Is the Spreading of Quantum Mechanical Wave Packets Indeed Inevitable?

TL;DR

This paper challenges the common belief that quantum wave packets inevitably spread, showing that non-dispersive solutions exist but are non-normalizable, implying spreading remains unavoidable for physical states.

Contribution

It demonstrates the theoretical existence of non-dispersive solutions to the Schrödinger equation, clarifying the limitations on constructing normalizable, non-spreading wave packets.

Findings

Non-dispersive solutions to the Schrödinger equation exist.

Normalizable wave packets cannot be constructed from these solutions.

Wave packet spreading remains inevitable for physical states.

Abstract

It is demonstrated that -- contrary to the common belief -- it is possible to construct solutions of the non-relativistic Schr\"odinger equation of a free particle, that do not exhibit dispersion. However, it seems that no normalizable wave packets can be built up by their use, so the spreading of the wave packets is indeed inevitable.