Abstract
The energy eigenvalues with any l≠0 states and mass of heavy quark-antiquark system (quarkonium) are obtained by using Asymptotic Iteration Method in the view of nonrelativistic quantum chromodynamics, in which the quarks are considered as spinless for easiness and are bounded by Cornell potential. A semianalytical formula for energy eigenvalues and mass is achieved via the method in scope of the perturbation theory. The accuracy of this formula is checked by comparing the eigenvalues with the ones numerically obtained in this study and with exact ones in literature. Furthermore, semianalytical formula is applied to cc-, bb-, and cb- meson systems for comparing the masses with the experimental data.
Highlights
Investigation of an atomic or subatomic system is done by achieving an energy spectrum of the system
In order to do this, various mathematical methods are used in quantum mechanics
We attempted to get the energy eigenvalues and masses of heavy mesons by using Asymptotic Iteration Method in the view of nonrelativistic quantum chromodynamics (NRQCD), in which the quarks are considered as spinless for easiness and are bounded by Cornell potential
Summary
Investigation of an atomic or subatomic system is done by achieving an energy spectrum of the system. We attempted to get the energy eigenvalues (for any l ≠ 0 states) and masses of heavy mesons by using Asymptotic Iteration Method in the view of NRQCD, in which the quarks are considered as spinless for easiness and are bounded by Cornell potential. We achieved a semianalytical formula for constructing the energy spectrum and obtaining the masses of the mesons, using the method in scope of the perturbation theory The accuracy of this formula was cross-checked by comparing the eigenvalues with the ones numerically obtained in this study and with the exact ones in literature. AIM has been firstly applied to Schrodinger equation for Cornell potential by Hall and Saad in [21] They have used Airy function as an asymptotic form of the wavefunction and have got highly-accurate numerical results in their study. The energy eigenvalue of an nth level is obtained through q iterations where q ≥ n
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