Isgur–Wise function in a QCD-inspired potential model with WKB approximation

Abstract

We use WKB Approximation in the calculation of slope and curvature of Isgur-Wise function in a QCD inspired potential model.This work is an extension of the approximation methods to the QCD inspired potential model.The approach hints at an effective range of distance for the calculation of slope and curvature of Isgur-Wise function.Comparision is also made with those of Dalgarno and VIPT to see the advantages of using WKB Approximation.

Mass Spectrum of Mesons via the WKB Approximation Method

“…(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)…”

“…The solution of the wave equation with some potentials are exactly solvable for 0 l  , whereas other potentials are insoluble and nontrivial for any arbitrary angular momentum quantum number ( 0) l  . In this case, numerical methods and approximate analytical techniques are required to obtain the solutions of the quantum system of choice [27,28]. Owing to the non-trivial mathematical properties of the quark-antiquark interaction potentials, several analytical techniques and approximate methods have been used to calculate the energy and mass spectra.…”