量子谐振子

推出了经典谐振子的动量-位置不确定关系，并且给出它和量子谐振子的不确定关系之间的对应关系。

In this paper , the author deduces the momentum-position uncertainty relation of the classical harmonic oscillator , and gives the correspondence relation between it and the uncertainty relation of quantum harmonic oscillator .

一维量子谐振子能量的相对论修正

A Relativistic Revision of the Energy in a Quantum Harmonic 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 .

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 .

在位相空间中求解外力含时的受迫量子谐振子

Solving forced quantum oscillator with time-dependent external force in phase space

具有坐标和动量一阶耦合的两量子谐振子的演化

Evolution of two quantum harmonic oscillators with coordinate and momentum first-order coupling

二维耦合量子谐振子的本征值和本征函数

The eigenvalue and eigenfunction of a coupled quantum oscillator

多维耦合受迫量子谐振子的普遍解

General solution for multi-dimensional coupled and forced quantum oscillator

量子谐振子与量子系统的经典极限

Quantum oscillator and classical limit of quantum system

基于粒子群算法的量子谐振子模型

Quantum Oscillator Model of Particle Swarm System

利用不变量本征算符求解二维耦合量子谐振子的能级间隔

Derivation of the energy-level gap of two-dimensional coupled quantum harmonic oscillators by invariant eigen-operator method

量子谐振子能级的一种修正方法

One Correction of Quantum Resonator Energy Level

经典谐振子与量子谐振子

Classics Harmonic Oscillator and Quantum Harmonic Oscillator

量子谐振子的经典类比

Classical Analogies of Quantum Oscillator

利用不变本征算符法给出了坐标-动量耦合的三模耦合量子谐振子的能级信息。

The energy levels for three-dimensional coordinate-momentum coupled quantum harmonic oscillators are presented by using invariant eigen-operator method .

通过测试函数的仿真实验证明了量子谐振子粒子群算法的全局收敛能力优于一般粒子群算法。

The vast number of experiment results show that the new swarm intelligence algorithm has much stronger global searching ability compared to the classical PSO algorithm .

计算了两个量子耦合谐振子系统的Berry相，并与量子一经典混合系统的结果进行了比较。

Furthermore , the Berry phase for a system of two coupled oscillators is calculated and the result is compared with that of the quantum-classical hybrid system .

量子非线性谐振子的一致有效渐近解

The uniformly valid asymptotic solution of quantum non-linear harmonic oscillator

在文献[5]的基础上，分析了两个耦合的量子非谐振子，并讨论了一种典型的实例。

Based on reference [ 5 ] , two quantum anharmonic oscillators are analysed , and a typical coupled example is discussed .

本文先介绍用不确定关系粗略计算一维线性谐振子零点能，然后再结合普朗克量子假设给出谐振子能级公式。

In this paper we introduced how to use uncertain relationship to simply calculate the zero position energy of one dimension linear harmonic oscillator , and then the resonant energy grade equation were gotten based on Planck hypothesis .

量子阻尼受迫谐振子的精确波函数

The Exact Wave Function of A quantum Damping Propelled Oscillator

应用多尺度微扰理论研究了弱耦合非简谐参数的经典和量子四次非谐振子，得到了四次非简谐运动方程的经典和量子二阶解。

Classical and quantum oscillators of quartic anharmonicity are solved analytically up to the second power of ( weak-coupling constant ) by using the multiple-scale perturbation theory .

利用具有量子群对称性的q变形量子谐振子Fock态│n>q生成q变形量子谐振子的Glauber相干态（q-Glauber相干态│a>q）。

By making use of the Fock States of the q-deformed quantum oscillator which possesses the symmetry of quantum group , we construct the Glauber coherent state of the q-deformed quantum oscillator ( the q-Glauber coherent state ㄧα > q ) .

应用广义量子线性变换理论求解二维耦合量子谐振子

Utilizing the General Linear Quantum Theroy to Solve the Two-dimensional Coupled Quantum Harmonic Oscillator

运用广义线性量子变换的普遍理论求解多维耦合受迫量子谐振子，给出了系统演化算符的矩阵元、波函数、力学量期望值和配分函数的严格表达式。

Utilizing the general linear quantum transformation theory , we give the exact expressions of evolutionary operator 's matrix elements , wave function , expectation value of an observable and partition function , for multi-dimensional coupled and forced quantum oscillator .

在Dantas等人所作量子振子工作的基础上提出了二个相互耦合的量子谐振子的演化问题，通过引进几个算符和辅助函数，求出了问题的精确解。

Based on Dantas ' work of quantum harmonic oscillator , an evolutionary problem of two coupled quantum harmonic oscillators is put forward , and the exact solution is derived by introduction of the appropriate operators and auxiliary functionals .