On a relativistic particle and a relativistic position-dependent mass particle subject to the Klein–Gordon oscillator and the Coulomb potential

• Published in: Annals of physics Vol. 370; no. Complete; pp. 128 - 136
• Main Authors: Vitória, R.L.L., Furtado, C., Bakke, K.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.07.2016; Elsevier BV
• Subjects: Biconfluent Heun equation; BOUND STATE; CHARGED PARTICLES; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COULOMB FIELD; Coulomb potential; Coulomb-type potential; Dynamic tests; Dynamical systems; Dynamics; Energy levels; Ground state; GROUND STATES; KLEIN-GORDON EQUATION; Klein–Gordon oscillator; Linear scalar potential; MASS; MATHEMATICAL SOLUTIONS; OSCILLATORS; Particle physics; Particles (of physics); Position-dependent mass; POTENTIALS; QUANTUM NUMBERS; Quantum physics; Relativistic bound states; RELATIVISTIC RANGE; SCALARS; Klein–Gordon oscillator; Position-dependent mass; Linear scalar potential; Biconfluent Heun equation; Coulomb-type potential; Relativistic bound states
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/j.aop.2016.03.016

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 a relativistic position-dependent mass particle subject to the Klein–Gordon oscillator and the Coulomb potential.