Potentials versus Geometry

TL;DR

This paper explores the relationship between quantum mechanics with potentials and free particles on geometries, showing how geometries can regularize singular potentials, thus providing new insights into quantum regularization techniques.

Contribution

It introduces equivalence relations between potential-based and geometry-based quantum mechanics, highlighting how geometries can serve as regularization tools for singular potentials.

Findings

Selected geometries can regularize singular potentials.

Equivalence relations link potential-based and geometry-based quantum mechanics.

Geometries provide alternative frameworks for quantum regularization.

Abstract

We discuss some equivalence relations between the non-relativistic quantum mechanics for particles subjected to potentials and for particles moving freely on background geometries. In particular, we illustrate how selected geometries can be used to regularize singular potentials.