We discuss the three neutrino flavor evolution problem with general,
flavor-diagonal, matter potentials and a fully parameterized mixing matrix that
includes CP violation, and derive expressions for the eigenvalues, mixing
angles and phases. We demonstrate that, in the limit that the mu and tau
potentials are equal, the eigenvalues and matter mixing angles theta_12 and
theta_13 are independent of the CP phase, although theta_23 does have CP
dependence. Since we are interested in developing a framework that can be used
for S matrix calculations of neutrino flavor transformation, it is useful to
work in a basis that contains only off-diagonal entries in the Hamiltonian. We
derive the "non-adiabaticity" parameters that appear in the Hamiltonian in this
basis. We then introduce the neutrino S matrix, derive its evolution equation
and the integral solution. We find that this new Hamiltonian, and therefore the
S matrix, in the limit that the mu and tau neutrino potentials are the same, is
independent of both theta_23 and the CP violating phase. In this limit, any CP
violation in the flavor basis can only be introduced via the rotation matrices,
and so effects which derive from the CP phase are then straightforward to
determine. We show explicitly that the electron neutrino and electron
antineutrino survival probability is independent of the CP phase in this limit.
Conversely, if the CP phase is nonzero and mu and tau matter potentials are not
equal, then the electron neutrino survival probability cannot be independent of
the CP phase