Bound states for a Coulomb-type potential induced by the interaction between a moving electric quadrupole moment and a magnetic field

TL;DR

This paper investigates how a Coulomb-like potential, generated by the interaction of a moving electric quadrupole with a magnetic field, leads to bound states and affects the quantum harmonic oscillator's properties.

Contribution

It introduces a novel Coulomb-type potential arising from electric quadrupole-magnetic field interaction and explores its impact on bound states and oscillator frequency quantization.

Findings

Bound states exist due to the Coulomb-type potential.

The Coulomb potential influences the allowed angular frequencies.

Quantum numbers determine the permissible oscillator frequencies.

Abstract

We discuss the arising of bound states solutions of the Schr\"odinger equation due to the presence of a Coulomb-type potential induced by the interaction between a moving electric quadrupole moment and a magnetic field. Furthermore, we study the influence of the Coulomb-type potential on the harmonic oscillator by showing a quantum effect characterized by the dependence of the angular frequency on the quantum numbers of the system, whose meaning is that not all values of the angular frequency are allowed.