  We perform momentum-conserving tunneling spectroscopy using a GaAs
cleaved-edge overgrowth quantum wire to investigate adjacent quantum Hall edge
states. We use the lowest five wire modes with their distinct wave functions to
probe each edge state and apply magnetic fields to modify the wave functions
and their overlap. This reveals an intricate and rich tunneling conductance fan
structure which is succinctly different for each of the wire modes. We
self-consistently solve the Poisson-Schr\"odinger equations to simulate the
spectroscopy, reproducing the striking fans in great detail, thus confirming
the calculations. Further, the model predicts hybridization between wire states
and Landau levels, which is also confirmed experimentally. This establishes
momentum-conserving tunneling spectroscopy as a powerful technique to probe
edge state wave functions.
