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American Journal of Physics

A demonstration of decoherence for beginners

L. Lerner

Published Oct 17, 2017• 4 citations
Publisher

Abstract

We present a simplified analysis suitable for a beginners' course in quantum mechanics of a recently presented model of positional decoherence in a gas of scatterers. As such, no reference is made to the density matrix formalism, many body theory, or even operator algebra. We only make use of the properties of quantum states and the position and momentum wavefunctions, which students typically encounter in a first quantum mechanics course.

DOI
10.1119/1.5005526

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We present a simplified analysis suitable for a beginners' course in quantum mechanics of a recently presented model of positional decoherence in a gas of scatterers. As such, no reference is made to the density matrix formalism, many body theory, or even operator algebra. We only make use of the properties of quantum states and the position and momentum wavefunctions, which students typically encounter in a first quantum mechanics course.
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Abstract Learning quantum mechanics (QM) is widely recognized as a challenging task, as it involves highly abstract concepts and requires a significant shift from classical physics reasoning. Developing expertise in QM requires students to represent physical concepts using multiple formalisms, such as Dirac notation and algebraic representations, and to move flexibly between them. This study investigates two main categories of student difficulties related to Dirac notation. The first concerns difficulties in expressing a generic state vector in the position and momentum representations. The second relates to challenges in writing the eigenvectors of the position and momentum operators in Dirac notation. To explore these issues, we administered questionnaires to third-year undergraduate physics students enrolled in a QM course at the Lyon 1 University. We present a detailed analysis of student responses, identify the principal difficulties encountered, and compare our findings with results reported in prior American studies. Our results show that many students struggle to establish a clear connection between Dirac notation and its functional algebraic representation. In particular, students find it easier to recognize state vectors and eigenvectors than to construct them explicitly. Additionally, common difficulties include confusion between bras (e.g. x | and p |) and the corresponding operators, as well as confusion between the Dirac delta distribution and the Kronecker delta. Finally, we propose some interpretations of our results in light of those reported in previous studies.
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