  Just at the beginning of quantum stochastic calculus Hudson and Parthasarathy
proposed a quantum stochastic Schrodinger equation linked to dilations of
quantum dynamical semigroups. Such an equation has found applications in
physics, mainly in quantum optics, but not in its full generality. It has been
used to give, at least approximately, the dynamics of photoemissive sources
such as an atom absorbing and emitting light or matter in an optical cavity,
which exchanges light with the surrounding free space. But in these cases the
possibility of introducing the gauge (or number) process in the dynamical
equation has not been considered. In this paper we show, in the case of the
simplest photoemissive source, namely a two-level atom stimulated by a laser,
how the full Hudson-Parthasarathy equation allows to describe in a consistent
way not only absorption and emission, but also the elastic scattering of the
light by the atom. Morever, we study the differential and total cross sections
for the scattering of laser light by the atom, as a function of the frequency
of the stimulating laser. The resulting line-shape is very interesting. Not
only a Lorentzian shape is permitted, but the full variety of Fano profiles can
be obtained. The dependence of the line shape on the intensity of the
stimulating laser is computed; in particular, the resonance position turns out
to be intensity dependent, a phenomenon known as lamp shift.
