The purpose of this study is to identify students' conceptual and mathematical difficulties in learning the core concepts of introductory quantum mechanics, with the eventual goal of developing instructional material to help students with these difficulties. We have investigated student understanding of several core topics in the introductory courses, including quantum measurement, probability, Uncertainty Principle, wave functions, energy eigenstates, recognizing symmetry in physical systems, and mathematical formalism.

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.

Materials developed by the Visual Quantum Mechanics project teach some basic ideas of quantum mechanics to high school and introductory college students by integrating hands-on activities and computer visualization. During field tests of the materials we obtained data concerning student understanding of some quantum concepts including potential energy diagrams, energy levels and spectra in atoms, energy bands in solids, wave functions and probability, and quantum tunneling. Data were collected from written responses of students structured interviews and a concept map.

Research studies on students' conceptions in the area of quantum physics are, in contrast to other areas of physics, rather rare. The present study gives results from quantitative and qualitative data with grade 13 students (age 19) in German high schools, taken before and after instruction as well as from transcripts during instruction. Only students from classes, which used a Schroedinger approach to understand atoms and electron orbitals, were taken. As a first result, we describe students' beliefs about models.

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.

Research in the teaching and learning of undergraduate quantum mechanics is being conducted at the University of Washington [1] and Grand Valley State University [2]. Because of its central role in quantum mechanics, we are investigating how students come to learn about probability. Our research has included the analysis of individual demonstration interviews, ungraded quizzes, and course examinations. We will show evidence that many students inappropriately use their intuition about classical mechanics in order to predict or account for quantum mechanical phenomena.