  We develop a variational wave function for the ground state of a
one-dimensional bosonic lattice gas. The variational theory is initally
developed for the quantum rotor model and later on extended to the Bose-Hubbard
model. This theory is compared with quasi-exact numerical results obtained by
Density Matrix Renormalization Group (DMRG) studies and with results from other
analytical approximations. Our approach accurately gives local properties for
strong and weak interactions, and it also describes the crossover from the
superfluid phase to the Mott-insulator phase.
