GAUSSIAN TIME-DEPENDENT VARIATIONAL PRINCIPLE FOR BOSONS - CONTACT INTERACTION IN ONE-DIMENSION

We investigate the Dirac time-dependent variational method using a Gau ssian trial functional for an infinite one-dimensional system of boson s interacting through a repulsive contact interaction. The method prod uces a set of nonlinear time-dependent equations for the variational p arameters. By solving the static equations we have calculated the grou nd state energy per particle. We have also considered small oscillatio ns about the equilibrium and obtain mode equations which lead us to a gapless dispersion relation. The existence of an exact numerical solut ion for the ground-state energy and excitations obtained by Lieb allow us to compare with the Gaussian results. We can also, as the system b ecomes less dilute, see the improvement of the results as compared wit h the Bogoliubov scheme.