  We study the quantum tunnelling of a very complex object of which only part
is coupled to an external potential ( the potential barrier ). We treat this
problem as the tunnelling of a particle (part of the system affected by the
potential) coupled to a ``heat bath" ( all of the remaining degrees of freedom
) from the point of view of the wavefunction of the whole system. We obtain an
effective scattering equation for this wavefunction which resembles the
integral equation for the wavefunction of the particle in the absence of the
bath. We show that the effect of the interaction is to renormalize the mass and
the potential of the problem and that these new parameters can be solely
described in terms of the spectral function of the excitations of the system.
