Euler-Schrodinger Transformation

TL;DR

This paper introduces a novel transformation linking quantum mechanics and fluid dynamics, mapping the Schrödinger equation to incompressible Euler equations with physical surface tension representing quantum potential.

Contribution

It presents a new transformation that connects Schrödinger and Euler equations, providing a physical interpretation of quantum potential as surface tension.

Findings

Quantum potential corresponds to physical surface tension.

Schrödinger equation maps to incompressible Euler equations.

Bohm equation relates to particle motion on fluid surface.

Abstract

Here we present a transformation that maps the Schrodinger equation of quantum mechanics to the incompressible Euler equations of fluid mechanics. The transformation provides a wave solution and a potential function based on fluid properties that satisfy the Schrodinger equation given that the fluid velocity potential and pressure satisfy the Euler equations. Interestingly, in our transformation, the equivalent of quantum potential becomes the physical surface tension. This is contrary to the Madelung transformation that maps the Schrodinger equation to the compressible Euler equations where there is no physical counterpart for the quantum potential. Lastly, we show that using this transformation, the Bohm equation can be mapped to a particle's equation of motion moving on the free surface of the fluid.