Mass Spectra of Heavy and Light Mesons Using Asymptotic Iteration Method

Abstract

The non-relativistic radial Schrödinger equation is analytically solved using asymptotic iteration method within the framework of a general interaction potential whose special cases are the Cornell and Cornell plus harmonic potentials. The energy eigenvalues expression is derived in three dimensional space, which is further used to calculate the mass spectra of cc, bb, bc, cs, bs and bq mesons. The obtained results of this work are in good agreement with experimental and other relativistic results and also improved in comparison with other non-relativistic recent studies.

Mass Spectrum of Mesons via the WKB Approximation Method

“…Also, the results for the Charmed-strange meson tabulated in Table 4, are in excellent agreement with the ones obtained in Refs. [15,30] and experimental data such as the excited 1D-state [62]. Furthermore, in Table 3, the mass spectrum of the bottom-charmed meson are very close to the ones obtained with the artificial neural network method [19] and also to the 2S state experimental data [60] indicating an improvement compared to the other methods.…”

“…(24) and (25), we can write the sum and products of the turning points as (28) (29) substituting Eqs. (28) and (29) into (27), we obtained the expression (30) Finally, using the respective notations and given in Eqs. (17)(18)(19), we obtained the energy eigenvalue expression for the KPIQP as (31)…”

Bound State Solution Schrödinger Equation for Extended Cornell Potential at Finite Temperature

“…The bound state solutions to the wave equations under the quark-antiquark interaction potential such as the ordinary, extended, and generalized Cornell potentials and combined potentials such as the Cornell with other potentials have attracted much research interest in atomic and highenergy physics within ordinary and supersymmetric quantum mechanics methods as in [28][29][30][31][32][33][34][35].…”

Charmonium Properties Using the Discrete Variable Representation (DVR) Method

“…The Schrödinger equation for most of the q q potentials (including the Cornell potential) cannot be solved analytically; hence, numerical solutions are called for. Some of the methods found in literature for solving the Schrödinger equation for q q systems are numerical methods based on Runge-Kutte approximation [28,29], Numerov matrix method [30][31][32], asymptotic iteration method [33][34][35], Fourier grid Hamiltonian method [36], variational method [37,38], etc. Another method for numerically solving the Schrödinger equation is the discrete variable representation (DVR) method.…”