Analytical Solutions of the Schrödinger Equation with Kratzer-screened Coulomb Potential for a Quarkonium System

Abstract

In this work, we obtain the Schrödinger equation solutions for the Kratzer potential plus screened Coulomb potential model using the series expansion method. The energy eigenvalues is obtained in non-relativistic regime and the corresponding unnormalized eigenfunction. Three special cases were obtained. We applied the present results to calculate heavy-meson masses of charmonium cc and bottomonium bb , and we got the numerical values for 1S, 2S, 1P,2P, 3S, 4S ,1D,2D and 1F states. The results are in good agreement with experimental data and the work of other researchers.

Application of Eckart-Hellmann potential to study selected diatomic molecules using Nikiforov-Uvarov-Functional analysis method

“…( 34) is consistent with the result obtained in Eq. (38) in Ref. [24] The corresponding wavefunction is given as…”

“…The development of these methods allows one to derive the analytic eigen-solutions of the relativistic and non-relativistic wave equations which play a crucial role in interpreting the behavior of quantum mechanical systems. The frequently used analytical methods are the Nikiforov-Uvarov method (NU) , Asymptotic iterative method (AIM) [31], Laplace transformation approach [32], ansatz solution method [33], super-symmetric quantum mechanics approach (SUSYQM) [34,35], exact and proper quantization methods [36,37], series expansion method [38][39][40][41][42][43][44][45], the recent study via the Heun function approach has been used widely to study those soluble quantum systems which could not be solved before,e.g. the systems including the Mathieu potential,rigid rotor problem,sextic type problem, Konwent potential and others [46][47][48][49][50][51][52][53][54] The Schrödinger equation (SE) can be studied for different quantum-mechanical processes with the above analytical methods [55][56][57][58].…”

Analyzing the effects of magnetic and Aharonov‐Bohm (AB) flux fields on the energy spectra and thermal properties of N2, NO, CO and H2 diatomic molecules

“…Many researchers have recently used various analytical techniques to obtain the solutions of the SE with interacting potentials [3][4][5][6]. Examples include the series expansion method [7], WKB approximation method [8,9], asymptotic iteration method (AIM) [10,11], Nikiforov-Uvaforov (NU) method [12][13][14][15], NU-functional analysis (NUFA) approach [16], and others.…”

The Effect of Topological Defect on the Mass Spectra of Heavy and Heavy-Light Quarkonia

“…The mesonic wave function was computed using the eigenvalues. To examine the MS of mesons, researchers have recently modeled exponential-type potentials to study the MS of quarkonia [23]. The prediction of the MS of the heavy mesons (HMs), potential models such as Varshni [24], Hulthen plus Hellmann potential [25], and others have been used.…”