波尔共振实验中基于旋转矢量的相位差分析

在波尔共振实验中,通过引入两个旋转矢量分别描述受迫振动和强迫力,解决了实验中频闪法测相位差原理阐述不清的问题.针对有机玻璃转盘上白线与刻度盘零刻线分别成锐角和钝角的情况,由旋转矢量法分别给出了受迫振动与强迫力的相位差.研究发现,无论白线指向刻度盘的哪个区域,受迫振动与强迫力的相位差始终为-π/2与有机玻璃转盘的白线所指向角度之差.     

Relativistic Electromagnetic Solitary Wave in a Cylindrical Magnetized Plasma

In the presence of an applied static and uniform magnetic field, a cylindrical Kadomtsev-Petviashivili equation is derived for a relativistic electromagnetic solitary wave propagating in collisionless plasma consisting electrons, positrons, and ions in the case of weak relativistic limit. This equation is solved in a stationary frame to obtain explicit expression for the velocity, amplitude and width of solitons. The amplitude of the solitary wave has a maximum value at a critical αc of the ratio of the ion equilibrium density to the electron one, and it increases as the applied magnetic field becomes larger.     

Two-dimensional relativistic electromagnetic dromion-like soliton in a cold transparent plasma

By using a standard multiple scale method, a Davey--Stewartson (DS) equation has been derived and also applied to a multi-dimensional analytical investigation on the interaction of an ultra-intense laser pulse with a cold unmagnetized transparent electron-ion plasma. The regions of instability are found by considering the modulation instability of a plane wave solution of the DS equation. The DS equation is just of the Davey--Stewartson 1 (DS1) type and admits a dromion solution, i.e. a two-dimensional (2D) dromion soliton decaying exponentially in all spatial directions. A 2D relativistic electromagnetic dromion-like soliton (2D REDLS) is derived for a vector potential.     

直尺衍射现象及分析

衍射是光的波动性的一个重要特征,而光栅衍射则是其中一类常见且重要的衍射现象.当激光束入射直尺边缘或表面时会出现半圆形衍射光斑,其产生机理并不清楚.针对直尺边缘与表面的半圆形衍射光斑,本文理论结合实验分析了其产生机理.研究发现,当直尺表面或侧面存在规则的类光栅结构时,其衍射光斑为半圆形.利用标准二值光栅模型分析了直尺衍射问题,发现半圆形衍射光斑起源于多套光栅衍射的叠加.     

Fluorescence properties in a single driven four-level atomic system

The spontaneous emission decay dynamics of a tripod configuration four-level atom driven by a single laser field is studied.Under different initial conditions,we discuss the effects of quantum interference and detuning of external driving field on atomic spontaneous emission properties.For the larger detuning,the interesting phenomena of the spectral line narrowing are found which stem from the contribution of external driving field.     

半无界空间上函数的傅里叶-贝塞尔积分展开

柱坐标系中,本征函数族贝塞尔函数构成完备正交系,因此可作为广义傅里叶级数展开的基.本文从定义在有限区间[0,ρ0]上函数的广义傅里叶级数展开出发,利用贝塞尔函数的渐近展开公式以及贝塞尔函数零点的近似公式,讨论了半无界空间上函数的傅里叶-贝塞尔积分展开问题,得到了本征函数模方的近似表达式.当ρ0趋于无穷时,不连续参量变成连续参量,得到了函数的傅里叶-贝塞尔积分及其展开系数公式.     

Effect of atomic initial phase difference on spontaneous emission of an atom embedded in photonic crystal

<正>We investigate the effect of initial phase difference between the two excited states of a V-type three-level atom on its steady state behaviour of spontaneous emission.A modified density of modes is introduced to calculate the spontaneous emission spectra in photonic crystal.Spectra in free space are also shown to compare with that in photonic crystal with different relative positions of the excited levels from upper band-edge frequency.It is found that the initial phase difference plays an important role in the quantum interference property between the two decay channels.For a zero initial phase,destructive property is presented in the spectra.With the increase of initial phase difference,quantum interference between the two decay channels from upper levels to ground level turns to be constructive.Furthermore, we give an interpretation for the property of these spectra.     

分离变量法教学内容优化及本征值问题引入方式研究

现有数学物理方法教学体系中, 分离变量法在前, 本征值问题在后. 而分离变量过程中, 又涉及到本征 值问题. 这样的安排导致学生在学习分离变量法过程中, 不能很好地理解本征值问题是分离变量法的基础, 不利于 学生严密逻辑思维能力的培养. 针对这个问题我们开展了分离变量法教学内容优化的研究, 提出一种更有利于学 生严密逻辑思维能力培养的分离变量法教学方案. 将本征值问题提前, 将其置于定解问题之后、 分离变量法之前. 进而, 为避免直接引入S t u r m L i o u v i l l e方程而导致的突兀性问题, 给出了分离变量法教学顺序调整后的S t u r m L i o u v i l l e方程的引出方案