How to build a non-spreading wave packet in quantum mechanics

Abstract

Quantum mechanics asserts that a wave packet must inevitably spread as time progresses since the dispersion relation for the quantum waves is assumed to be quadratic in the momentum k. However, this assumption does not consider the standard frequency Doppler shift formula of Galilean relativity. In this article a non-dispersive wave packet is constructed by appropriately considering the transformation rules between the laboratory and the (particle's) rest inertial reference frames.