  We derive an equation which gives the tree-level scattering amplitudes for
tachyons in the black hole background using the exact states of the collective
field hamiltonian corresponding to a deformed matrix model recently proposed by
Jevicki and Yoneya. Using directly the symmetry algebra we obtain explicit
expression for a class of amplitudes in the tree approximation. We also study
the quantum effects in the corresponding collective field theory. In
particular, we compute the ground state energy and the free energy at finite
temperature up to two loops, and the first quantum correction to the two-point
function.
