  We present a new, simple renormalization group method of investigating
groundstate properties of interacting bosonic systems. Our method reduces the
number of particles in a system, which makes numerical calculations possible
for large systems. It is conceptually simple and easy to implement, and allows
to investigate the properties unavailable through mean field approximations,
such as one- and two-particle reduced density matrices of the groundstate. As
an example, we model a weakly interacting 1D Bose gas in a harmonic trap.
Compared to the mean-field Gross-Pitaevskii approximation, our method provides
a more accurate description of the groundstate one-particle density matrix. We
have also obtained the Hall-Post lower bounds for the groundstate energy of the
gas. All results have been obtained by the straightforward numerical
diagonalization of the Hamiltonian matrix.
