On time and space double-slit experiments

TL;DR

This paper presents an analytic solution to the time-dependent Schrödinger equation explaining time double-slit interference experiments, confirming wave-particle duality and the complementarity of which-path and interference patterns.

Contribution

It provides a schematic analytic derivation of experimental results using boundary conditions aligned with actual setups, addressing coherence issues in time quantum interference.

Findings

Analytic solution matches experimental interference patterns

Demonstrates complementarity of which-path and interference in time

Supports wave-particle duality with time-based experiments

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.