Interfering Quantum Trajectories Without Which-Way Information

TL;DR

This paper compares de Broglie-Bohm and modified de Broglie-Bohm quantum trajectories in explaining interference in a double-slit experiment, highlighting how MdBB avoids which-way information while matching standard interference results.

Contribution

It demonstrates that MdBB trajectories can explain stationary interference without revealing which-way information, unlike dBB trajectories.

Findings

MdBB trajectories do not provide which-way information.

Both dBB and MdBB produce accurate interference patterns.

Numerical results agree with standard quantum mechanics predictions.

Abstract

Quantum trajectory-based descriptions of interference between two coherent stationary waves in a double-slit experiment are presented, as given by the de Broglie-Bohm (dBB) and modified de Broglie-Bohm (MdBB) formulations of quantum mechanics. In the dBB trajectory representation, interference between two spreading wave packets can be shown also as resulting from motion of particles. But a trajectory explanation for interference between stationary states is so far not available in this scheme. We show that both the dBB and MdBB trajectories are capable of producing the interference pattern for stationary as well as wave packet states. However, the dBB representation is found to provide the `which-way' information that helps to identify the hole through which the particle emanates. On the other hand, the MdBB representation does not provide any which-way information while giving a satisfactory explanation of interference phenomenon in tune with the de Broglie's wave particle duality. By counting the trajectories reaching the screen, we have numerically evaluated the intensity distribution of the fringes and found very good agreement with the standard results.