中文摘要：

本文基于谐振子及群论方法，对声在空气中传播建立了一个新的哈密顿数学模型。研究将分子链作为一系列谐振子组合，声传播以能量的形式传播，对于介质里的每个振动的质点而言，它总是在不断地吸收和放出能量。从能量的概念出发，将声传播问题转换成求解谐振子的波函数以及能量本征值的问题。本文将谐振子模型引入到气体声波传播的问题中，在确定气体声波传播过程中的分子振动模式、能级简并时，引入群论，以探索气动声学研究的新方法。

英文摘要：

In this paper, based on the harmonic oscillator and the group theory, a new Hamiltonian mathematical model is established for sound propagation in the air. Molecular chain is regarded as a series of harmonic oscillator combination and sound propagation spread as the way of energy, for each vibration particle in the media, it is always constantly absorb and release energy. From the point of view in energy, the problem of the sound propagation is converted into solving the harmonic oscillator wave functions as well as the energy eigenvalues. In order to explore the new method of aeroacoustics research, the harmonic oscillator model is introduced into the study of acoustic wave propagation in the gas, the group theory is introduced to determine molecular vibrational modes and degeneracy of energy levels during acoustic wave propagation in the air.