On a relativistic scalar particle subject to the Klein-Gordon oscillator, the Coulomb potential and a linear scalar potential

TL;DR

This paper explores the relativistic quantum behavior of a charged scalar particle influenced by the Klein-Gordon oscillator, Coulomb, and linear scalar potentials, revealing quantum-dependent oscillator frequencies and bound state conditions.

Contribution

It introduces the concept of quantum-number-dependent angular frequency for the Klein-Gordon oscillator in a relativistic setting, and analyzes bound states with combined potentials.

Findings

Angular frequency depends on quantum numbers.

Bound states exist only for specific oscillator frequencies.

Ground state energy and frequency are explicitly calculated.

Abstract

The relativistic quantum dynamics of an electrically charged particle subject to the Klein-Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed: a dependence of the angular frequency of the Klein-Gordon oscillator on the quantum numbers of the system. The meaning of this behaviour of the angular frequency is that only some specific values of the angular frequency of the Klein-Gordon oscillator are permitted in order to obtain bound state solutions. As an example, we obtain both the angular frequency and the energy level associated with the ground state of the relativistic system. Further, we analyse the behaviour of an electrically charged particle subject to the Klein-Gordon oscillator, the Coulomb potential and a linear scalar potential.