in this paper, for a system of independent harmonic oscillators in the condition of constant temperature, we give a method of resolving the operator exp (-β) by group theory to calculate the partition function z_n(β) of the system.

1、

the energy eigenvalue of the common double couplings with non-identical harmonic oscillators was studied by transformation of coordinates under the effects of coupling-λ x_1x_2+ vp_1p_2.

利用坐标变换技巧，研究了两个质量和频率均不相同的玻色谐振子体系，得到了在-λx1x2+vp1p2耦合作用下能量本征值的精确解。

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2、

based on the research on the microscopic mechanism of heat radiation of ionic crystals, a model of harmonic oscillators was established to calculate the heat radiation characteristics of ionic crystals.

从对离子晶体热辐射的微观机理的研究出发，利用谐振子模型对离子晶体的热辐射特性进行了研究与计算，利用该模型可以计算出离子晶体材料的红外光谱图。

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3、

the expansion method of mixed basis vectors of lower-energy states and harmonic oscillators in calculation of bound states of few-body systems

少体束缚态的低能态和简谐振子混合基矢展开方法

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4、

the energy-level gap of coordinate-momentum cross coupling harmonic oscillators

坐标-动量交叉耦合谐振子的能级间隔

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5、

the particle-number representation is very useful in the research of energy levels and the coherent states of linear harmonic oscillators.

在研究线性谐振子的能级和相干态时，占有数表象是十分有用的。

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6、

three-mode entanglement and squeezing of coupled harmonic oscillators in the non-markovian reservoir

非马尔可夫库中谐振子系统的三模纠缠和压缩

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7、

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

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

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8、

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

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。

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9、

energy eigenvalue of the double coupling non-identical harmonic oscillators was solved accurately by transformation of coordinates

一般双耦合非全同玻色谐振子能量本征值的精确解

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10、

k band gaas fet harmonic oscillators stabilized by dielectric resonators

K波段介质谐振器稳频GaAs FET谐波振荡器

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11、

quantum refrigeration cycle working with the harmonic oscillators

谐振子量子制冷循环

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12、

stability analysis of harmonic oscillators

谐波振荡器稳定性分析

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13、

solving energy eigenvalue of n module coupling harmonic oscillators by virtue of quadratic form

利用二次型求解n模耦合谐振子能量本征值精确解

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14、

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

具有坐标和动量一阶耦合的两量子谐振子的演化

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15、

coherent state representation of the partition function and its application to the system of harmonic oscillators

配分函数的相干态表示及其对谐振子系统的应用

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16、

simulation study on noise in harmonic oscillators

谐波振荡器噪声特性的模拟研究

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17、

analysis of millimeter wave gunn harmonic oscillators by a circuit model

毫米波Gunn器件谐波振荡器电路分析

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18、

a model for the small oscillation of non-harmonic oscillators

一种非简谐的微振动模型

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19、

by the delayed stochastic differential equa-tion theory, we deduce the synchronization conditions for the networks of coupled harmonic oscillators with random perturbation and time delays.

利用时滞随机微分方程理论，推导了带随机扰动的耦合时滞谐振子网络达到同步的充分条件。

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20、

on the double harmonic oscillators model of the baryon and regge trajectory

重子的双谐振子模型和瑞奇轨迹

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