  We apply the maximum entropy method to extract the spectral functions for
pseudoscalar and vector mesons from hadron correlators previously calculated at
four different lattice spacings in quenched QCD with the Wilson quark action.
We determine masses and decay constants for the ground and excited states of
the pseudoscalar and vector channels from position and area of peaks in the
spectral functions. We obtain the results, $m_{\pi_1} = 660(590)$ MeV and
$m_{\rho_1} = 1540(570)$ MeV for the masses of the first excited state masses,
in the continuum limit of quenched QCD. We also find unphysical states which
have infinite mass in the continuum limit, and argue that they are bound states
of two doublers of the Wilson quark action. If the interpretation is correct,
this is the first time that the state of doublers is identified in lattice QCD
numerical simulations.
