Measurement of electron wave functions and confining potentials via   photoemission
  Wave functions and electron potentials of laterally-confined surface states are determined experimentally by means of photoemission from stepped Au(111) surfaces. Using an iterative formalism borrowed from x-ray diffraction, we retrieve the real-space wave functions from the Fourier transform of their momentum representations, whose absolute values in turn are directly measured by angle-resolved photoemission. The effective confining potential is then obtained by introducing the wave functions into Schroedinger's equation. 
A. Mugarza, J.E. Ortega, F.J. Himpsel, and F.J. Garcia de Abajo