Schrodinger dynamics as a two-phase conserved flow: an alternative trajectory construction of quantum propagation

TL;DR

This paper presents a novel two-phase hydrodynamic formulation of the Schrödinger equation, enabling deterministic trajectory-based quantum propagation and revealing entangled trajectories even in separable states.

Contribution

It introduces an alternative two-phase quantum hydrodynamic model that reformulates Schrödinger dynamics as coupled conservation equations with a new trajectory construction method.

Findings

The model provides an exact scheme for wavefunction evolution from deterministic trajectories.

Entangled trajectories can appear in separable quantum states.

The formulation extends to Euclidean and five-dimensional geometries.

Abstract

It is shown that the Schrodinger equation can be cast in the form of two coupled real conservation equations, in Euclidean spacetime in the free case and in a five-dimensional Eisenhart geometry in the presence of an external potential. This implies a novel two-phase quantum hydrodynamic model whose Lagrangian picture provides an exact scheme to calculate the time-dependent wavefunction from a continuum of deterministic trajectories where two points are linked by at most two orbits. Properties of the model are examined, including the appearance of entangled trajectories in separable states. Wavefunction constructions employing alternative two-phase models are proposed.