  We use the coordinate Bethe ansatz to exactly calculate matrix elements
between eigenstates of the Lieb-Liniger model of one-dimensional bosons
interacting via a two-body delta-potential. We investigate the static
correlation functions of the zero-temperature ground state and their dependence
on interaction strength, and analyze the effects of system size in the
crossover from few-body to mesoscopic regimes for up to seven particles. We
also obtain time-dependent nonequilibrium correlation functions for five
particles following quenches of the interaction strength from two distinct
initial states. One quench is from the non-interacting ground state and the
other from a correlated ground state near the strongly interacting
Tonks-Girardeau regime. The final interaction strength and conserved energy are
chosen to be the same for both quenches. The integrability of the model highly
constrains its dynamics, and we demonstrate that the time-averaged correlation
functions following quenches from these two distinct initial conditions are
both nonthermal and moreover distinct from one another.
