【摘要】 对于复杂的体系,组成体系的各粒子间的相互作用决定其能量状态。对于不同势场,描述粒子运动规律的Schrodinger方程是不同的微分方程。本文在原来的Hamilton谐振子数学模型基础上,通过引入Morse势能函数代替原来的简谐振子势模型,研究了一维气体分子链中声传播的问题。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,建立配分函数与热力学量之间的关系,以Morse势能函数的振子模型构造的声传播模型求取声压及声能量。通过比较,经典方法与量子谐振子模型计算的一维声压吻合。更多还原

【Abstract】 For a complex system,the reciprocal function of the particles constituting the system decides its energy state.Schrodinger equation which describes the particles moving rule will vary in different potential field.In this paper,based on the mathematic model in Hamilton harmonic oscillator researched before,Morse potential energy function which replace the harmonic oscillator potential model is introduced to study sound propagation in the one-dimensional gas molecule chain.From the standpoint of energy,the problem about sound propagation is converted into the problem of the harmonic wavelet function and the energy Eigen values.The relationship between the partition function and the thermodynamics quantity is built and sound propagation model based on oscillator model of Morse potential energy functions is used to get sound pressure and sound energy.Finally the one-dimensional sound pressure results got by quantum oscillator model agree well with classical approach results.更多还原