  Nambu-Goto action of bosonic string predicts the quark-antiquark potential to
be $ V (r) = \frac{\gamma}{r} + \sigma r +\mu_0 $. The coefficient$ \gamma = -
\frac{\pi(d-2)}{24} $ is the universal L\"{u}scher coefficient of the L\"uscher
term $ \frac{\gamma}{r}$, which depends upon the space-time dimension `d'. We
take linear term in potential as parent and L\"uscher term as perturbation for
the generation of wave function for meson in d space-time dimension.The wave
function comes out in terms of Airy's infinite polynomial series. With this
wave function in higher dimension, we then study the Isgur-Wise function for
heavy-light mesons and its derivatives.
