Analysis of quantum systems subject to inverse trigonometry Scarf plus Coulomb potential in N-dimensions

• Published in: Physica scripta Vol. 98; no. 11; pp. 115256 - 115266
• Main Author: Özfidan, Aysel
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.11.2023
• Subjects: hyperspherical coordinates; inverse trigonometric scarf potential; klein-gordon equation
• ISSN: 0031-8949; 1402-4896
• DOI: 10.1088/1402-4896/ad0345

We present approximate solutions of the N-dimensional Klein–Gordon equation in the presence of a superposition of inverse trigonometry Scarf potential and Coulomb potential through asymptotic iteration approach. With the purpose of dealing with the l N − 1 -state, we use Greene-Aldrich approximation which is valid for the small values of the screening parameter. The analytical expressions for the relativistic energy eigenvalues and the corresponding eigenfunctions are established in hyperspherical coordinates. The normalized hyper-radial wavefunction is expressed in terms of hypergeometric and Jacobi polynomials. We analyze the dependences of the relativistic energy levels on the dimensions. We also discuss the effect of the screening parameter on the relativistic energy spectrum. The expectation values of inverse position r − 1 , the square of inverse position r − 2 , kinetic energy T and square of momentum p 2 in N-dimensional space are reported using the Hellmann-Feynmann theorem. Discussing the special cases of the relevant potential, we show the accuracy of our results.