2D Relativistic Oscillators with a Uniform Magnetic Field in Anti-deSitter Space

TL;DR

This paper analytically solves the energy spectra and wave functions of charged particles with spin in a 2D Anti-deSitter space under a magnetic field, revealing the influence of spin and space curvature on quantum states.

Contribution

It provides exact solutions for relativistic oscillators in Anti-deSitter space, including spin effects, using the Nikiforov-Uvarov method, and explores their thermodynamic properties.

Findings

Exact energy eigenvalues for Klein-Gordon and DKP particles.

Wave functions derived analytically for both cases.

Demonstrates the role of spin in non-relativistic energy behavior.

Abstract

We study analytically the two dimensional deformed bosonic oscillator equations for charged particles (both spin 0 and spin 1 particles) subject to the effect of a uniform magnetic field. We consider the presence of a minimal uncertainty in momentum caused by the Anti-deSitter model and we use the Nikiforov-Uvarov method to solve the system. The exact energy eigenvalues and the corresponding wave functions are analytically obtained for both Klein-Gordon and scalar Duffin-Kemmer-Petiau cases. For spin 1 DKP case, we deduce the behaviour of the DKP equation and write the non-relativistic energies where we show the fundamental role of the spin in this case. Finally, we study the thermodynamic properties of the system.