Neutrinos play an important role in understanding nature’s behavior, from the suggestion of their existence, to the experimental issues found in the way of trying to present evidence for it. The oscillation induced by mass is supported by overwhelming experimental evidence. This work proposes a theoretical revision of the quantum mechanical descrip-tion of neutrino oscillations, discussing the inconsistencies of the usual ap-proaches and giving a more precise one. Moreover, the mechanism for oscilla-tions in matter is studied with the purpose of finding the differential equation to solve for the evolution of the neutrino states. For finding the evolved states, a code for solving the Schr¨odinger equation nu-merically was developed. The resu...