Students' Difficulties with the Dirac Delta Function in Quantum Mechanics

Autor/inn/en	Tu, Tao; Li, Chuan-Feng; Xu, Jin-Shi; Guo, Guang-Can
Titel	Students' Difficulties with the Dirac Delta Function in Quantum Mechanics
Quelle	In: Physical Review Physics Education Research, 19 (2023) 1, Artikel 010104 (24 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Tu, Tao)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
Schlagwörter	Quantum Mechanics; Science Instruction; Problem Solving; Scientific Concepts; Barriers; Mechanics (Physics); Equations (Mathematics); Computation; College Students; Foreign Countries; College Science; China + Suchen Sie Ihr Suchwort? Quantenmechanik; Teaching of science; Science education; Natural sciences Lessons; Naturwissenschaftlicher Unterricht; Problemlösen; Mechanik; Equations; Mathematics; Gleichungslehre; Collegestudent; Ausland
Abstract	In the context of quantum mechanics, students are often asked to use delta functions to solve problems. Here, we investigate three typical problem-solving processes using delta functions: a delta function potential well problem, a position space delta function problem, and a momentum space delta function problem. We studied students'solutions in written exams and conducted think-aloud interviews. We use the activation, construction, execution, and reflection framework for our analysis. We find that students encountered various difficulties in solving quantum mechanics problems using delta functions. Common challenges included difficulty with establishing expressions of delta functions for position eigenstates, difficulty with expressing the orthonormality of eigenfunctions with continuous spectra using delta functions, difficulty with boundary conditions for delta function potentials, and difficulty with calculating integrals involved delta functions. In particular, students rarely used effective reflective methods to gain confidence in their solutions. We commonly observed this challenge for students in all questions we investigated. In addition, we compare the similarities and differences in the use of delta functions in electrostatics and in quantum mechanics, and discuss possible explanations for the reasoning mechanisms that cause these difficulties. Finally, we discuss the potential pedagogical implications of our findings. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01