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.