  We prove variationally that at weak coupling in one, two, and three
dimensions there exist correlated electron-phonon states below the approximate
ground states characteristically found by adiabatic polaron theory. Besides
differing non-trivially in quantitative aspects such as the value of the ground
state energy, these improved ground states are found to differ significantly in
qualitative aspects such as correlation structure and scaling behavior. These
differences are sufficiently severe as to require a reevaluation of the
physical meaning attached to such widely used terms as "large polaron" and
"self-trapping transition".
