P. Vansant et al., STRONG-COUPLING LIMIT FOR ONE-DIMENSIONAL POLARONS IN A FINITE BOX, Zeitschrift fur Physik. B, Condensed matter, 99(3), 1996, pp. 345-351
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.