型”的“严格”演变态之一的adiabatic approximation情形.据此,可以把Berry几何位相理论推广到本文所研究的“四种类型”的“严格”演变中.     

复物体的恢复

为了恢复一个复值物函数,本文提出了利用透镜后1f距离,2f距离及3f距离处的强度信息来恢复物函数的振幅分布和位相分布.计算表明,此算法具有广泛的实用性;并能给出很好的收敛结果.     

Coupling Between Spin and Gravitational Field and Equation of Motion of Spin

In general relativity, the equation of motion of the spin is given by the equation of parallel transport, which is a result of the space-time geometry. Any result of the space-time geometry cannot be directly applied to gauge theory of gravity. In gauge theory of gravity, based on the viewpoint of the coupling between the spin and gravitational field,an equation of motion of the spin is deduced. In the post Newtonian approximation, it is proved that this equation gives the same result as that of the equation of parallel transport. So, in the post Newtonian approximation, gauge theory of gravity gives out the same prediction on the precession of orbiting gyroscope as that of general relativity.     

几种超弹性多次碰撞的讨论

本文分析了几种超弹性碰撞多次连续碰撞的过程，以期对照弹性碰撞的进一步理解．实现这些物理过程对物理教学是相当有趣的．     

稀土发光和光谱理论的研究进展

简述了近20多年以来我们在稀土发光和光谱理论方面所做的主要工作、取得的进展和成果。包括:(1)关于(4f)^N组态内单光子跃迁强度:推广Judd-Ofelt三参量公式,在其中计入"J混合"(偶宇称晶场成分造成的)导致的修正;澄清了国际上关于Judd-Ofelt全参量公式中"静力学项"和"动力学项"相对正负号的争论(仍为负号)。(2)关于(4f)^N组态内双光子过程强度:提出直接计算强度方法(放弃缔合近似,利用Ce³⁺的5d和左邻RE³⁺的(4f)^N能级-波函资料,近似模拟出最重要的虚中间组态(4f)^N-15d的能级-波函结构)来讨论和改进Judd-Ofelt缔合近似。(3)固体中声子辅助的稀土离子间能量传输理论:发现HLO理论关于单声子过程中的"干涉相消"实际只适合于对角过程,而非对角过程则是"干涉相加",因而,后者首要的是单声子而非双声子过程;同时,用"晶体格波模"取代"Debye模"描述能量传输中的声子,给出了新模型下计算对角和非对角过程速率等物理量的整套公式。并由之看出:波矢q=0和对应色散曲线扁平段的光学声子对单声子非对角过程速率有完全不能忽略的贡献,这些都不同于或超出于HLO理论。(4)提出和发展了分析指认4f-5d跃迁光谱的简单理论模型,用能量和跃迁强度同时进行近似拟合,成功地分析指认了从(4f)³到(4f)¹³离子在几种基质中的4f→5d吸收(激发)谱,也成功用于若干5d→4f辐射谱。(5)对跃迁的初末晶场态同时引用有效自旋哈密顿描述稀土离子间超交换作用,成功地解释了低温10 K时立方结构的纯稀土冰晶石晶体Cs₂NaLnCl₆(Ln=Er,Yb)等的吸收谱中0声子线(量级为几个cm^-1)的精细分裂。     

迈克尔逊干涉仪实验中的三个问题

本文对在大学物理实验迈克尔逊干涉仪调节和使用题目中被教师忽略却常被学生提出的三个问题进行了细致分析和讨论，并给出了解决建议。     

Luminescence of silver chloride microcrystals upon photoexcitation by different methods

The luminescence spectra of AgCl microcrystals were measured in two different regimes: in the regime of excitation of stationary luminescence and in the regime of photostimulated burst of luminescence. Differences between the spectra of stationary luminescence and the spectra of photostimulated-luminescence burst in the range between 430 and 590 nm have been found. The luminescence spectra are complex; the ratio of intensities for elementary components changes with the technique of excitation. Differences in the form and composition of complex luminescence bands obtained under different conditions of registration are attributed to the recombination interaction of the luminescence centers. It is shown that analysis of the dependences of intensity ratios for the elementary components of a complex luminescence band on the exciting-radiation intensity allows one to evaluate the mechanism of recombination in elementary bands provided that the mechanism is known for at least one luminescence band.__________Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 1, pp. 85–89. January–February, 2005.     

The Antikythera mechanism and the mechanical universe

Astronomers have two approaches to trying to determine the age of the Universe. They can estimate the ages of individual objects in the Universe and specifically in our Galaxy. These estimates use either the observed properties of stars and theoretical ideas concerning stellar evolution or the abundances of long-lived radioactive isotopes and their decay products. Alternatively they can use cosmological theories and observations to try to determine the age of the entire Universe. Obviously the Universe must be older than its component parts but neither of the above methods is sufficiently reliable that this is true of the deduced ages. As a result, it is from time to time reported that some object in the Universe is older than the Universe itself. In this article we discuss the methods that are currently being used to determine the age and we emphasize the problems in obtaining reliable results. It is not at present possible to provide a definite value for the age of the Universe.     

对质点系角动量定理的讨论

对理论力学教材中角动量定理的各种不同表达式进行了归纳、比较、讨论、明确了它们之间的区别、联系及其适用条件。     

正态分布随机数发生器及其在模拟光传输软件中的应用

 利用计算机高级语言提供的伪随机数发生器,通过“高斯筛选”和“求平均值”两种方法,开发出满足正态分布的随机数发生器。将其应用于分析大型激光装置光路稳定性的模拟软件中,成功地完成了对“神光Ⅲ原型装置四程放大器”的光路稳定性分析。     

First approximation to the Hugoniot equation of state of the lanthanides

Summary The semi-empirical Hugoniot equation of state is obtained by using the third-order tangency between the isentropic and the Hugoniot curves at the origin of coordinates. The results of this model are in good agreement with Carter’s experimental data for fourteen elements from the lanthanides series in the lower phase only. Due to postal troubles with Lebanon, it was impossible to send proffs to the author as he requested.     

Coupling Between Spin and Gravitational Field and Equation of Motion of Spin

In general relativity, the equation of motion of the spin is given by the equation of parallel transport, which is a result of the space-time geometry. Any result of the space-time geometry cannog be directly applied to gauge theory of gravity. In gauge theory of gravity, based on the viewpoint of the coupling between the spin and gravitational field, an equation of motlon of the spin is deduced. In the post Newtonian approximation, it is proved that this equation gives the same result as that of the equation of parallel transport. So, in the post Newtonian approximation, gauge theory of gravity gives out the same prediction on the precession of orbiting gyroscope as that of general relativity.