  We study the dynamics of multi-dimensional quantum tunneling by introducing a
complex absorbing potential to a two-dimensional model for spontaneous fission.
We fist diagonalize the Hamiltonian with the complex potential to determine a
resonance state as well as its life-time. We then solve the time-dependent
Schr\"odinger equation with such basis in order to investigate the tunneling
path. We compare this method with the semi-classical method for
multi-dimensional tunneling with imaginary time. A good agreement is found both
for the life-time and for the tunneling path.
