  We investigate the spectrum and eigenstates of a Bose-Hubbard chain
containing two bosons with fixed boundary conditions. In the noninteracting
case the eigenstates of the system define a two-dimensional normal-mode space.
For the interacting case weight functions of the eigenstates are computed by
perturbation theory and numerical diagonalization. We identify paths in the
two-dimensional normal-mode space which are rims for the weight functions. The
decay along and off the rims is algebraic. Intersection of two paths (rims)
leads to a local enhancement of the weight functions. We analyze
nonperturbative effects due to the degeneracies and the formation of two-boson
bound states.
