semimicroscopic between microscopic and macroscopic lengths, and it is good to approximate the initial and final states using plane waves if the typical scales of targets and interaction lengths are microscopic.

The wave packets have been applied in various areas of physics such as electromagnetic wave propagations[@Brillouin], particle scatterings,[@Goldberger] and neutrino oscillations. [@Giunti] Moreover, the fundamental problems of quantum mechanics that are connected with measurements and their implications in quantum information, entanglements, and others are tested using beams of electrons, neutrons, and of photons or its coherent states, lasers. However, in these cases, either the wave is classical or the coherence lengths of waves in quantum physics are much larger than the typical scales of microscopic objects. The interactions of these waves with microscopic objects were studied using plane waves. A detailed qualitative study of microscopic physics, particularly of particle physics, has not been made for wave packets.

We found that the situation has been changed now and there are many occasions where the wave packet’s effects are important.[@Asahara] Particularly in the present problems of fundamental physics where high precision, high energy, long distance, and other new circumstances are required, these effects are expected to be important. Qualitative theoretical investigations 