On the ground-state wave function of the one-dimensional polaron in the strong-coupling limit

Abstract: We consider the one-dimensional Froehlich polaron localized in a symmetric decreasing electric potential. It is known that the non-linear Pekar functional corresponding to our model admits a unique minimizer. In the strong-coupling limit, we show that any approximate ground-state wave function of our model- after integrating out its phonon modes- converges in the weak sense to this unique minimizer.