  We perform a fully quantum mechanical numerical calculation for the problem
of a single electron (or excitation) propagating in a N-site one-dimensional
chain in the presence of a single Holstein impurity. We compute the long-time
averaged probability for finding the electron on the impurity site as a
function of the nonlinearity parameter, defined in terms of the electron-phonon
coupling strength and the oscillator frequency. The results, in the
intermediate nonlinearity parameter range, differ substantially from the ones
obtained through the use of the discrete nonlinear Schroedinger equation, even
in the high-frequency regime.
