  In this work, we present a complete analysis of the quantisation of the
classical Brans-Dicke Theory using the method of affine quantisation in the
Hamiltonian description of the theory. The affine quantisation method is based
on the symmetry of the phase-space of the system, in this case the (positive)
half-plane, that is identified with the affine group. We consider a FLRW-type
spacetime, and since the scale factor is always positive, the affine method
seems to be more suited than the canonincal quantisation for our Quantum
Cosmology. We find the wave function of the Brans-Dicke universe, and its
energy spectrum. A smooth bounce is expected at the semi-classical level in the
quantum phase-space portrait. We also adress the problem of equivalence between
the Jordan and Einstein frames.
