Phenomenology of neutrino mixing in vacuum and matter

Neutrino oscillation is the new physics beyond standard model. In this paper we have revisited the issue of neutrino oscillation in simple and delicate manner. Starting from the fundamental quantum mechanical treatment for the neutrinos, we calculated the probabilities for the neutrino oscillating within three flavors. Normal and inverted hierarchy have been taken into account for the solar and atmospheric cases, in vacuum and matter. The probabilities have been plotted for all the cases and discussed.