Improving student understanding of dirac notation by using analogical reasoning in the context of a three-dimensional vector space

Abstract

. Dirac notation is a compact and elegant notation taught to students in advanced quantum mechanics courses. However, students struggle to master Dirac notation and have difficulty translating between the Dirac notation and representations of the same quantum mechanical entity in different situations. We discuss an investigation of student difficulties with Dirac notation in the context of a three-dimensional vector space and the development, validation and evaluation of a Quantum Interactive Learning Tutorial (QuILT) that uses analogical reasoning to improve student understanding of this notation. The QuILT uses analogical reasoning and builds on students’ prior knowledge of three-dimensional vectors in the familiar context of introductory mechanics to help students build a coherent understanding of Dirac notation before transitioning to the quantum mechanical context. We summarize the development and validation of the QuILT and findings from the in-class evaluation.