# Quantum Mechanics on Sharply Bent Wires via Two-Interval Sturm-Liouville Theory

## TL;DR

This paper introduces a method to analyze quantum mechanics on sharply curved wires using two-interval Sturm-Liouville theory, providing a practical approximation when the wire's precise shape is unknown or highly curved.

## Contribution

It develops a boundary condition-based approximation scheme for quantum systems on curved wires, linking geometric potential regularization to Sturm-Liouville parameters.

## Key findings

- Parameters depend on wire regularization
- Method effective for highly curved wires
- Provides a necessary approximation scheme

## Abstract

We study quantum mechanics on a curved wire by approximating the physics around the curved region by three parameters coming from the boundary conditions given by the two interval Sturm-Liouville theory. Since the geometric potential on a highly curved wire is strong an non-integrable, these parameters depend on the regularization of the curved wire. Hence, unless we know precisely the shape of the wire, the presented method becomes not only a useful approximation, but also a necessary scheme to deal with quantum mechanics on highly curved wires.