Derivation of the Generalized Time-independent Schrodinger Equation. The New Stochastic Quantum Mechanics: Think and calculate

TL;DR

This paper derives a generalized time-independent Schrödinger equation from a stochastic process model of a particle's random motion, linking quantum mechanics to stationary stochastic processes and extending applicability to macrocosmic systems.

Contribution

It introduces a novel derivation of the Schrödinger equation based on stochastic process characteristics, connecting quantum and macrocosmic stochastic systems.

Findings

Derived a generalized Schrödinger equation from stochastic processes

Expressed Planck constant in terms of stochastic process parameters

Applicable to both microcosm and macrocosm stochastic systems

Abstract

In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the Schrodinger equation is proposed; the Planck constant h is expressed in terms of the characteristics of the stationary stochastic process under consideration; the probability distribution density of the n-order derivative for a n-times differentiable stationary stochastic process is determined; it is shown that the obtained generalized Schrodinger equation is applicable not only to describe the possible states of microcosm objects, but also for discrete states of a number of macrocosm stochastic systems