Direct evidence of a continuous transition between waves and particles

The correlation between particle and wave descriptions of electron-matter interactions is analyzed by measuring the delocalization of an evanescent field using electron microscopy. Its spatial extension coincides with the energy-dependent, self-coherence length of propagating wave packets that obey the time-dependent Schr\"odinger equation and undergo a Goos-H\"anchen shift. In the Heisenberg limit they are created by self-interferences during coherent-inelastic Coulomb interactions with a decoherence phase {\Delta}{\phi} = 0.5 rad and shrink to particle-like dimensions for energy losses of more than 1000 eV.