On time and space double-slit experiments (1304.1767v3)

Abstract: Time double-slit interference experiments have been achieved and presented as complementary to spatial double-slit interference experiments, providing a further confirmation of the wave-particle duality. Numerical solutions of the free particle time dependent Schr\"odinger equation were presented as explanation of the experimental results, but have been objected to on the basis that the standard non relativistic quantum theory does not have the property of coherence in time. In this note the theoretical and experimental results are derived in a schematic but analytic solution of the TDSE with appropiate initial boundary conditions. The particular boundary conditions are justified by the experimental setups that actually result in having only a single electron at any given time in the double-slit arrangement; and consequently achieve the construction of double peak single electron wave packets. The progressive complementarity of "which-path" ("which-time") information and "space interference" ("oscillating time transient") pattern build up is also exhibited.