  The interaction between ultrashort light pulses and non-absorbing materials
is dominated by Impulsive Stimulated Raman Scattering (ISRS). The description
of ISRS in the context of pump\&probe experiments is based on effective
classical models describing the interaction between the phonon and pulsed
electromagnetic fields. Here we report a theoretical description of ISRS where
we do not make any semi-classical approximation and we treat both photonic and
phononic degrees of freedom at the quantum level. The results of the quantum
model are compared with semiclassical results and validated by means of
spectrally resolved pump\&probe measurements on $\alpha$-quartz.
