  A generic method to investigate many-body continuous-variable systems is
pedagogically presented. It is based on the notion of matrix product states
(so-called MPS) and the algorithms thereof. The method is quite versatile and
can be applied to a wide variety of situations. As a first test, we show how it
provides reliable results in the computation of fundamental properties of a
chain of quantum harmonic oscillators achieving off-critical and critical
relative errors of the order of 10^(-8) and 10^(-4) respectively. Next, we use
it to study the ground state properties of the quantum rotor model in one
spatial dimension, a model that can be mapped to the Mott insulator limit of
the 1-dimensional Bose-Hubbard model. At the quantum critical point, the
central charge associated to the underlying conformal field theory can be
computed with good accuracy by measuring the finite-size corrections of the
ground state energy. Examples of MPS-computations both in the finite-size
regime and in the thermodynamic limit are given. The precision of our results
are found to be comparable to those previously encountered in the MPS studies
of, for instance, quantum spin chains. Finally, we present a spin-off
application: an iterative technique to efficiently get numerical solutions of
partial differential equations of many variables. We illustrate this technique
by solving Poisson-like equations with precisions of the order of 10^(-7).
