Passive, lecture-based forms of instruction are often ineffective in helping students develop deep conceptual understanding of scientific concepts. Student-centered forms of instruction based in a constructivist framework, where students are guided toward actively constructing their understanding, have been met with greater success. However,…

The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing…

The impact of lecture instruction on student conceptual understanding in physics has been the subject of research for several decades. Most studies have reported disappointingly small improvements in student performance on conceptual questions despite direct instruction on the relevant topics. These results have spurred a number of attempts to…