Strong-coupling limit for one-dimensional polarons in a finite box

The strong coupling limit is studied for a Pekar-Frohlich polaron confined to a one-dimensional (1D) structure. The non-linear effective Schrodinger equation is solved exactly in the case of two different external potentials which imitate a finite size 1D sample: an infinite and a finite deep rectangular well. The ground state and excited states are calculated. We found that taking the limit of a finite size box to an infinitely large box leads to additional solutions which are not found in a treatment on an infinite axis. The additional solutions, which have a 1/n(2) discrete spectrum, correspond to polaron states in which the wave function is split up in identical parts which are infinitely apart from each other.