*39%*:**Investigating Student Difficulties with Dirac Notation***34%*:**Student difficulties with representations of quantum operators corresponding to observables***31%*:**Student use of a material anchor for quantum wave functions***31%*:**Students' dynamic geometric reasoning about quantum spin-1/2 states***29%*:**Student Understanding of Superposition: Vectors and Wave Functions***27%*:**Student Difficulties with the Dirac Delta Function***26%*:**University students' reasoning on physical information encoded in quantum state at a point in time***24%*:**Student difficulties with determining expectation values in quantum mechanics***24%*:**Student difficulties in translating between mathematical and graphical representations in introductory physics***23%*:**Improving studentsâ€™ understanding of quantum measurement. I. Investigation of difficulties***23%*:**Algebra-Based Students and Vector Representations: Arrow vs. ijk***22%*:**Investigating Student Understanding of Perturbation Theory and the Inner Products of Functions***22%*:**Student understanding of the measurable effects of relative phases in superposition states***21%*:**Students' difficulties with unit vectors and scalar multiplication of a vector***21%*:**Investigating Student Difficulties with Time dependence of Expectation Values in Quantum Mechanics***21%*:**Comparing Student Use of Mathematical and Physical Vector Representations***20%*:**Student understanding of potential, wavefunctions and the Jacobian in hydrogen in graduate-level quantum mechanics***20%*:**Investigating the Influence of Visualization on Student Understanding of Quantum Superposition***20%*:**Student Objections to and Understanding of Non-Cartesian Unit Vector Notation in Upper-Level E&M**