The infinite square well potential and the evolution operator method for the purpose of overcoming misconceptions in quantum mechanics

Aguilar, L. M. Arévalo; Luna, Félix Denegri; Robledo-Sánchez, Carlos; Carrasco, M. L. Arroyo

doi:10.1088/0143-0807/35/2/025001

Cited by 15 publications

(14 citation statements)

References 18 publications

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“…In the physical sciences, students' struggles with the probabilistic nature of quantum physics (Bao & Redish, 2002) and nuclear decay (Santostasi et al, 2017) have been established by prior research, but the underlying reasons and mechanisms remain less researched than in evolution. Research into students' misconceptions has started to address this gap (Aguilar et al, 2014;Marshman & Singh, 2015;Stefani & Tsaparlis, 2009) and the findings mirror the position of Batanero et al (1994). Specifically, the concepts of probability are taught abstractly and in such a way that does not build upon the ideas that students already hold, the experiences that students have, and the language that students use.…”

Section: Uncertainty In Science Educationmentioning

confidence: 99%

Making Sense of Uncertainty in the Science Classroom: A Bayesian Approach

Rosenberg¹,

Kubsch²,

Wagenmakers³

2021

Preprint

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Uncertainty is ubiquitous in science, but scientific knowledge is often represented to the public and in educational contexts as certain and immutable. Adding to this issue is that when scientists try to communicate their uncertainty, research has demonstrated that many people--learners and experts alike--struggle to interpret the statistics that are often used to make inferences about evidence from scientific data. We conjecture that a Bayesian perspective can offer a coherent, holistic approach to teaching, learning, and sense-making about a persistent but sometimes unsettling tension for science, dealing with uncertainty. Central to this approach is viewing uncertainty probabilistically, as doing so provides a language for expressing the degree of uncertainty in knowledge across a range of scientific domains and socio-scientific issues. To frame the problem and opportunity at hand, we describe prior research on uncertainty and probability in science (and science education) and review how people learn about these ideas. Then, we provide an accessible primer on Bayes Theorem and discuss general principles relevant to science education that follow from Bayes Theorem. Finally, we provide examples of how a Bayesian perspective could inform efforts around both science literacy and science education with an emphasis upon building trust in science. We conclude with a call for future research to use a Bayesian perspective to bolster trust in science and to provide a coherent frame for considering variability and uncertainty in data and evidence both outside of and within pre-collegiate science classrooms.

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Section: Uncertainty In Science Educationmentioning

confidence: 99%

Making Sense of Uncertainty in the Science Classroom: A Bayesian Approach

Rosenberg¹,

Kubsch²,

Wagenmakers³

2021

Preprint

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“…Devido a sua simplicidade o potencial de um poço quadrado infinito tem sido usado para exemplificar a aplicação do método variacional [44,45], do método do operador evolução [46], entre outros [36,47].…”

Section: Conclusões E Considerações Finaisunclassified

Análise da repentina duplicação da largura de um poço quadrado infinito 1-dim: um resultado surpreendente à primeira vista

Suave

Ferreira

Nogueira

2020

Rev. Bras. Ensino Fís.

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Resumo Neste trabalho, chamamos a atenção de como um exercício comumente sugerido em livros-texto de Mecânica Quântica pode conduzir a um resultado surpreendente à primeira vista e como a elucidação deste resultado surpreendente pode ajudar na sedimentação dos conceitos de Mecânica Quântica envolvidos. O problema é o de uma partícula no interior de um poço quadrado infinito, o qual tem sua largura repentinamente dobrada. A surpresa está em que resultados diferentes podem ser obtidos quando o poço é tratado como não simétrico ou como simétrico, embora, como se sabe bem, ambos sejam fisicamente idênticos.

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“…However, in the scientific literature, we can find proposals that treat the external degrees of freedom (EDF) as a quantum variable giving a quantum description of the evolution of the EDF; see [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 13 ]. Nevertheless, in a recent paper, we gave a complete quantum treatment of the SGE [ 5 , 6 ], as it was originally thought of by Scully et al [ 9 ], by using the evolution operator method [ 21 , 22 , 23 , 24 , 25 ] and obtaining the solution to the Schrödinger equation; this allows us to see the quantum features of the EDF. It is worth mentioning that in Figure 1 of [ 5 ], we are replacing the usual continuous path by a dotted one to stress the absence of classical paths.…”

Section: The Sge In a Complete Quantum Treatmentmentioning

confidence: 99%

“…Recently, we argued that the SGE could easily be used to introduce the concept of entanglement between the external and internal degrees of freedom in the teaching of quantum mechanics [ 5 , 6 ], to exemplify the entanglement generation between discrete and continuous variables and between pure and mixed states, as well. To show these properties of the SGE, we have used the evolution operator method [ 21 , 22 , 23 , 24 , 25 ]; to see an independent test of this method, see [ 26 , 27 ].…”

Section: Introductionmentioning

confidence: 99%

Quantum Nonlocality and Quantum Correlations in the Stern–Gerlach Experiment

Martínez

Rodríguez

Fierro

et al. 2018

Entropy

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Abstract:The Stern-Gerlach experiment (SGE) is one of the foundational experiments in quantum physics. It has been used in both the teaching and the development of quantum mechanics. However, for various reasons, some of its quantum features and implications are not fully addressed or comprehended in the current literature. Hence, the main aim of this paper is to demonstrate that the SGE possesses a quantum nonlocal character that has not previously been visualized or presented before. Accordingly, to show the nonlocality into the SGE, we calculate the quantum correlations C(z, θ) by redefining the Banaszek-Wódkiewicz correlation in terms of the Wigner operator, that is C(z, θ) = Ψ|Ŵ(z, p z )σ(θ)|Ψ , whereŴ(z, p z ) is the Wigner operator,σ(θ) is the Pauli spin operator in an arbitrary direction θ and |Ψ is the quantum state given by an entangled state of the external degree of freedom and the eigenstates of the spin. We show that this correlation function for the SGE violates the Clauser-Horne-Shimony-Holt Bell inequality. Thus, this feature of the SGE might be interesting for both the teaching of quantum mechanics and to investigate the phenomenon of quantum nonlocality.

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The infinite square well potential and the evolution operator method for the purpose of overcoming misconceptions in quantum mechanics

Cited by 15 publications

References 18 publications

Making Sense of Uncertainty in the Science Classroom: A Bayesian Approach

Making Sense of Uncertainty in the Science Classroom: A Bayesian Approach

Análise da repentina duplicação da largura de um poço quadrado infinito 1-dim: um resultado surpreendente à primeira vista

Quantum Nonlocality and Quantum Correlations in the Stern–Gerlach Experiment

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