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Neutrino Oscillation

Neutrino oscillation describes the phenomenon where neutrinos change their flavor (electron, muon, tau) as they travel, due to mass differences.
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The statement of the theorem

Consider the evolution of the neutrino state ∣ν(L)⟩|\nu(L)\rangle over a distance LL. The flavor state ∣να⟩|\nu_{\alpha}\rangle evolves according to the Hamiltonian HH: \niddL∣ν(L)⟩=H∣ν(L)⟩i \frac{d}{dL} |\nu(L)\rangle = H |\nu(L)\rangle \nwhere H=Udiag(E1,E2,E3)U†H = U \text{diag}(E_1, E_2, E_3) U^{\dagger}, with UU being the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix, and EiE_i are the energies of the mass eigenstates, related to the squared mass differences Δmij2\Delta m_{ij}^2 by Ei≈p+mi22pE_i \approx p + \frac{m_i^2}{2p}. The probability of transition Pα→βP_{\alpha \to \beta} is given by the survival probability formula derived from this evolution.
Source: Wikipedia