A quantum trajectory analysis of singular wave functions

TL;DR

This paper uses quantum trajectory analysis to reinterpret the formation of singularities in wave functions, linking blowup behavior to local phase variations and velocity fields, offering new insights into quantum dynamics.

Contribution

It introduces a trajectory-based perspective to understand singular wave functions, connecting phase variations to blowup phenomena in quantum evolution.

Findings

Singularities are driven by local phase variations.

Quantum flux concentrates toward singular regions.

Trajectory analysis offers new interpretative tools.

Abstract

The Schr\"{o}dinger equation admits smooth and finite solutions that spontaneously evolve into a singularity, even for a free particle. This blowup is generally ascribed to the intrinsic dispersive character of the associated time evolution. We resort to the notion of quantum trajectories to reinterpret this singular behavior. We show that the blowup can be directly related to local phase variations, which generate an underlying velocity field responsible for driving the quantum flux toward the singular region.