On Wave Function Representation of Particles as Shock Wave Discontinuities

TL;DR

This paper analyzes how quantum wave functions can develop shock wave discontinuities due to quantum forces, and identifies localized quantum density waves as the only non-discontinuous representation of particles.

Contribution

It demonstrates that quantum forces induce shock discontinuities in wave packet descriptions, except for localized quantum density waves which remain free of such discontinuities.

Findings

Quantum force causes wave packet dispersion and shock formation.

Localized quantum density waves do not develop shock discontinuities.

Wave function representations with localized density waves are free of shock discontinuities.

Abstract

In quantum theory particles are represented as wave packets. Shock wave analysis of quantum equations of motion shows that wave function representation in general and wave packet description in particular contains discontinuities due to a non-zero quantum force. The quantum force causes wave packet dispersion which results in the intersection of characteristic curves developing a shock discontinuity. Since quantum force vanishes for localized quantum density waves [1], it is thus established that localized quantum density waves form the only class of wave function representation of particles in quantum theory without shock wave discontinuities.