  We study the quench dynamics of one dimensional bosons or fermion quantum
gases with either attractive or repulsive contact interactions. Such systems
are well described by the Gaudin-Yang model which turns out to be quantum
integrable. We use a contour integral approach, the Yudson approach, to expand
initial states in terms of Bethe Ansatz eigenstates of the Hamiltonian. Making
use of the contour, we obtain a complete set of eigenstates, including both
free states and bound states. These states constitute a larger Hilbert space
than described by the standard String hypothesis. We calculate the density and
noise correlations of several quenched systems such as a static or kinetic
impurity evolving in an array of particles.
