轻阻尼振子阻尼现象的量子力学处理

采用正则变数（Ｘ，Ｐ）表象讨论轻阻尼振子，并对量子力学含时微扰的狄拉克方法加以修改，得出量子能级有位移和宽度，以及波函数出现随时间指数衰减的行为。     

轻阻尼振子的经典力学处理和量子力学处理

本文讨论了对于微观轻阻尼（β／ω１＜＜１）振子体系，借助正则化变换技巧，可采用通常简便的量子力学方法进行处理．其结果表明了体系的量子效应，既与始值条件相关，且又随阻尼按指数规律（ｅ～（－２βｔ））衰减．量子力学的处理方法和结果均与经典力学处理呈显明的对应关系．     

量子阻尼振子的两种解析解法

应用u变换与不变量理论，求解一维量子阻尼振子，两种解法的不同仅在于交换了u变换与相因子的顺序。     

量子阻尼振子产生的压缩

用有序算符内的积分技术,求解一维量子阻尼振子的时间演化态.结果表明系统的时间演化态是压缩态.     

关于线性阻尼振子第一积分的研究

通过引入一维线性阻尼振子基本积分来构造其他第一积分, 包括不含时的积分. 将这种方法推广到多维情形, 构造二维和n维线性阻尼振子不同形式的第一积分; 证明不同类型的二维线性阻尼振子都存在三个独立的不含时的第一积分, n维线性阻尼振子存在2n-1个独立的不含时的第一积分. 利用变量变换将线性阻尼振子的第一积分变换成简谐振子形式的第一积分. 关键词： 线性阻尼振子 第一积分 基本积分 简谐振子     

一类线性阻尼振子的随机共振研究

针对随机有色噪声参数激励和周期调制噪声外激励联合作用下的线性阻尼振子,利用Shapiro-Loginov公式推导了系统响应的一、二阶稳态矩的解析表达式.发现这类系统存在传统的随机共振、广义的随机共振和“真正”的随机共振;当乘性噪声强度和调制噪声强度的比值大于等于1时,系统出现随机多共振现象.通过数值计算的系统响应功率谱,验证了理论分析结果. 关键词： 随机共振 周期调制的噪声 线性阻尼振子     

基于Phyphox的气垫导轨上弹簧振子的阻尼系数研究

组装ESP32开发板和超声波测距传感器,让装有Phyphox软件的智能手机通过蓝牙接收传感器的信号,研究弹簧振子在气垫导轨上做阻尼运动中不同挡板面积对阻尼系数的影响。实验结果显示,阻尼系数与挡板面积呈线性关系。     

幂级数展开法计算周期阻尼振子路径积分短时传播子

文章用Schwinger方法与Makri等人发展的幂级数展开法研究了周期阻尼简谐振子的传播子.研究表明,这两种方法所获得的短时传播子非常接近,但是后者比前者要简单得多,这给研究复杂系统的传播子提供了一个简单可靠的方法.     

用跃变旋转矢量研究滑动摩擦空气阻尼弹簧振子

运用跃变旋转矢量法,即通过旋转矢量的起点、长度和相位的变化规律对受到空气弱阻尼作用和滑动摩擦力作用的弹簧振子的振动进行了研究.讨论了在滑动摩擦力作用下空气阻尼为临界阻尼和欠阻尼情况下的弹簧振子的运动,根据阻尼和初值情况得出不同的振动曲线.并对弹簧振子4种相图和相图旋转矢量进行了比较.     

用计算机研究弹簧振子的运动规律

用计算机C语言程序建立一个弹簧振子模型 ,运用数值计算方法计算运动方程中的各个物理量 ,以研究弹簧振子的运动规律     

用智能手机App Video Physics研究竖直平面内的圆周运动

本实验用智能手机App Video Physics追踪小球在竖直平面内做圆周运动的情况,研究了不同质量的小球从同一高度静止释放到达最低点的速度关系,研究了从不同高度静止释放小球的速度与运动轨迹之间的关系,计算了小球在圆形轨道上运动时的向心力、角速度,以及当小球与圆形轨道等高静止释放时小球的脱离点速度.     

Flow Characteristics of Flapping Motion of a Plane Water Jet Impinging onto Free Surface

A submerged turbulent plane jet in shallow water impinging vertically onto the free surface will produce a large-scale flapping motion when the jet exit velocity is larger than a critical one. The flapping phenomenon is verified in this paper through a large eddy simulation where the free surface is modeled by volume of fluid approach. The quantitative results for flapping jet are found to be in good agreement with available experimental data in terms of mean velocity, flapping-induced velocity and turbulence intensity. Results show that the flapping motion is a new flow pattern with characteristic flapping frequency for submerged turbulent plane jets, the mean centerline velocity decay is considerably faster than that of the stable impinging jet without flapping motion, and the flapping-induced velocities are as important as the turbulent fluctuations.     

Velocity Quantization Approach of the One-Dimensional Dissipative Harmonic Oscillator

Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the constant of motion instead of the Hamiltonian. PACS: 03.20.+i, 03.30.+p, 03.65.−w,03.65.Ca     

Normally-Ordered Time Evolution Operator for Mass-Varying Harmonic Oscillator and Wigner Function of Squeezed Number State

For investigating dynamic evolution of a mass-varying harmonic oscillator we constitute a ket-bra integration operator in coherent state representation and then perform this integral by virtue of the technique of integration within an ordered product of operators. The normally ordered time evolution operator is thus obtained. We then derive the Wigner function of u（t）｜n,〉, where ｜n〉 is a Fock state, which exhibits a generalized squeezing, the squeezing effect is related to the varying mass with time.     

Normally-Ordered Time Evolution Operator for Mass-Varying Harmonic Oscillator and Wigner Function of Squeezed Number State

For investigating dynamic evolution of a mass-varying harmonic oscillator we constitute a ket-bra integration operator in coherent state representation and then perform this integral by virtue of the technique ofintegration within an ordered product of operators. The normally orderedtime evolution operator is thus obtained. We then derive the Wigner functionof$u(t)| n>, where | n> is a Fock state, which exhibits a generalized squeezing, the squeezing effect is related to the varying mass with time.     

二维各向同性谐振子的径向矩阵元计算的讨论

根据广义Laguerre多项式的数学性质，导出了较为简单的二维各向同性谐振子径向矩阵元的普遍公式，并在这基础上计算了一些重要特殊情形的径向矩阵元：矢径ρ整数次幂的平均值，电偶极跃迁矩阵元和电四极跃迁矩阵元。     

Clapp振荡器振荡幅度的实测、建模与分析

在振荡器正常工作的频段中,幅度会随频率而发生改变。要使振荡器正常工作,必须对其中的可调参数加以限制,使幅度增大从而起振。文章分析了实用Clapp振荡器幅度随频率变化的成因,并用软件拟合了器件取值对振荡幅度的影响,模拟结果对振荡器设计有一定的借鉴意义。     

Geodesic Motion in Spinning Spaces

In this paper the generalized equations for spinning space are investigated and the constants of motion are derived in terms of the solutions of these equations. We study the geodesic motion of the pseudo-classical spinning particles in the spacetime produced by an idealized cosmic string and the non-extreme stationary axisymmetric black hole spacetime. The bound state orbits in a plane are discussed. We also show, for a conical spacetime and the Kerr spacetime, that the geodesic motion of spinning particles is different.     

束测误差对阻尼系统的影响

讨论了束测误差对阻尼系统工作状况的影响．结果表明，束测误差将减低阻尼效果，增大为达到一定的阻尼速度所需阻尼系统功率，并导致闭轨畸变．给出了计算有关效应的公式．