p}_2)$. In this situation, one particle obtains a large uncertainty from many particles. Even though the momentum uncertainty of each particle is small, the effects of momentum uncertainties of these many particles are added constructively and affect this particle with a significant magnitude. Consequently, this particle is given a finite momentum uncertainty by these many particles and behaves as a wave packet.

This new mechanism is applied, for instance, when many particles are involved in the microscopic processes and they maintain coherence for a long time. This may be realized actually in the universe. Particularly around the decoupling time of cosmological background radiations in an early universe, where particle states are described using one wave function for a long time, a wave packet due to momentum uncertainty of this section is expected to play roles.

During the time evolution of one particle wave function, this particle interacts with surrounding particles. The effects of surrounding particles are studied next. We study the system of many electrons and many photons in which they interact by Thomson scattering. The Thomson scattering cross section is given in Appendix A. Photons and electrons interact also with protons. The number of protons is the same as 