WKB波函数连接公式的初等推导与一维势阱势垒的WKB近似解

本文用初等方法导出ＷＫＢ波函数的连接公式，其要点是在转折点邻近，用阶跃型势能曲线代替真实的势能曲线。给出了求一维势阱能级及一维势垒穿透因子的方法与结果。方法简便，可供初等量子力学与普通物理教学参考。     

平面电磁波基本性质的初等推导

平面电磁波的基本性质,在经典电磁场理论中占有重要地位。严格的理论推导必须应用电动力学的知识。在普通物理教学中,如何进行初等的讲授是教师颇感棘手的问题。姚启钧先生曾在“电偶极子辐射的图示问题”一文中进行过讨论。关于振荡电偶极子电磁场的初等推导方法,作者已在本刊中作过介绍。这里,我们再介绍一种关于平面电磁波基本性质的初等推导方法,以供教学参考。这种初等推导方     

波函数的量钢

量子力学中用来描述微观粒子状态的波函数，除了满足定义所要求的条件之外，还应满足量纲方面的要求．波函数的量纲山归一化条件确定．本文详细地讨论并给出了初等量子力学中常见的一些波函数的量纲．     

势垒隧穿含时演化的Julia数值模拟

势垒隧穿是初等量子力学中的一个重要模型,但由于求解其波函数涉及超越方程,因此在许多初等量子力学教材中往往着重对透射系数的讲解,很少提及其波函数演化,在部分教材中虽有提及,但往往采用图解法,不利于初学者对该过程的理解。本文针对这一问题,提出了一种便于初学者理解的数值计算方法。该方法根据矩阵力学的向量化思想,将薛定谔方程中的波函数与算符分别以向量和矩阵的形式进行离散化,并利用Julia编程对几种势垒情况下的波函数隧穿的含时演化进行数值模拟。     

对一个算符公式的修正

指出近日出版的《高等量子力学》一书中给出的一个算符公式在其推导中存在漏洞，因而结果也不正确讨论了正确的推导方法和修正的结果。     

用因式分解法求解薛定谔方程

利用德·拉·佩纳等人关于阶梯算符方法的表述形式，可以使因式分解法的步骤规范化，以利于在初等量子力学和量子化学教学中广泛应用．我们把这种方法应用于球坐标下的自由粒子、三维各向同性谐振子和二维氢原子，得到令人满意的结果．     

从氢原子的量子力学到两个新的物理学研究方向

翻开任何一本初等量子力学或者量子化学教材,氢原子的量子力学解是前半部分必须介绍的内容。理工科甚至一些文科学生,都接触过氢原子的束缚态解。有人可能以为氢原子已经研究得很成熟,不再有继续研究的余地。     

振荡电偶极子电磁场的初等推导

振荡电偶极子的电磁场,在经典电磁场理论中占有重要地位。严格的理论推导必须应用电动力学的知识。在物理教学中,它是一个难点。如何进行初等的讲授以帮助初学者理解有关的物理图象,是教师颇感棘手的问题。姚启钧先生曾就电偶极子辐射的图示问题进行过细致的讨论。本文介绍有关的初等推导方法,作为补充,以供教学参考。这种初等推导方法的特点是:计算简单,物理图象清楚,概念鲜明,并且可以推导出全部定量关系。但初等方法往往不免有漏洞。限于水平,不妥或错误之处在所难免,希望读者批评和指正。     

带电粒子在匀强磁场中运动的能量和磁通量量子化问题

一 本文试图探讨为大学低年级学生讲授带电粒子在磁场中运动的能量量子化及磁通量量子化问题.目的有两个.其一,可使没有机会专门攻读量子力学这门课程的大学生们了解更多的量子化现象.其二,对于专攻物理科学的大学生们,虽然他们在学习量子力学时将有机会从更严格的角度来解决这类问题,但在基础物理中介绍更多的量子化现象无疑将使他们在以后学习量子力学时减少困难. 以往以初等方法介绍量子化概念的主要例子之一是电子在有心的库仑场中运动.例如在氢原子中,电子绕质子运动,满足经典动力学方程.同时,电子具有波动性,在稳定轨道上运动的电子波…     

一种角动量算符的简便推导方法

在量子力学教本中推导(L)2及(L)z的球坐标表达式一般都采用由直角坐标系到球坐标系的变量代换的方法,运算过程十分复杂,本文利用了球坐标系中坐标变量r、θ、ψ对正交基矢er、eθ、eψ微分性质,采用球坐标系直接进行推导,简化量子力学中关于角动量算符(L)2及(L)z的的推导.     

Guided-Wave Two-Dimensional Acousto-Optic Scanner Using Proton-Exchanged Lithium Niobate Waveguide

Two-dimensional scanning of a 0.6328 mum guided-light beam has been realized using noncolinear acousto-optic (AO) coplanar Bragg diffraction together with colinear AO guided-mode to substrate radiation-mode conversion in a Z-cut Xpropagation LiNbO3 proton-exchanged (PE) waveguide. The two surface acoustic (SAW) waves utilized are at the center frequencies of 500 and 200 MHz, propagating in the Y and X axes, respectively. Two-dimensional scanning of approximately 720 resolvable light beam spots, namely, 18 40 (horizontal vertical) scanning, has been demonstrated using a light beam of 1.0 mm aperture. The total number of resolvable beam spots can be greatly increased from 720 by simply utilizing SAW transducers of larger bandwidth and a light beam of greater aperture. It should also be possible to significantly increase the diffraction efficiency from 3 % by optimizing the parameters of the PE waveguide and the SAWs.     

Femtosecond Transform-Limited Pulse Generation by Compensating for the Linear Chirp of SPM Spectra in Dispersion Shifted Fibers

A simple technique of pulse compression, based on the linear chirp compensation of self-phase modulation (SPM) spectra in dispersion shifted fibers, is demonstrated. The optimization procedure is carried out, for a short span of a single-mode fiber, using a parabolic law, which describes the behavior of the squared output pulse width versus the pump peak power in the case of Gaussian pulses. The experimental results give a minimum pulse duration of 233 fs, which is in good agreement with the model. Shorter and coherent pulses, down to 90 fs, have been obtained by inserting an interference filter at the optical output.     

Effect ofγ-radiation on the spectral luminescence characteristics of impure cadmium tungstate crystals

Results of a study of the effect of γ-radiation on the spectral luminescence properties of cadmium tungstate crystals doped with silver, bismuth, and molybdenum cations are presented. Spectral characteristics of the nondnnnoped crystals are briefly described. Absorption and photo and X-ray luminescence spectra of the crystals taken before and after exposure to γ-radiation (5.5·10⁴ Gy) are compared. It is found that the spectral characteristics of the crystals doped with silver, bismuth, and molybdenum cations do not change markedly after the exposure. The relation between the type of impurity-induced defects, individual characteristics of the impurity cations, and the character of the effect of γ-radiation on the spectral luminescence properties of impure crystals is analyzed (preliminarily). Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 1, pp. 55–60, January–February, 1997.     

Sorting of bending magnets for the SSRF booster

The Shanghai Synchrotron Radiation Facility(SSRF)booster ring,a full energy injector for the storage ring,is deigned to accelerate the electron beam energy from 150MeV to 3.5GeV that demands high extraction efficiency at the extraction energy with low beam loss rate when electrons are ramping.Closed orbit distortion(COD)caused by bending magnet field uniformity errors which affects the machine performance harmfully could be effectively reduced by bending magnet location sorting.Considering the affections of random errors in measurement,both ideal sorting and realistic sorting are studied based on measured bending magnet field uniformity errors and one reasonable combination of bending magnets which can reduce the horizontal COD by a factor of 5is given as the final installation sequence of the booster bending magnets in this paper.     

Measurement of nonlinear coefficient of optical fiber based on small chirped soliton transmission

We measure the waveform and phase curves of short optical pulses before and after transmission over different lengths of fibers by use of the pulse analyzer with the frequency-resolved optical gating (FROG),and numerically simulate pulse evolution under the experimental conditions.The nonlinear coefficient of the fiber is given by comparing the experimental results with the numerical ones.Difference between the experiment and numerical simulation is analyzed.     

Resonance scattering of canonical elastic shells in absorbing fluid medium

Resonance scattering of elastic spherical shell and cylindrical shell while the surrounding fluid medium has absorption is studied. The normal mode solution derived using exact elastic theory and the separation of variables is still applicable. However, the scattering form function has to be modified for the absorbing medium, otherwise the unreasonable result would be obtained. The backscattering form function in the absorbing medium is redefined, and the form function of elastic spherical and cylindrical shell with vacuum or solid matter filled is calculated in various absorption conditions. The results show that the absorption of surrounding fluid leads to notable attenuation of the coincidence resonances in the mid-frequency, but it has a little influence on the low-frequency resonance scattering induced by the filler inside the shell.     

Single-beam self-referenced phase-sensitive surface plasmon resonance sensor with high detection resolution

A versatile and low-cost single-beam self-referenced phase-sensitive surface plasmon resonance(SPR)sensing system with ultra-high resolution performance is presented.The system exhibits a root-mean-square phase fluctuation of ±0.0028.over a period of 45 min.i.e.a resolution of±5.2×10-9 refractive index units.The enhanced performance has been achieved through the incorporation of three design elements:a true single-beam configuration enabling complete self-referencing so that only the phase change associated with SPR gets detected,a differential measurement scheme to eliminate spurious signals not related to the sensor response,and the elimination of retardation drifts by incorporating temperature stabilization in the liquid crystal phase modulato .Our design should bring the detection sensitivity of non-labeling SPR biosensing closer to that achievable by conventional fluorescence-based techniques.     

Influences of SiO2 protective layers and annealing on the laser-induced damage threshold of Ta2O5 films

Ta2O5 films are prepared on BK7 substrates with conventional electron beam evaporation deposition.The effects of SiO2 protective layers and annealing on the laser-induced damage threshold (LIDT) of the films are investigated.The results show that SiO2 protective layers exert little influence on the electric field intensity(EFI)distribution,microstructure and microdefect density but increase the absorption slightly.Annealing iS effective on decreasing the microdefect density and the absorption of the films.Both SiO2 protective layers and annealing are beneficial to the damage resistance of the films and the latter is more effective to improve the LIDT.Moreover,the maximal LIDT of Ta2O5 films is achieved by the combination of SiO2 protective layers and annealing.     

A stereo matching algorithm using multi-peak candidate matches and geometric constraints

Gray cross correlation matching technique is adopted to extract candidate matches with gray cross correla- tion coefficients less than some certain range of maximal correlation coefficient called multi-peak candidate matches. Multi-peak candidates are extracted corresponding to three closest feature points at first. The corresponding multi-peak candidate matches are used to construct the model polygon. Correspondence is determined based on the local geometric relations between the three feature points and the multi-peak candidates. The disparity test and the global consistency checkout are applied to eliminate the remaining ambiguous matches that are not removed by the local geometric relational test. Experimental results show that the proposed algorithm is feasible and accurate.