The students´ interpretation of quantum mechanics concepts from the Feynman´s Sum of All Paths applied to light

FANARO, MARIA DE LOS ANGELES; ELGUE, MARIANA; MARÍA RITA OTERO; ARLEGO, MARCELO

san pablo

Congreso; 2nd World Conference on Physics Education; 2016

GIREP-MPTL

In this work we analyze part of the implementation of a didactic sequence [1;2;3] to teach different aspects of light in a unified non traditional framework. The goal was to propose the quantum theory of light as a universal framework to describe different phenomena observed. The sequence was carried out in four courses of two secondary schools, with N=83 students aged 15-16, during 23 school hours approximately. The syllabus corresponding to this age group (second to last) in high school advocates the teaching of light phenomena. The Feynman approach was used in undergraduate courses for non-specialists (Taylor et al., 1998; Styer, 2000), in teacher training (Cuppari et al., 1997). Furthermore, in the Advancing Physics AS (2000) project of an A-level physics course for the British high school system the quantum physics chapter is treated using the sum over paths approach. However, there are still no results about the viability of introducing this alternative way of quantum mechanics teaching in high school.The data analysis, using a qualitative methology, was based on all the students? productions. An answer categorization was formulated, considering among other aspects the one of the quantum reformulation of experiences shown herein. This analysis seeks to understand the student´s conceptualization process [4] about quantum interpretation. In this way it is possible to know how viable the sequence would be and which changes could be necessary for future implementations. The didactic sequence started from the students´ prediction of the results of the experiences of reflection, refraction and the double slit experiment (DSE). Then these experiences were carried out in the classroom, using a laser light source. Later the results of the DSE showing individual detections were presented through a sequence of real images of the DSE with very low intensity light. This enabled to show the individual detection events on the screen, which evolved into a definite pattern of alternated fringes on the screen.The laws of quantum mechanics for light using the Feynman´s ?Sum of all Paths? approach (SAP), adapted to the mathematical level of the students was proposed as a model to explain the experiences. Graphic representations and basic operations with vectors capturing the essential aspects of the theory, were used. Simulations made with the software GeoGebra(R) were created to help students visualize the SAP technique results to the simple case of light emission and detection, and light reflection and refraction. Then the SPA was applied to the DSE to describe those results obtained in the situation relative to the localized detection and the alternated fringes pattern.Here we present the results regarding the way that the students applied the SAP technique and interpreted the previous experiences using the quantum framework. Regarding the reformulation of refraction and reflection laws in quantum terms, more than half of the students (n=67) could interpret the experiences using the concepts of SAP technique (e.g. light minimum time trip). However only n=16 students remained in a classical context, or they used the SPA technique inappropriately; they confused the vector angle with the light path angle shown in the Geogebra(R) simulation. Considering the DSE, n=38 students interpreted the results of the DSE as individual detection events in terms of probability, then they could also interpret the graph of P(x) and finally they linked the graph with the results obtained in the DSE realized in the classroom. Additionally, they recognized the discrete aspect of light. Besides a good number of students (n=36) conceptualized adequately the quantum concepts presented, they could explain the fringes of light and darkness regarding the graph of the function P(x) previously obtained in the classroom. The graphic representations created by these students during their explanations were notable. Only n=9 students had difficulties interpreting the DSE from SAP technique, making poor resolutions of the situations. We conclude that is possible to teach basic quantum concepts from Feynman?s approach to the secondary school students. However, minor changes in the sequence would be necessary to prevent some obstacles identified in the conceptualization process. These changes mainly aim at reformulating the situations to attain a better qualitative understanding and improve the students´ visualizations of the model.References[1] ARLEGO, M, FANARO, M y OTERO M. R.(2012) Teaching different aspects of light in the unified framework of quantum mechanics. In Proceedings of The World Conference on Physics Education 2012 pp.795-799 [2]FANARO, M y OTERO M.R and ELGUE M. (2014) Implementation of a proposal to teach quantum mechanics concepts from the Multiple Paths of Feynman applied to the light, Proceedings of GIREP-MPTL International Conference on Teaching/Learning Physics: Integrating Research into Practice. Pp.225-232[3]FANARO, M ; ARLEGO, M, y OTERO M.R.(2014) The double slit experience with light from Feynman´s Sum of Multiple Paths viewpoint REVISTA BRASILEIRA DE ENSINO DE FÍSICA Sociedade Brasileira de Física. v. 36, n. 2 pp. 2308-1 a 2308-7 [4]OTERO, M.R; FANARO, M; SUREDA, P; LLANOS, V C; ARLEGO, M. (2014) La Teoría de los Campos Conceptuales y la conceptualización en el aula de Matemática y Física ISBN 978-987-02-7406-3. Editorial Dunken, Abril 2014, 124p.