Energy levels of classical interacting fields in a finite domain in 1+1 dimensions

We study the behaviour of bound energy levels for the case of two classical interacting fields phi and chi in a finite domain (box) in 1+1 dimensions upon which we impose Dirichlet boundary conditions. The total Lagrangian co ntains a lambda/4 phi(4) self-interaction and an interaction term given by g phi(2)chi(2). We calculate its energy eigenfunctions and its correspondin g eigenvalues and study their dependence on the size of the box (L) as well as on the free parameters of the Lagrangian: mass ratio beta = M-chi(2)/M- phi(2), and interaction coupling constants lambda and g. We show that for s ome configurations of the above parameters, there exist critical sizes of t he box for which instability points of the field chi appear.