Solusi Persamaan Klein Gordon dengan Kombinasi Potensial Hiperbolik dalam 3D Koordinat Silinder - Elviyanti, Isnaini Lilis; Syukron, Ahmad Aftah (Schrodinger Jurnal Ilmiah Mahasiswa Pendidikan Fisika, 2024)
This research focuses on the relativistic energy and wave function for spin-zero particles using the Klein-Gordon Equation influenced by a combination of hyperbolic potentials, specifically the Hultn potential and the hyperbolic Scarf potentials type I and II. The main problem addressed is how to solve the Klein-Gordon Equation under anti-particle conditions, where the scalar potential is equal to the negative vector potential, and in separable non-central cylindrical coordinates.The objective of this research is to determine the relativistic energy and wave function of spin-zero particles under the mentioned conditions. To achieve this objective, the asymptotic iteration method (AIM) is used to solve the Klein-Gordon Equation, which has been reduced to three one-dimensional Schrdinger equations. This approach allows for the separation of variables in cylindrical coordinates, breaking the three-dimensional non-central cylindrical potential into radial (r), angular (?), and axial (z) components.The results of the research indicate that the relativistic energy and wave function can be obtained using the AIM. The relativistic energy is derived from the radial component, and the wave function is presented in the form of a hypergeometric equation. These results are presented as equations that show the relationship between energy and wave function with the involved variables.