  Using scanning tunneling spectroscopy in ultra-high vacuum at low temperature
(T = 0.3 K) and high magnetic fields (B < 12 T), we directly probe electronic
wave functions across an integer quantum Hall transition. In accordance with
theoretical predictions, we observe the evolution from localized drift states
in the insulating phases to branched extended drift states at the quantum
critical point. The observed microscopic behavior close to the extended state
indicates points of localized quantum tunneling, which are considered to be
decisive for a quantitative description of the transition.
