Structural Features of Algebraic Quantum Notations

Autor/inn/en	Gire, Elizabeth; Price, Edward
Titel	Structural Features of Algebraic Quantum Notations
Quelle	In: Physical Review Special Topics - Physics Education Research, 11 (2015) 2, S.020109-1 (11 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1554-9178
DOI	10.1103/PhysRevSTPER.11.020109
Schlagwörter	Quantum Mechanics; Algebra; Undergraduate Students; Science Instruction; Interviews; Physics; Majors (Students); Scientific Concepts; Logical Thinking; Energy; Video Technology; Prompting; Equations (Mathematics); Matrices; Coding; Oregon + Suchen Sie Ihr Suchwort? Quantenmechanik; Teaching of science; Science education; Natural sciences Lessons; Naturwissenschaftlicher Unterricht; Interviewing; Interviewtechnik; Physik; Energie; Benutzerführung; Equations; Mathematics; Gleichungslehre; Matrizenrechnung; Codierung; Programmierung
Abstract	The formalism of quantum mechanics includes a rich collection of representations for describing quantum systems, including functions, graphs, matrices, histograms of probabilities, and Dirac notation. The varied features of these representations affect how computations are performed. For example, identifying probabilities of measurement outcomes for a state described in Dirac notation may involve identifying expansion coefficients by inspection, but if the state is described as a function, identifying those expansion coefficients often involves performing integrals. In this study, we focus on three notational systems: Dirac notation, algebraic wave-function notation, and matrix notation. These quantum notations must include information about basis states and their associated complex probability amplitudes. In this theory paper, we identify four structural features of quantum notations, which we term individuation, degree of externalization, compactness, and symbolic support for computational rules. We illustrate how student reasoning interacts with these structural features with episodes from interviews with advanced undergraduate physics majors reasoning about a superposition state of an infinite square well system. We find evidence of the students coordinating different notations through the use of Dirac notation, using an expression in Dirac notation to guide their work in another notation. These uses are supported by the high degree of individuation, compactness, and symbolic support for computation and the moderate degree of externalization provided by Dirac notation. [This paper is part of the Focused Collection on Upper Division Physics Courses.] (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01