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We report some improved wave function for mesons taking linear confinementterm in standard QCD potential as parent and Coulombic term as perturbationwhile applying quantum mechanical perturbation technique in solving Schrodingerequation with such a potential. We find that Airy's infinite series appears inthe wave-function of the mesons. We report our calculations on the Isgur-Wisefunction and its derivatives for heavy-light mesons, within this framework.

Isgur-Wise function within a QCD quark model with Airy's function as the wave function of heavy-light mesons