  We consider neutrino oscillations in non-uniform matter in a quantum field
theoretic (QFT) approach, in which neutrino production, propagation and
detection are considered as a single process. We find the conditions under
which the oscillation probability can be sensibly defined and demonstrate how
the properly normalized oscillation probability can be obtained in the QFT
framework. We derive the evolution equation for the oscillation amplitude and
discuss the conditions under which it reduces to the standard
Schr\"odinger-like evolution equation. It is shown that, contrary to the common
usage, the Schr\"odinger-like evolution equation is not applicable in certain
cases, such as oscillations of neutrinos produced in decays of free pions
provided that sterile neutrinos with $\Delta m^2\gtrsim 1$ eV$^2$ exist.
