用简单方法求解谐振子波包的演化

用简单方法求出一系列谐振子波包的波函数随时间演化的显式．该方法不需用到特殊函数的任何知识。     

基于Mathematica的波包模型演示实验

利用计算机代数系统Mathematica.6.0,设计了一个波包模型的仿真实验。该演示实验有助于加深学生对微观粒子的运动特征——波粒二象性的理解。     

一般波包在均匀场中的运动

求出了一般波包的中心和宽度在一维均匀场中的变化规律，波包的中心遵循经典粒子的运动规律，宽度的平方则以时间的二次函数增长，但动量空间的相应波包却保持其宽度不变，特别是平面波在运动过程中仍保持为平面波，对Gauss波包，求出了波函数随时间变化的显式，验证了一般结论。     

量子谐振子与经典谐振子的比较

运用广义线性量子变换的普遍理论求解了量子谐振子,同经典谐振子比较给出了量子谐振子趋近于经典极限的条件,并得出相干态是最理想的经典极限态．     

波包动力学-飞秒激光操纵波包过程

本文介绍了波包动力学的基本理论和数值模拟方法,尤其是在飞秒激光与分子相互作用领域中的应用,探讨了飞秒激光引起的波包过程（包括波包的制备、波包的干涉）,以及利用调频脉冲、脉冲串和优化脉冲形状控制波包动力学的方案。     

波包动力学-飞秒激光操纵波包过程

本文介绍了波包动力学的基本理论和数值模拟方法,尤其是在飞秒激光与分子相互作用领域中的应用,探讨了飞秒激光引起的波包过程（包括波包的制备、波包的干涉）,以及利用调频脉冲、脉冲串和优化脉冲形状控制波包动力学的方案。     

一维线性谐振子的宇称解法

基于一维线性谐振子的势函数Ｕ（ｘ）具有对称性，所以其波函数具有确定的宇称，本应用波函数的这一性质求其能量及波函数。     

Michelangelo Wave Packets and Interference Forces

The spreading of a quantum mechanical particle in the absence of a classical force is a well-known effect.However, there exist situations when this phenomenon is suppressed or even completely stimulated. In the present talk we first briefly summarize various non-spreading wave packets emphasizing in particular the Michelangelo wave packets which have recently been verified experimentally. We then turn to the example of contracting wave packets in D = 2 dimensions. Here the shrinking effect results from quantum interference which is very peculiar in D = 2. In particular, we show that this interference force can be understood in terms of correlations of position and momentum which do not exist in classical physics.     

耦合谐振子的双波描述

采用双波函数量子理论 ,研究了耦合谐振子力学量的时间演化方程及其经典极限 ,进一步验证了双波函数描述的是单个粒子 ,而单个波函数描述的是量子系综的结论     

Wave function of the harmonic oscillator in classical statistical mechanics

The notion of wave function of the classical harmonic oscillator is discussed. The evolution equation for this wave function is obtained using the classical Liouville equation for the probability-distribution function of the harmonic oscillator. The tomographic-probability distribution of the classical oscillator is studied. Examples of the ground-like state and the coherent state of the classical harmonic oscillator are considered.     

量子力学矩阵元的经典极限

本文研究了量子力学矩阵元的经典极限;用新的方法证明了如下定理;在分立谱情况下;量子力学矩阵元ｆｎｍ的经典极限是相应经典力学量ｆ（ｔ）之Ｆｏｕｒｉｅｒ级数展开的第ｎ－ｍ个分量;在连续谱情况下;量子力学矩阵元ｆＥＥ与Ｐｌａｃｋ常量ｈ的乘积ｈｆＥＥ的经典极限相应经典力学量ｆ（ｔ）之Ｆｏｒｉｅｒ积分展开的第ω次分量。     

原子链与弦中波包演化的比较分析

分析了一维单原子链中与连续弦中的波包的演化过程.弦中的波包以恒定速度移动,且保持形状不变;而原子链中的波包在演化过程中形状不断地发生变化.通过比较分析一维单原子链与弦振动的色散关系,讨论了波包演化的不同以及离散的原子链到连续弦的过渡.     

Wave Mechanics or Wave Statistical Mechanics

By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.     

Equity prices as a simple harmonic oscillator with noise

The centred return on the London Stock Exchange's FTSE All Share Index is modelled as a simple harmonic oscillator with noise over the period from 1 January, 1994 until 30 June 2006. Our empirical results are compatible with the hypothesis that there is a period in the FTSE All Share Index of between two and two and one half years. This means the centred return will on average continue to increase for about a year after reaching the minimum in its oscillatory cycle; alternatively, it will continue on average to decline for about a year after reaching a maximum. Our analysis also shows that there is potential to exploit the harmonic nature of the returns process to earn abnormal profits. Extending our analysis to the low energy states of a quantum harmonic oscillator is also suggested.     

Classical limit of scattering in quantum mechanics—A general approach

The classical and quantum physics seem to divide nature into two domains macroscopic and microscopic. It is also certain that they accurately predict experimental results in their respective regions. However, the reduction theory, namely, the general derivation of classical results from the quantum mechanics is still a far cry. The outcome of some recent investigations suggests that there possibly does not exist any universal method for obtaining classical results from quantum mechanics. In the present work we intend to investigate the problem phenomenonwise and address specifically the phenomenon of scattering. We suggest a general approach to obtain the classical limit formula from the phase shiftδ _l, in the limiting value of a suitable parameter on whichδ _l depends. The classical result has been derived for three different potential fields in which the phase shifts are exactly known. Unlike the current wisdom that the classical limit can be reached only in the high energy regime it is found that the classical limit parameter in addition to other factors depends on the details of the potential fields. In the last section we have discussed the implications of the results obtained.