Characterizing quantum physics students' conceptual and procedural knowledge of the characteristic equation

Research on student understanding of eigentheory in linear algebra has expanded recently, yet few studies address student understanding of the Characteristic Equation. In this study, we explore quantum physics students' conceptual and procedural knowledge of deriving and using the Characteristic Equation. We developed the Conceptual and Procedural Knowledge framework for classifying the quality of students' conceptual and procedural knowledge of both deriving and using the Characteristic Equation along a continuum. Most students exhibited deeper conceptual and procedural knowledge of using the Characteristic Equation than of deriving the Characteristic Equation. Furthermore, most students demonstrated deeper procedural knowledge than conceptual knowledge of deriving the Characteristic Equation. Most students demonstrated conceptual knowledge that was as deep or deeper than their procedural knowledge of using the Characteristic Equation. Examples of student work are provided, including descriptions of student work exhibiting rich knowledge of the characteristic equation. Implications for instruction and future research are discussed.