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  Session: PER: Student Content Understanding, Problem-Solving and Reasoning
  Paper Type: Contributed
  Title: How Students' Understanding of Normalization Changes After Taking Quantum Mechanics
  Meeting: 2018 Summer Meeting: Washington, DC
  Location: N/A
  Date:
  Time: 2:40PM
  Author: Kevin L. Watson,, Virginia Tech,
8013720105, wk223@vt.edu
  Co-Author(s): None
  Abstract: Normalization is a particularly important concept within quantum mechanics due to the probabilistic nature of quantum systems. However, students' understanding of normalization has not been well studied in the past. In this contributed talk, I will share insights from analyzing physics students' understanding of normalization through the use of a framework for students' understanding of mathematical norms and normalization of vectors. More specifically, I will compare and contrast students' understandings of normalization before and after taking an introductory quantum mechanics course. Through the results, I will demonstrate that a majority of physics students enter quantum mechanics with a narrow or incomplete understanding of normalization, but through learning quantum mechanics content and introduction of new notational systems (i.e., Dirac notation), these students can leave quantum mechanics with a more complete understanding of normalization and its importance to physics.
  Footnotes: None
  Presentation: HowStudentsUnderstandNormalization.pdf

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