We report on a multi-year, multi-institution study to investigate students' reasoning about energy in the context of quantum tunnelling. We use ungraded surveys, graded examination questions, individual clinical interviews and multiple-choice exams to build a picture of the types of responses that students typically give. We find that two descriptions of tunnelling through a square barrier are particularly common. Students often state that tunnelling particles lose energy while tunnelling.

We have investigated student difficulties in understanding and interpreting probability and its relevant technical terms as it relates to quantum measurement. These terms include expectation value, probability density, and uncertainty. From this research, it is evident that tstudents have difficulties in understanding these terms and often fail to differentiate among similar but different concepts. In addition, students' difficutlies with the concepts of probability often interfere with their understanding and applications of the Uncertainty Principle.

The Physics Education Research Group at University of Maryland has been studying student learning of quantum mechanics. Our previously reported research shows that student difficulties exist with classical concepts that are prerequisite for learning quantum mechanics. In this talk, we report detailed studies of student difficulties in quantum mechanics arising from confusions with the classical concept of energy.

We investigated student difficulties in learning quantum mechanics in an upper division quantum course at the University of Maryland. A set of exam questions and interviews has been developed to probe student understandings of the quantum wavefunction. We find that many students are confused about the relation between the wavefunction and the kinetic energy and often appear to interpret the wave function as an energy. They often display a strong "friction-like" model in which the wave function "loses energy" in tunneling through a barrier.

Probability plays a critical role in making sense of quantum physics, but most science and engineering undergraduates have very little experience with the topic. A probabilistic interpretation of a physical system, even at a classical level, is often completely new to them, and the relevant fundamental concepts such as the probability distribution and probability density are rarely understood.

A good understanding of how students understand physics is of great importance for developing and delivering effective instructions. This research is an attempt to develop a coherent theoretical and mathematical framework to model the student learning of physics. The theoretical foundation is based on useful ideas from theories in cognitive science, education, and physics education.