  Charmonium dissociation temperatures are studied in a quenched anisotropic
lattice QCD with standard plaquette gauge action and O(a) improved Wilson
fermion action. Simulations are carried out at temperatures in the range
0.88T_c to 2.3T_c. From the meson correlators, we first subtract the
contribution of constant mode, which was reported to mislead the analysis of,
in particular, P wave signals. We then calculate effective masses and
Bethe-Salpeter wave functions for ground (1S, 1P) and excited states (2S, 2P)
using the multi-state variational analysis. To distinguish between bound states
and scattering states, we apply two methods: First, we compare effective masses
for charmonium correlation functions with finite spatial momenta under
different spatial boundary conditions. Since the scattering state energies are
sensitive to the boundary conditions, we expect finite volume effects when the
charmonium dissociates. Second, we study the Bethe-Salpeter wave function,
which should become broad when the charmonium bound state turns into a
scattering state. With both methods, we have fond no clear evidences of
dissociation for the ground and exited charmonium states up to 2.3T_c so far.
