Eigen solutions of the D-dimensional Schrӧdinger equation with inverse trigonometry scarf potential and Coulomb potential

Abstract

The approximate analytical solutions of the D-dimensional space of the Schrӧdinger equation is studied with a newly proposed potential model. The proposed potential is a combination of Coulomb potential and inverse trigonometry scarf-type potential. The energy equation and the corresponding wave function are obtained using parametric Nikiforov-Uvarov method. The energy equations for Coulomb potential and inverse trigonometry scarf-type potential are respectively obtained by changing the numerical values of the potential strengths. It is found that the results obtained are equivalent to that previously obtained for Hellmann potential which is a combination of Coulomb potential and Yukawa potential. It is also found that the results for inverse trigonometry scarf potential are equivalent to the results previously obtained for Yukawa potential. Also, the Onicescus information energy of a system under the influence of the newly proposed potential is investigated in detail.

Approximate solutions of the Schrödinger equation with Hulthén-Hellmann Potentials for a Quarkonium system

“…where the parameters A 1 and A 2 denote the strength of Coulomb and Yukawa potentials respectively, α denotes the screening parameter, and r is the distance between two particles. These potentials have been used to study bound state problems by many researchers [14][15][16][17][18][19][20]. Recently, Inyang et al [21] obtained the Klein-Gordon equation solutions for the Yukawa potential using the Nikiforov-Uvarov (NU) method.…”

Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén – Hellmann potential model

“…The study of this potential is essential in investigating the interaction existing between two particles [30]. The superposition of Yukawa and Coulomb potential, otherwise known as Hellmann potential [31], has been extensively used by many authors to obtain the energy of the bound state in atomic, nuclear, and particle physics [32][33][34][35][36][37][38][39][40][41]. The Hellmann potential is useful in the study of transitions of alkali metal molecules in condensed matter physics.…”

“…Recently, a lot of interest has been directed towards combining two or more potentials in relativistic and nonrelativistic regimes [35]. The essence of combining two or more physical potential models is to have a broader range of applications [36]. Hence, in the present study, we attempt to study the radial Schrödinger equation with a newly proposed potential, obtained from a combination of Hulthén and Hellmann's potential (HHP).…”

Diatomic Molecules and Mass Spectrum of Heavy Quarkonium System with Kratzer- Screened Coulomb Potential (KSCP) through the Solutions of the Schrödinger Equation

“…Many researchers are concerned about combining two or more potentials. The fundamental nature of combining potential models is to have a broader array of applications [51], [52]. Motivated by the above studies, we attempt to investigate the SE with a potential obtained from the combination of KP (1) and SCP (2) using the SEM to obtain the energy spectra of some selected diatomic molecules and mass spectra of heavy quarkonium system.…”