Abstract
A physical picture is presented for the energy spectrum of a quantum particle localized by a deformable nonlinear medium. For a strongly coupled electron-lattice system interacting by a deformation potential, quantum fluctuations of the lattice lead to an exponential band tail at zero temperature in the zero-phonon sector of the lattice Hilbert space which terminates at the polaron ground state. This has an exponentially small overlap with a coexisting free-polaron band.