Fundamentals of neutrino oscillations in vacuum and matter

Effects of the wave-packet size of neutrinos on the neutrino oscillations in vacuum and the concept of the coherence length are discussed. In order to elucidate the physics involved, the authors present a pictorial description of neutrino oscillations. When neutrinos pass through a medium, they feel an effective potential which induces dramatic changes in their mass and mixing angles in the medium (MSW effect). This effect may play a crucial role in solving the solar and atmospheric neutrino problems, yielding a clue to the fundamental properties of the neutrinos. After a pedagogical review of the MSW effect, including its pictorial description and the treatment of three generations of neutrinos, the authors present some preliminary results of recent analyses of the data on the solar and atmospheric neutrinos