Neutrino Oscillation: A Basic Pedagogical Review

In this note, I review standard neutrino oscillation in matter at entry level. Based on Mikheyev-Smirnov-Wolfenstein (MSW) effects, I introduce the approximated solution for two and three flavor neutrino oscillation in matter with slowly varying density, with basic examples of neutrino oscillations in the sun and supernova. Based on Caylay-Hamilton method as well as sum rules, I introduce the exact solutions which can be used for three flavor neutrino oscillation in the matter with arbitrary density. Non-standard neutrino interaction parameters and the sterile flavor(if exists) can be added if needed. Based on the exact solutions and for the two cases CP violation angle δ=0 and δ=π/2, I calculate the neutrino's oscillation patterns as they travel through the earth, with the help of Preliminary Reference Earth Model(PREM). Also, I introduce a method called CP diagrams which might help determining CP-violation angle δ and the Δ m²₃₁.