# Geometric Description of Schr\"{o}dinger Equation in Finsler and Funk Geometry

## TL;DR

This paper translates quantum Schr"{o}dinger equations into a geometric framework using Finsler and Funk geometries, revealing a unified coupling through different metrics in these geometries.

## Contribution

It introduces a novel geometric interpretation of quantum equations within Finsler and Funk geometries, establishing a connection between these frameworks.

## Key findings

- Quantum equations can be represented geometrically in Finslerian manifolds.
- Finsler and Funk geometries lead to the same coupling in quantum systems.
- The geometric approach provides new insights into quantum mechanics in non-Euclidean spaces.

## Abstract

For a system of $n$ non-relativistic spinless bosons, we show by using a set of suitable matching conditions that the quantum equations in the pilot-wave limit can be translated into a geometric language for a Finslerian manifold. We further link these equations to Euclidean timelike relative Funk geometry and show that the two different metrics in both of these geometric frameworks lead to the same coupling.