Analysis of the interaction of an electron with radial electric fields in the presence of a disclination

TL;DR

This paper investigates how topological disclinations in an elastic medium affect the quantum behavior of a spinless electron interacting with radial electric fields, using the WKB approximation to find bound states.

Contribution

It introduces a modified centrifugal term in the radial equation to account for topological defects and explores bound state solutions in specific electric field configurations.

Findings

Modified the radial equation to include topological effects.

Derived bound state solutions for electron-electric field interactions.

Analyzed the influence of disclinations on quantum states.

Abstract

We consider an elastic medium with a disclination and investigate the topological effects on the interaction of a spinless electron with radial electric fields through the WKB (Wentzel, Kramers, Brillouin) approximation. We show how the centrifugal term of the radial equation must be modified due to the influence of the topological defect in order that the WKB approximation can be valid. Then, we search for bound states solutions from the interaction of a spinless electron with the electric field produced by this linear distribution of electric charges. In addition, we search for bound states solutions from the interaction of a spinless electron with radial electric field produced by uniform electric charge distribution inside a long non-conductor cylinder.