谐振子

谐振子在周期运动中是特别重要的。

The harmonic oscillator is an exceptionally important example of periodic motion .

电场中带电谐振子在高温弱简并情况下的热力学性质

Thermodynamical property of the harmonic oscillator with electrical charge in the electric field under high temperature and weak degeneration

一维多项式非谐振子的REDUCE程序

A reduce approach to one dimensional polynomial anharmonic oscillators

C（60）分子的一维谐振子模型

One Dimension Harmonic Oscillator of C_ ( 60 ) Molecule

各向异性n模耦合谐振子的精确求解

Exact solution for non-identical n modes coupled harmonic oscillators

经典q变形谐振子及其h量子化

Classical q-deformed Harmonic Oscillators and their h quantization

Lie代数与OPT：耦合谐振子

Lie Algebra and OPT : Coupled Linear Oscillators

线性谐振子与q变形振子量子运动的新描述

New Description for Quantum Motions of Linear Harmonic Oscillator and Q-deformed Harmonic Oscillator

非线性非谐振子的SU（1，1）Lie代数

SU ( 1 , 1 ) Lie Algebra of Nonlinear Nonharmonic Oscillator

以一维量子谐振子为例，经过分析，认为量子系统经典极限条件也可表示为h→0。

By analysing one-dimensional quantum oscillator , the classical limit conditions of the quantum system also expresses as → 0 .

D维q变形谐振子模型

D-dimensional q - deformed harmonic oscillator

有限维q非谐振子广义相干态振幅N次方压缩

N-th Power Squeezing of the Field-amplitude on Generalized Single-parameter q-Deformation Coherent State of an Anharmonic Oscillator in a Finite-dimension Hilbert Space

研讨了温度为T时量子谐振子系统处在第n态的概率，并讨论了结果的物理意义。

The probability of the quantized harmonic oscillator being in the nth quantum state in a system at temperature T are studied and discussed .

利用因式分解方法，重新定义了N（N≥2）维各向同性谐振子的两类升、降算子。

Employing the factorization method , a new definition of four kinds of raising and lowering operators of an N dimensional isotropic oscillator is given .

用explicitEuler方法研究含时受迫谐振子的演化及对系统循环初态的讨论

Solution of time-dependent harmonic oscillator system using explicit Euler method and discussion of the cyclic initial states

半球谐振子的Q值对半球陀螺的性能指标有重大的影响。

We know the performance of hemispherical resonator gyroscope ( HRG ) is influenced by the Q value of hemispherical resonator .

同时，当q→1时，所有结论回复为普通二维谐振子的相关结果。

At the same time , when q → 1 the theory reduces to the common two dimensional harmonic oscillator theory .

用泛函Euler方程求解线性谐振子的基态能量和波函数

Solving ground state energy and wave function of a linear harmonic oscillator by Euler equation

REDCE语言是用计算机推导解析公式的有力工具，本文用REDUCE语言计算了高次非谐项对非谐振子的效应。

The Reduce language is a useful tool for deriving analytical formula on the computer . We calculate the effect of the high - power anharmonic terms in the anharmonic oscillator .

最后，以普通物理中的受迫谐振子问题为例，突出体现了Green函数方法的优点，并进一步说明了Green函数方法应用的普遍性。

The excellence and basic thinking of Green function method is shown because forced harmonic oscillator is discussed , further more , that the Green function method is used widely is clarified .

具有含时频率和边界条件的谐振子量子态的Berry相位

The Berry phase of the quantum state of a harmonic oscillator with time dependent frequency and boundary conditions

球谐振子径向算符r~（2s）的平均值的解析公式

Explicit Expressions of Average Values of Radial Operator r ~ ( 2s ) for Spherical Harmonic Oscillator

进而用（q，r）变形熵讨论了在弱变形的情况下谐振子系统分布的一级关联。

Then , applying this ( q , r ) - deformed entropy , we derive the first-order correction to the Planck distribution of harmonic oscillator system in weak deformation .

一维时间相关的经典谐振子是一个SU（1,1）非自治经典系统，是物理学中的一个重要模型。

The one-dimentional classical harmonic oscillator is an su ( 1 , 1 ) nonautonomous classical system which is an important model in physics .

用有限元法建立了圆筒谐振子的模型，通过MATLAB软件编程，计算出合理的谐振子参数，对其频率密度特性进行了分析，并给出了振子的振型分布。

FEM Model is made and programmed in MATLAB , reasonable size is worked out , relation between frequency and density is analyzed , and the vibratory mode shape is given .

关于双参数量子代数SU（qs）（2）和双参数形变谐振子的若干结果

Some Remarks on a Two-Parameter Quantum Algebra SU_ ( qs )( 2 ) and a Two-Parameter Deformed Harmonic Oscillator

关于在Fabry－Perot空腔中的变质量谐振子

Harmonic Oscillator with Variable Mass in the Fabry-Perot Cavity

利用泛函极值满足的Euler方程，解出了线性谐振子的基态能量和波函数。

The ground state energy and the wave function of a linear harmonic oscillator are solved by Euler equation comforted to functional extremum .

广义四维谐振子位势的B-S波函数

B-S wave function for a generalized four-dimensional harmonic oscillator

线性谐振子势的相对论效应Ⅰ：Klein-Gordon方程

Relativistic effects of linear harmonic oscillator ⅰ: Klein-Gordon equations