Using stochastic methods, general formulas for average kinetic and potential energies for anharmonic, undamped (frictionless), classical oscillators are derived. It is demonstrated that for potentials of | x | ν , ( ν > 0) type energies are equipartitioned for the harmonic potential only. For potential wells weaker than parabolic potential energy dominates, while for potentials stronger than parabolic kinetic energy prevails. Due to energy conservation, the variances of kinetic and potential energies are equal. In the limiting case of the infinite rectangular potential well ( ν → ∞) the whole energy is stored in the form of the kinetic energy and variances of energy distributions vanish.

中文翻译：

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非谐波，无阻尼经典振荡器的能量分配

使用随机方法，得出了非谐振，无阻尼（无摩擦）经典振荡器的平均动能和势能的通用公式。它证明了|的潜力。x | ν，（ν> 0）型能量仅针对谐波电位进行均分。对于势阱，弱于抛物线的势能占优势，而对于势阱比抛物线的动能强。由于能量守恒，动能和势能的方差相等。在无限矩形势阱（ν→∞）的极限情况下，全部能量以动能的形式存储，并且能量分布的方差消失。