Newton equation and Schrödinger equation for the harmonic oscillator with probability distributions in frequency

Won Sang Chung, Hassan Hassanabadi and Jan Kr̆íz̆

Physica A: Statistical Mechanics and its Applications, 2020, vol. 558, issue C

Abstract: 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.

Keywords: Harmonic oscillator; Probability distribution; Superstatistical (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:558:y:2020:i:c:s0378437120305057

DOI: 10.1016/j.physa.2020.124967

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