We show in detail the general relationship between the Schrödinger equation approach to calculating the MSW effect and the quantum field theoretical S-matrix approach. We show the precise form a generic neutrino propagator must have to allow a physically meaningful "oscillation probability" to be decoupled from neutrino production fluxes and detection cross-sections, and explicitly list the conditions-not realized in cases of current experimental interest-in which the field theory approach would be useful.14.60. Pq, 26.65.+t, 97.60.Bw, 13.15.+g