Dynamics of the Klein–Gordon Oscillator in Anti-de Sitter Space
DOI:
https://doi.org/10.15407/ujpe71.9.727Keywords:
Klein–Gordon equation, curved spacetime, AdS spacetime, relativistic harmonic oscillator, thermodynamic properties, Heun functionAbstract
This study investigates the quantum dynamics of bosonic particles within Anti-de Sitter (AdS) space, structured into two complementary analyses. Initially, exact solutions are derived for a bosonic particle subjected to a stationary electric field, elucidating the field’s impact on the thermodynamic characteristics of quantum oscillators. Subsequently, the analysis extends to incorporate a linear interaction term into the Klein–Gordon equation, forming the Klein–Gordon oscillator (KGO). Exact analytical solutions for this modified system are obtained and comprehensively interpreted. The theoretical framework employs quantum operator symmetry algebra, offering profound insights into the intricate behavior of bosonic particles in curved spacetime environments. Employing quantum operator symmetry algebra as a foundational approach, this research provides comprehensive insights into both the microscopic quantum states and macroscopic thermodynamic behavior of bosonic systems within curved AdS geometries.
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