with atoms or other particles frequently, the distance in which a particle moves freely, the mean free path, becomes short. A particle is described using one wave function during a mean free time, which is a period for a particle to move freely, and is given by dividing the mean free path by its velocity. This wave function that has a finite coherence length is described using a wave packet.

Second, we study one particle surrounded by many particles where the particle’s mean free path is long. In this system, particles have long mean free paths, and the direct effects of the mean free path are negligible. However, the many-particle state is described using one wave function. If a one-particle state in a many-particle system is regarded as a linear combination of momentum states, this particle is expressed using a wave packet. This wave packet has a different origin from that of the first case and plays important roles in dilute medium.

Third, we study a one-particle state in a system where a particle measurement is made. If a particle is measured with uncertainties of position and momentum, this particle state is described using a wave packet of these uncertainties. 