We seek a quantum-theoretic expression for the probability that a "fermionic" particle which is initially in a well-defined flavor, linear combination of mass-eigenstates, will be found, at later times, in another flavor state. We approach this problem by using the Dirac equation as evolution equation for the mass-eigenstates. The Dirac formalism is useful and essential in keeping clear many of the conceptual aspects of quantum oscillation phenomena that naturally arise in a relativistic spin one-half particle theory. Our study leads to the conclusion that the fermionic nature of the particles and the interference between positive and negative frequency components of mass-eigenstate wave packets modify the standard oscillation probability, obtained by implicitly assuming a "scalar" nature of the mass-eigenstates. Nevertheless, under particular assumptions, i.e. ultra relativistic particles, strictly peaked momentum distributions and minimal slippage, these modifications introduce correction factors proportional to m(1)(2),(2) /p(0)(2) practically un-detectable by any experimental analysis.209681689