**Abstract: **
The first experimantal realization of Bose-Einstein consensate in 1995
attracted a lot attention to these problems. The subsequent development
of technical instruments brought, in particular, a progress in manipulating
ultracold particles by optical methods. A large part of Bose gas experiments
is at present realized using so-called optical lattices. It is an instrument
to capture and control bosons which allows us to observe interesting effects.
In the first part we will present and discuss a model describing a Bose gas
in a one-dimensional optical lattice. The next part is devoted to description
of the * Density Matric Renormalization Group * algorithm (DMRG) which
can be used in an elegant way just to analyse one-dimensional systems.
Finally the algorithm will be applied to derive information about properties
of the above mentioned model.