Penerapan Konsep Minimal Length pada Penyelesaian Persamaan Dirac Potensial Extended Hulthen-Yukawa Menggunakan Asymptotic Iteration Method (AIM)

Abstract

This study investigates the application of the minimal length concept to the Dirac equation with the extended Hulthen-Yukawa potential under the spin symmetry condition. The Dirac equation is modified by incorporating the minimal length correction and subsequently reduced to the Dirac equation with a Q-deformed central potential to facilitate analytical treatment. The resulting equation is solved using the Asymptotic Iteration Method (AIM) to obtain the relativistic energy eigenvalues and corresponding wave functions. Numerical calculations of the relativistic energy spectrum are then performed using Matlab based on the derived energy equation, while the wave functions are visualized to illustrate the characteristics of the obtained solutions. The results indicate that the relativistic energy spectrum depends on the quantum numbers and the potential parameters. Furthermore, the inclusion of the minimal length correction significantly affects the energy spectrum. An increase in the minimal length correction parameter leads to a corresponding increase in the relativistic energy values. These findings demonstrate that the minimal length effect plays an important role in modifying the solutions of the Dirac equation with the extended Hulthen-Yukawa potential and provides useful insight into the development of relativistic quantum mechanics incorporating quantum gravity effects at microscopic scales.