  A one-dimensional system of two trapped bosons which interact through a
contact potential is studied using the optimized configuration interaction
method. The rapid convergence of the method is demonstrated for trapping
potentials of convex and non-convex shapes. The energy spectra, as well as
natural orbitals and their occupation numbers are determined in function of the
inter-boson interaction strength. Entanglement characteristics are discussed in
dependence on the shape of the confining potential.
