wave packet scatterings such as the evolution of wave packets and slight violations of energy and momentum conservations in many-body reactions. The consistency of the nonorthogonality of wave packets with the fundamental requirement of quantum mechanics in many-body scatterings was also shown.

In the present paper, we study the formations of wave packets that have finite uncertainties of position and momentum and the transmutations of these uncertainties in various reactions. We present the coherence length of wave packets and other universal properties in the potential scatterings and other many-body reactions.

This paper is organized as follows. In §2, several mechanisms of forming wave packets are studied. In §3, we study the potential scatterings of wave packets, and in §4, we present the transformations of wave packets. In §5 the particle’s coherence in refraction and reflection is studied, and many-body processes are studied in §6. A summary is given in §7.

Wave packet formations
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In this section, we study one-particle states in various situations and show that the wave packets are good wave functions for particles in medium and for particles in measurements.

First, we study a system where the particle’s mean free path is short. If a particle interacts 