Geometry-induced Coulomb-like potential in helically twisted quantum systems

TL;DR

This paper demonstrates how geometric torsion in helically twisted quantum systems induces an intrinsic Coulomb-like potential, leading to novel quantum confinement effects without external fields, supported by exact solutions and numerical validation.

Contribution

It reveals that torsion in twisted spaces naturally produces Coulomb-like potentials, providing new insights into geometry-induced quantum effects and confinement mechanisms.

Findings

Torsion induces an attractive Coulomb-like potential.

Exact solutions for bound states are derived.

Numerical results confirm analytical predictions.

Abstract

In this paper, we investigate the Schr\"odinger equation in a three-dimensional helically twisted space characterized by a non-trivial torsion parameter. By applying exact separation of variables, we derive the radial equation governing the dynamics of quantum particles in this geometric background. Remarkably, the intrinsic coupling between angular and longitudinal momenta induced by the torsion gives rise to an attractive Coulomb-like potential term that emerges purely from the underlying geometry, without introducing any external fields or interactions. We obtain exact analytical solutions for the bound states, including both the energy spectrum and the normalized wave functions. Numerical calculations are also performed, and excellent agreement with the exact results is found. The interplay between the torsion parameter and the effective Coulomb-like interaction is analyzed in detail, showing how geometric deformation generates novel quantum confinement mechanisms in twisted spaces.