  One of the most intriguing and fundamental properties of topological
materials is the correspondence between the conducting edge states and the
gapped bulk spectrum. So far, it has been impossible to access the full
evolution of edge states with critical parameters such as magnetic field due to
poor resolution, remnant bulk conductivity, or disorder. Here, we use a GaAs
cleaved edge quantum wire to perform momentum-resolved tunneling spectroscopy.
This allows us to probe the evolution of the chiral quantum Hall edge states
and their positions from the sample edge with unprecedented precision from very
low magnetic fields all the way to high fields where depopulation occurs. We
present consistent analytical and numerical models, inferring the edge states
from the well known bulk spectrum, finding excellent agreement with the
experiment -- thus providing direct evidence for the bulk to edge
correspondence. In addition, we observe various features beyond the
single-particle picture, such as Fermi level pinning, exchange-enhanced spin
splitting and signatures of edge-state reconstruction.
