Now let's turn to neutrino oscillations. Suppose that the weak eigenstate neutrinos, i.e., the ones that are produced along with a definite lepton in weak transitions, are mixtures of the neutrinos of definite mass,
where 
, 
, or a sterile neutrino
. 
and 
are mass eigenstates and
and 
are weak eigenstates. In a weak decay one produces a
definite weak eigenstate, e.g.,
There will then be quantum mechanical oscillations, just as for any two state system. At a later time there will be a probability that the final state
is different from the initial one. In particular, there is a survival probability
of measuring a 
( i.e., a probability 1 - P of 
disappearance), and a probability
of the appearance of the other neutrino flavor. Here 
is the difference between squared masses, and 
has
been assumed. The last argument can be written as 
,
where 
is in 
, L is in m, and E is in MeV.
