Constructive interference causes it to be possible to observe a neutrino created with a given flavor to change its flavor during its propagation. The probability that a neutrino originally of flavor will later be observed as having flavor is This is more conveniently written as where The phase that is responsible for oscillation is often written as (with and restored) where 1.27 is unitless. In this form, it is convenient to plug in the oscillation parameters since: The mass differences, , are known to be on the order of eV = ( eV) Oscillation distances, , in modern experiments are on the order of kilometers Neutrino energies, , in modern experiments are typically on order of MeV or GeV. If there is no CP-violation ( is zero), then the second sum is zero. Otherwise, the CP asymmetry can be given as In terms of Jarlskog invariant the CP asymmetry is expressed as Two-neutrino case The above formula is correct for any number of neutrino generations. Writing it explicitly in terms of mixing angles is extremely cumbersome if there are more than two neutrinos that participate in mixing. Fortunately, there are several meaningful cases in which only two neutrinos participate significantly. In this case, it is sufficient to consider the mixing matrix Then the probability of a neutrino changing its flavor is Or, using SI units and the convention introduced above This formula is often appropriate for discussing the transition in atmospheric mixing, since the electron neutrino plays almost no role in this case. It is also appropriate for the solar case of where is a mix (superposition) of and These approximations are possible because the mixing angle is very small and because two of the mass states are very close in mass compared to the third. Classical analogue of neutrino oscillation The basic physics behind neutrino oscillation can be found in any system of coupled harmonic oscillators. A simple example is a system of two pendulums connected by a weak spring (a spring with a small spring constant). The first pendulum is set in motion by the experimenter while the second begins at rest. Over time, the second pendulum begins to swing under the influence of the spring, while the first pendulum's amplitude decreases as it loses energy to the second. Eventually all of the system's energy is transferred to the second pendulum and the first is at rest. The