Semiclassical trajectories in the double-slit experiment

We provide a semiclassical description of the double-slit experiment given by the momentous quantum mechanics. This formulation allows the study of quantum systems by an effective augmented Hamiltonian. The use of canonical variables enables us to comprise all the quantum information into a finite system of equations. We show the evolution of individual particles and their semiclassical trajectories, and how their collective behavior seems to reproduce the well-known quantum interference pattern. We are able to follow the individual evolution of each particle and its interaction with the effective quantum potential, showing that, contrary to the non-crossing rule present in Bohmian mechanics, particle trajectories actually cross each other in our description. By discussing the quantum-effective potential obtained, we mention possible extensions and applications to other areas.

Automated summary

We present a semiclassical description of the double-slit experiment using an augmented Hamiltonian and canonical variables. Our framework allows for the study of quantum systems and captures the evolution and collective behavior that reproduces the quantum interference pattern. Unlike Bohmian mechanics, our description allows particle trajectories to cross each other. We also discuss the potential extensions and applications of this quantum-effective potential.