In this paper, we discuss Newton equation for the harmonic oscillator with probability distributions in frequency, where the frequency is a stochastic variable with a suitable probability distribution. A new type of Newton equation is obtained by taking the stochastic average of Newton equation with harmonic force with respect to the fluctuating frequency. This method is also applied to the Schrödinger equation with harmonic potential.

中文翻译：

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具有频率概率分布的谐振子的牛顿方程和薛定ding方程

在本文中，我们讨论了具有频率概率分布的谐波振荡器的牛顿方程，其中频率是具有适当概率分布的随机变量。通过求取具有相对于波动频率的谐波力的牛顿方程的随机平均值，可以得到一种新型的牛顿方程。该方法也适用于具有谐波电位的薛定ding方程。