• Corpus ID: 252532036

Direct evidence of a continuous transition between waves and particles

  title={Direct evidence of a continuous transition between waves and particles},
  author={Christian Kisielowski and Petra Specht and Stig Helveg and Fujun Chen and Bert Freitag and Joerg R. Jinschek and Dirk Van Dyck},
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 Schrödinger equation and undergo a Goos-Hänchen shift. In the Heisenberg limit they are created by self-interferences during coherent-inelastic Coulomb interactions with a… 

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Spatial (bold solid black) and temporal (bold dash-dot gray) self-coherence versus reciprocal energy loss in coherent-inelastic electron scattering

    URL will be inserted by publisher] for supporting experimental data and common solutions of Schrödingers time dependent equation

      A strict dependence x i (ΔE) = 1/aΔE is uncovered. Two different illumination conditions are used as indicated. The fitting parameter a relates to the propagation velocity v of wave packets

        Figures Fig. 4. Energy dependence of the penetration depth and its relation to self-coherence