E. Nelson 量子力学随机诠释的发展：薛定谔-欧拉-泊松方程的推导
Development of a Stochastic Interpretation of Quantum Mechanics by E. Nelson. Derivation of the Schrodinger-Euler-Poisson Equations
AI总结：
本文通过平衡有序与混沌的矛盾，将最小作用量原理和最大熵原理统一为平均效率极值原理，推导出与薛定谔方程一致的随机薛定谔-欧拉-泊松方程，并给出约化普朗克常数与粒子质量之比基于三维随机过程平均特征的表达，从而发展 E. Nelson 的量子力学随机诠释。
摘要：
本文旨在通过平衡“有序”与“混沌”之间的系统内矛盾（即反对称性），发展 E. Nelson 的量子力学随机诠释。为完成所设定的任务，提出将两个相互对立的系统形成原理——“最小作用量原理”和“最大熵原理”——结合为一个“平均效率极值原理”。在详细考察混沌游走粒子的平均状态时，得到了与时间无关（稳态）和与时间相关的随机薛定谔-欧拉-泊松方程，作为求取所研究随机系统全局平均效率泛函极值的条件。所得的随机方程在系数上（除系数外）与相应的薛定谔方程一致。在这种情况下，约化普朗克常数与粒子质量之比通过所考虑的游走粒子参与其中的三维随机过程的平均特征来表示。所得到的随机方程适用于描述任意尺度随机系统的量子态。
英文摘要：
The aim of the article is to develop the stochastic interpretation of quantum mechanics by E. Nelson on the basis of balancing the intra-systemic contradiction (i.e., antisymmetry) between "order" and "chaos". For the set task, it is proposed to combine two mutually opposite system-forming principles: "the principle of least action" and "the principle of maximum entropy" into one the "principle of averaged efficiency extremum". In a detailed consideration of the averaged states of a chaotically wandering particle, the time-independent (stationary) and time-dependent stochastic Schrodinger-Euler-Poisson equations are obtained as conditions for finding the extremals of the functional of the globally averaged efficiency functional of the stochastic system under study. The resulting stochastic equations coincides with the corresponding Schrodinger equations up to coefficients. In this case, the ratio of the reduced Planck constant to the particle mass is expressed through the averaged characteristics of a three-dimensional random process in which the considered wandering particle participates. The obtained stochastic equations are suitable for describing the quantum states of stochastic systems of any scale.
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