STRONG-COUPLING LIMIT FOR ONE-DIMENSIONAL POLARONS IN A FINITE BOX

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