path, one particle interacts with other surrounding particles many times while maintaining quantum coherence. If these surrounding particles have momentum uncertainties, they are transmuted to one particle. This particle is described using a wave packet that has an origin in the momentum uncertainty.

One example of a wave that is extended in the momentum is a spherical wave around a short-range potential. A spherical wave is a superposition of plane waves and is decomposed into plane waves of continuous momentum. Hence, the spherical wave is extended in the momentum. In a normal scattering, a particle is measured at a certain scattering angle. The probability of observing this particle at a certain angle is proportional to the square of the absolute value of the amplitude. It is not easy to verify directly the fact that the wave function is extended in momentum variables. In our objective of studying interference phenomena in systems of large scales, this type of momentum extension is important as a new mechanism of the wave packet.

We study the coherence length of a particle surrounded by many particles and whole states are described using one wave function based on the correlation in the momentum variables $C({\vec p}_1,{\vec 