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. The confined nature of the wave function makes it possible to use an iterative formalism borrowed from x-ray diffraction where real-space wave functions are retrieved from the absolute values of their Fourier transforms. The latter are measured by angle-resolved photoemission. The effective confining potential is then obtained by introducing the wave functions into Schr\"odinger's equation.