Doubly anharmonic oscillator under the topological effects of a screw dislocation

TL;DR

This paper analytically solves the Schrödinger equation for a doubly anharmonic oscillator in an elastic medium with a screw dislocation, revealing how topological defects alter its energy spectrum.

Contribution

It provides exact solutions for the energy levels of the doubly anharmonic oscillator influenced by a screw dislocation, a novel topological effect.

Findings

Energy spectrum is modified by the screw dislocation.

Exact ground state energies are derived.

Topological defects influence quantum oscillator behavior.

Abstract

We consider an elastic medium with the distortion of a circular curve into a vertical spiral, and investigate the influence of this topological defect on the doubly anharmonic oscillator. We show that the Schr\"odinger equation for the doubly anharmonic oscillator in the presence of this linear topological defect can be solved analytically. We also obtain the exact expressions for the permitted energies of the ground state of the doubly anharmonic oscillator, and show that the topology of the screw dislocation modifies the spectrum of energy of the doubly anharmonic oscillator.