基于路径积分的声传播微观特性的研究

运用量子力学的Feynman路径积分理论,尝试研究空气中声传播的计算方法及其微观特性。选取一小团空气(小体元)为研究对象,将声传播过程中一列振动的空气小体元近似为一组谐振子集合,用路径积分方法给出系统的能量方程及波函数,研究并分析声传播的某些机制和它的微观特性。在量子分子状态下,用密度矩阵将系统概率波幅(跃迁幅)与配分函数相关联,给出了谐振子处于能量E_n的概率p(E_n)和能量的平均值(?)。

Study on the Microscopic Properties of Sound Propagation Based on the Path Integral

The Feynman path integral of the quantum mechanics theory was used to study the calculation methods and its microscopic properties of sound propagation in air.A small group of air (body element) was selected for the study,A list of vibrating air micro mass in the process of sound propagation approximately regarded as a subset of a group of harmonic oscillators.The path integral method was used to obtain the energy equation and the wave function of the system,and used to study and analyze some of the mechanisms of sound propagation and its microscopic properties.In the quantum molecular state,The probability amplitude(transition rate) of the system was associated with the partition function by the density matrix,the probability p(E_n) of the energy level E_n and the average energy E of a subset of harmonic oscillators were given.