Derivation of the time-dependent Schr\"odinger equation from Fisher information

TL;DR

This paper demonstrates how the time-dependent Schrödinger equation can be derived from Fisher information principles, establishing a link between classical and quantum mechanics through information theory.

Contribution

It introduces a novel derivation of the Schrödinger equation based on the principle of minimum Fisher information, connecting classical and quantum frameworks.

Findings

Schrödinger equation derived from Fisher information principles

Establishes a theoretical bridge between classical and quantum mechanics

Highlights the role of information theory in quantum physics

Abstract

Fisher information measures a disorder system, which is specified by a corresponding probability, the likelihood. In this article, we provide a bridge to connect classical and quantum mechanics by using Fisher information. Following the principle of minimum Fisher information, we can derive the time-dependent Schr\"odinger equation step by step.