Describing analytically the matter-enhanced two-neutrino transitions in a medium

A general exact analytic expression for the probability of matter-enhanced two-neutrino transitions in a medium (MSW, RSFP, generated by neutrino FCNC interactions, etc.) is derived. The probability is expressed in terms of three real functions of the parameters of the transitions: the “jump” probability and two phases (angles). The results obtained can be utilized, in particular, in the studies of the matter-enhanced transitions/conversions of solar and supernova neutrinos. An interesting similarity between the Schroedinger equation for the radial part of the non-relativistic wave function of the hydrogen atom and the equation governing the MSW transitions of solar neutrinos in the exponentially varying matter density in the Sun is also briefly discussed.