  We study the influence of boundary conditions on energy levels of interacting
fields in a box and discuss some consequences when we change the size of the
box. In order to do this we calculate the energy levels of bound states of a
scalar massive field $\chi$ interacting with another scalar field $\phi$
through the lagrangian ${\cal L}_{int} = 3/2 g\phi^{2}\chi^{2}$ in an
one-dimensional box, on which we impose Dirichlet boundary conditions. We have
found that the gap between the bound states changes with the size of the box in
a non-trivial way. For the case the masses of the two fields are equal and for
large box the energy levels of Dashen-Hasslacher-Neveu (DHN model) (Dashen et
al, 1974) are recovered and we have a kind of boson condensate for the ground
state. Below to a critical box size $L\sim 2.93 2\sqrt{2}/M$ the ground state
level splits, which we interpret as particle-antiparticle production under
small perturbations of box size. Below another critical sizes $(L\sim 6/10
2\sqrt{2}/M)$ and $(L\sim 1.71 2\sqrt{2}/M)$ of the box, the ground state and
first excited state merge in the continuum part of the spectrum.
