  The exact formula for the neutrino oscillation probability in matter with
constant density, which was discovered by Kimura, Takamura and Yokomakura, has
been applied mostly to the standard case with three flavor neutrino so far. In
this paper applications of their formula to more general cases are discussed.
It is shown that this formalism can be generalized to various cases where the
matter potential have off-diagonal components, and the two non-trivial examples
are given: the case with magnetic moments and a magnetic field and the case
with non-standard interactions. It is pointed out that their formalism can be
applied also to the case in the long baseline limit with matter whose density
varies adiabatically as in the case of solar neutrino.
