Non-relativistic quantum effects on the harmonic oscillator in a spacetime with a distortion of a vertical line into a vertical spiral

TL;DR

This paper investigates how a topological spacetime defect, modeled as a vertical spiral, influences the quantum behavior of a harmonic oscillator, revealing energy spectrum modifications and an Aharonov-Bohm-type effect.

Contribution

It provides analytical solutions to the Schrödinger equation in a spiral spacetime, demonstrating the impact of topology on quantum energy levels and bound states.

Findings

Energy spectrum of the harmonic oscillator is altered by the spacetime topology.

An Aharonov-Bohm-type effect is observed for bound states.

Spacetime distortion leads to measurable quantum effects.

Abstract

Non-relativistic quantum effects of the topology of the spacetime with the distortion of a vertical line into a vertical spiral on the harmonic oscillator are investigated. By searching for analytical solutions to the Schr\"odinger equation in this topological defect background, it is shown that the topology of the spacetime modifies the spectrum of energy of the harmonic oscillator. Besides, it is shown that there exists an Aharonov-Bohm-type effect for bound states.