*54%*:**Student difficulties with quantum states while translating state vectors in Dirac notation to wave functions in position and momentum representations***49%*:**Student understanding of the measurable effects of relative phases in superposition states***44%*:**Algebra-Based Students & Vectors: Assessing Physical Understanding in Arrow vs ijk***44%*:**Studentsâ€™ use of conceptual resources for understanding superposition***41%*:**Improving student understanding of Dirac notation by using analogical reasoning in the context of a three-dimensional vector space***41%*:**Investigating Student Understanding of Perturbation Theory and the Inner Products of Functions***41%*:**Student understanding of potential, wavefunctions and the Jacobian in hydrogen in graduate-level quantum mechanics***40%*:**Testing Studentsâ€™ Understanding of Vector Concepts***40%*:**Student use of a material anchor for quantum wave functions***38%*:**Investigating the Influence of Visualization on Student Understanding of Quantum Superposition***38%*:**Investigation of Student Understanding of the Wave-Like Properties of Light and Matter***37%*:**Students' difficulties with unit vectors and scalar multiplication of a vector***37%*:**Improving studentsâ€™ understanding of quantum measurement. I. Investigation of difficulties***36%*:**A research-based approach to improving student understanding of the vector nature of kinematical concepts***36%*:**Student understanding of the wave nature of matter: Diffraction and interference of particles***36%*:**Examining consistency of student errors in vector operations using module analysis***35%*:**Test of understanding of vectors: A reliable multiple-choice vector concept test***35%*:**Enhancing student visual understanding of the time evolution of quantum systems***34%*:**Student Objections to and Understanding of Non-Cartesian Unit Vector Notation in Upper-Level E&M**