  The $B$(E1;$1/2^+\to1/2^-$) strength for $^{11}$Be has been extracted from
intermediate energy Coulomb excitation measurements, over a range of beam
energies using a new reaction model, the extended continuum discretized coupled
channels (XCDCC) method. In addition, a measurement of the excitation cross
section for $^{11}$Be+$^{208}$Pb at 38.6 MeV/nucleon is reported. The $B$(E1)
strength of 0.105(12) e$^2$fm$^2$ derived from this measurement is consistent
with those made previously at 60 and 64 MeV/nucleon, i n contrast to an
anomalously low result obtained at 43 MeV/nucleon. By coupling a
multi-configuration description of the projectile structure with realistic
reaction theory, the XCDCC model provides for the first time a fully quantum
mechanical description of Coulomb excitation. The XCDCC calculations reveal
that the excitation process involves significant contributions from nuclear,
continuum, and higher-order effects. An analysis of the present and two earlier
intermediate energy measurements yields a combined B(E1) strength of 0.105(7)
e$^2$fm$^2$. This value is in good agreement with the value deduced
independently from the lifetime of the $1/2^-$ state in $^{11}$Be, and has a
comparable p recision.
