Recently, there have been many efforts to use the research techniques developed in the field of physics education research to improve the teaching and learning of quantum mechanics. In particular, part of this research is focusing on misconceptions held by students. For instance, a set of misconceptions is associated with the concept of stationary states. In this paper, we argue that a possible way to remove these is to solve the Schrodinger equation using the evolution operator method (EOM), and stress the fact that to find stationary states is only the first step in solving that equation. The EOM consists in solving the Schrodinger equation by direct integration, i.e. [psi](x, t) = U(t)[psi](x, 0), where U(t) = e[superscript -itH/h] is the time evolution operator, and [psi](x, 0) is the initial state. We apply the evolution operator method in the case of the harmonic oscillator. (Contains 5 figures.)