  The unquenched quark model for the light quarkonium and the charmonium states
is explored in the present work. The quark-pair creation operator in the
$^3P_0$ model, which mix the two-quark and four-quark components is modified by
considering the effects of the created quark pair's energy, as well as the
separation between the created quark pair and the valence quark pair. All the
wave functions needed including the mesons and the relative motion between two
mesons are all obtained by solving the corresponding Schr\"{o}dinger equation
with the help of the Gaussian expansion method. Our aim of the present work is
to find a new set of parameters which can give a good description of the mass
spectrum of the low-lying light quarkonium and charmonium states. Moreover,
some exotic states, for example $X(3872)$ can be described well in the
unquenched quark model.
