谐振子的热力学：维恩位移定律和普朗克谱
Thermodynamics of the Harmonic Oscillator: Wien's Displacement Law and the Planck Spectrum
摘要：
对谐振子进行了热力学分析。研究的动机是由黑体辐射光谱提供的，当黑体辐射被视为一个系统的非相互作用的谐振子模式，热力学遵循的谐振子。利用谐振子热力学系统在准静态的振荡频率变化下的行为，我们证明了热力学函数都可以从一个单一的函数w/T，类似于维恩的位移定理。高频和低频能量极限允许渐近能量形式涉及单独的T或单独的W，对应于能量均分和零点能量。应注意，具有零点辐射的普朗克谱对应于满足维恩位移结果的函数，该维恩位移结果提供了低频能量均分和高频零点能量之间的最平滑的可能插值。
英文摘要：
A thermodynamic analysis of the harmonic oscillator is presented. Motivation for the study is provided by the blackbody radiation spectrum; when blackbody radiation is regarded as a system of noninteracting harmonic oscillator modes, the thermodynamics follows from that of the harmonic oscillators. Using the behavior of a harmonic oscillator thermodynamic system under a quasi-static change of oscillator frequency w, we show that the thermodynamic functions can all be derived from a single function of w/T, analogous to Wien's displacement theorem. The high- and low-frequency energy limits allow asymptotic energy forms involving T alone or w alone, corresponding to energy equipartition and zero-point energy. It is noted that the Planck spectrum with zero-point radiation corresponds to the function satisfying the Wien displacement result which provides the smoothest possible interpolation between energy equipartition at low frequency and zero-point energy at high frequency.
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