About the hypothesis of same energy and momentum in the neutrino oscillation phenomena

Different hypotheses and assumptions usually used in neutrino oscillations physics are critically confronted with general aspects of quantum mechanics and with experimental situations. In this paper we review some aspects of the neutrino oscillations and show that Lorentz invariance implies that in general flavour neutrinos are superpositions of massive neutrinos with different energies and different momenta. This can clarify the controversy concerning the hypothesis of 'same momenta' or 'same energy' in the oscillation probabilities. In the relativistic approximation and the T ≅ L approximation, in the first order, the oscillation probability does not depend on the specific details of the production process. We also argue that a wave packet description of massive neutrinos is necessary in order to understand the physics of neutrino oscillations. (authors)