Pub Date : 2023-09-27DOI: 10.1088/1361-6404/acfdda
Alain Kirèche
Abstract After detailing the characteristics of space-proper time diagrams for Galilean relativity and special relativity, we show how they can be used to better visualize the progression of ideas about the absolute or relative nature of space and time, from Galilean relativity to special relativity. We conclude that space-proper time diagrams could be an interesting new tool for introducing special relativity.
{"title":"From Galilean relativity to Special relativity: The pedagogical contribution of the space-proper time diagrams","authors":"Alain Kirèche","doi":"10.1088/1361-6404/acfdda","DOIUrl":"https://doi.org/10.1088/1361-6404/acfdda","url":null,"abstract":"Abstract After detailing the characteristics of space-proper time diagrams for Galilean relativity and special relativity, we show how they can be used to better visualize the progression of ideas about the absolute or relative nature of space and time, from Galilean relativity to special relativity. We conclude that space-proper time diagrams could be an interesting new tool for introducing special relativity.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135534475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-25DOI: 10.1088/1361-6404/acf907
Joydip Mitra, Satadal Bhattacharyya
Abstract We clarify two comments made by Francisco M Fernández on our paper Bhattacharyya and Mitra (2022 Eur. J. Phys. 44 015101). The first one is regarding the calculation of the approximate partition function for a particle in a box that was derived earlier by others, and the second one is about the omission of the contribution to the continuous energy spectrum in the partition function calculation for a particle in a finite well.
我们澄清弗朗西斯科M Fernández对我们的论文Bhattacharyya and Mitra (2022 Eur。物理学报，44 (1);第一个问题是关于盒子中粒子的近似配分函数的计算，这是别人之前推导出来的，第二个问题是关于在有限井中粒子的配分函数计算中忽略了对连续能谱的贡献。
{"title":"Reply to the Comment on ‘Thermodynamics of a particle in square well potential’","authors":"Joydip Mitra, Satadal Bhattacharyya","doi":"10.1088/1361-6404/acf907","DOIUrl":"https://doi.org/10.1088/1361-6404/acf907","url":null,"abstract":"Abstract We clarify two comments made by Francisco M Fernández on our paper Bhattacharyya and Mitra (2022 Eur. J. Phys. 44 015101). The first one is regarding the calculation of the approximate partition function for a particle in a box that was derived earlier by others, and the second one is about the omission of the contribution to the continuous energy spectrum in the partition function calculation for a particle in a finite well.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"2013 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135769461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-25DOI: 10.1088/1361-6404/acf81c
P Martín-Luna, B Gimeno, D Esperante
Abstract In a recent paper (Bochko and Silagadze 2020 Eur. J. Phys. 41 045201), the authors carried out an analytical effort to arrive at an expression for the electrostatic potential and electric field of a uniformly charged disk everywhere in space. They obtained that the radial electric field has a term proportional to the Dirac delta function. In this comment, it is demonstrated that this term is not correct.
{"title":"Comment on ‘On the electrostatic potential and electric field of a uniformly charged disk’","authors":"P Martín-Luna, B Gimeno, D Esperante","doi":"10.1088/1361-6404/acf81c","DOIUrl":"https://doi.org/10.1088/1361-6404/acf81c","url":null,"abstract":"Abstract In a recent paper (Bochko and Silagadze 2020 Eur. J. Phys. 41 045201), the authors carried out an analytical effort to arrive at an expression for the electrostatic potential and electric field of a uniformly charged disk everywhere in space. They obtained that the radial electric field has a term proportional to the Dirac delta function. In this comment, it is demonstrated that this term is not correct.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135864380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-22DOI: 10.1088/1361-6404/acf905
Francisco Marcelo Fernandez
Abstract We argue that the approximate analytical expression for the canonical partition function for a particle in a box proposed recently was derived earlier by other authors in a more straightforward and efficient way. We also show that the canonical partition function for the particle in a finite box derived by the same authors is incorrect because they overlooked the contribution of the continuum spectrum.
{"title":"Comment on \"Thermodynamics of a particle in square well potential\"","authors":"Francisco Marcelo Fernandez","doi":"10.1088/1361-6404/acf905","DOIUrl":"https://doi.org/10.1088/1361-6404/acf905","url":null,"abstract":"Abstract We argue that the approximate analytical expression for the canonical partition function for a particle in a box proposed recently was derived earlier by other authors in a more straightforward and efficient way. We also show that the canonical partition function for the particle in a finite box derived by the same authors is incorrect because they overlooked the contribution of the continuum spectrum.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136010401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-21DOI: 10.1088/1361-6404/ad1420
Giulia Polverini, B. Gregorcic
The paper aims to fulfil three main functions: (1) to serve as an introduction for the physics education community to the functioning of Large Language Models (LLMs), (2) to present a series of illustrative examples demonstrating how prompt-engineering techniques can impact LLMs performance on conceptual physics tasks and (3) to discuss potential implications of the understanding of LLMs and prompt engineering for physics teaching and learning. We first summarise existing research on the performance of a popular LLM-based chatbot (ChatGPT) on physics tasks. We then give a basic account of how LLMs work, illustrate essential features of their functioning, and discuss their strengths and limitations. Equipped with this knowledge, we discuss some challenges with generating useful output with ChatGPT-4 in the context of introductory physics, paying special attention to conceptual questions and problems. We then provide a condensed overview of relevant literature on prompt engineering and demonstrate through illustrative examples how selected prompt-engineering techniques can be employed to improve ChatGPT-4’s output on conceptual introductory physics problems. Qualitatively studying these examples provides additional insights into ChatGPT’s functioning and its utility in physics problem solving. Finally, we consider how insights from the paper can inform the use of LMMs in the teaching and learning of physics.
{"title":"How understanding large language models can inform the use of ChatGPT in physics education","authors":"Giulia Polverini, B. Gregorcic","doi":"10.1088/1361-6404/ad1420","DOIUrl":"https://doi.org/10.1088/1361-6404/ad1420","url":null,"abstract":"The paper aims to fulfil three main functions: (1) to serve as an introduction for the physics education community to the functioning of Large Language Models (LLMs), (2) to present a series of illustrative examples demonstrating how prompt-engineering techniques can impact LLMs performance on conceptual physics tasks and (3) to discuss potential implications of the understanding of LLMs and prompt engineering for physics teaching and learning. We first summarise existing research on the performance of a popular LLM-based chatbot (ChatGPT) on physics tasks. We then give a basic account of how LLMs work, illustrate essential features of their functioning, and discuss their strengths and limitations. Equipped with this knowledge, we discuss some challenges with generating useful output with ChatGPT-4 in the context of introductory physics, paying special attention to conceptual questions and problems. We then provide a condensed overview of relevant literature on prompt engineering and demonstrate through illustrative examples how selected prompt-engineering techniques can be employed to improve ChatGPT-4’s output on conceptual introductory physics problems. Qualitatively studying these examples provides additional insights into ChatGPT’s functioning and its utility in physics problem solving. Finally, we consider how insights from the paper can inform the use of LMMs in the teaching and learning of physics.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"38 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139337911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-08DOI: 10.1088/1361-6404/acf81d
Theodosios G Douvropoulos
Abstract. In this paper, we calculate the swing period of the classical pendulum via semiclassical path integration. We point out the significance of the classical periodic orbits and the equivalence of the pendulum’s classical isochronism to the equidistance of the quantum energy levels. We derive the swing period in terms of the semiclassical tunneling time and the fractional revival period. A possible definition of a critical value for the quantum “bounce time” is proposed. This paper intends for graduate students as an illustrating example of applying quantum mechanics to a classical system. It offers valuable insight into some characteristics that the classical and quantum pendulums possess in common. It also intends for a specialist in quantum chemistry where the quantum pendulum dynamics appears in what is known as hindered rotation about some chemical bonds.
{"title":"Semiclassical calculation of the Pendulum Period","authors":"Theodosios G Douvropoulos","doi":"10.1088/1361-6404/acf81d","DOIUrl":"https://doi.org/10.1088/1361-6404/acf81d","url":null,"abstract":"\u0000 Abstract. In this paper, we calculate the swing period of the classical pendulum via semiclassical path integration. We point out the significance of the classical periodic orbits and the equivalence of the pendulum’s classical isochronism to the equidistance of the quantum energy levels. We derive the swing period in terms of the semiclassical tunneling time and the fractional revival period. A possible definition of a critical value for the quantum “bounce time” is proposed. This paper intends for graduate students as an illustrating example of applying quantum mechanics to a classical system. It offers valuable insight into some characteristics that the classical and quantum pendulums possess in common. It also intends for a specialist in quantum chemistry where the quantum pendulum dynamics appears in what is known as hindered rotation about some chemical bonds.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44276803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-08DOI: 10.1088/1361-6404/acf81e
Michael V Berry
For a quantum spin driven cyclically by a slowly-rotated magnetic field, geometric phases are well understood. If the cycle takes a long time T, the leading-order (dynamical) phase is proportional to T and the geometric phase is the contribution independent of T. The dynamical and geometric phases are the first two terms of a series in slowness 1/T. Here it is shown with an exactly solvable example that the corrections are of two types: smooth, proportional to powers of slowness, and oscillatory: essential singularities in 1/T, in the form of trigonometric functions of T divided by powers of T. The calculations are elementary and therefore suitable for presentation in graduate quantum theory courses.
{"title":"Smooth and oscillatory geometric phase corrections for driven spins","authors":"Michael V Berry","doi":"10.1088/1361-6404/acf81e","DOIUrl":"https://doi.org/10.1088/1361-6404/acf81e","url":null,"abstract":"For a quantum spin driven cyclically by a slowly-rotated magnetic field, geometric phases are well understood. If the cycle takes a long time T, the leading-order (dynamical) phase is proportional to T and the geometric phase is the contribution independent of T. The dynamical and geometric phases are the first two terms of a series in slowness 1/T. Here it is shown with an exactly solvable example that the corrections are of two types: smooth, proportional to powers of slowness, and oscillatory: essential singularities in 1/T, in the form of trigonometric functions of T divided by powers of T. The calculations are elementary and therefore suitable for presentation in graduate quantum theory courses.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46691276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-06DOI: 10.1088/1361-6404/acf746
Jongheon Baek
Mass–energy equivalence (MEE) has become a basis of modern physics. In spite of the current educational trends highlighting modern physics education, it has been pointed out that interpretations of MEE are still not in general agreement. In addition, the derivations of MEE found in textbooks gloss over some logical oversights. MEE is often introduced with only a declarative knowledge that mc 2 represents the rest energy of a particle, making the learning process difficult for students. To resolve the instructional challenges, distinguished papers on MEE are analyzed. By specifying common features of derivations in each paper, it is found that there are at least three types of MEE. By identifying the entire hierarchical structure of each one, a type of MEE is suggested that can potentially be useful in the establishment of the connection between the particle and field.
{"title":"Exploring mass–energy equivalence with consideration of quantum nature","authors":"Jongheon Baek","doi":"10.1088/1361-6404/acf746","DOIUrl":"https://doi.org/10.1088/1361-6404/acf746","url":null,"abstract":"Mass–energy equivalence (MEE) has become a basis of modern physics. In spite of the current educational trends highlighting modern physics education, it has been pointed out that interpretations of MEE are still not in general agreement. In addition, the derivations of MEE found in textbooks gloss over some logical oversights. MEE is often introduced with only a declarative knowledge that mc 2 represents the rest energy of a particle, making the learning process difficult for students. To resolve the instructional challenges, distinguished papers on MEE are analyzed. By specifying common features of derivations in each paper, it is found that there are at least three types of MEE. By identifying the entire hierarchical structure of each one, a type of MEE is suggested that can potentially be useful in the establishment of the connection between the particle and field.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46085722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-05DOI: 10.1088/1361-6404/acf6b9
Andrea Sacchetti
The ‘ball on a string’ demonstration is a common tool used in physics education to illustrate the concept of conservation of angular momentum. However, various confounding factors can cause significant deviations from the idealized case, particularly under extreme conditions or when using low-stiffness pivots or high coefficients of friction. These factors include air resistance, contact friction at the pivot point, the mass of the ball and string, the angle of the string due to gravity, and the wobbling of the pivot point due to the centrifugal forces acting on it. In this work, we critically review by means of accurate simulations the adequateness of the ‘ball on a string’ demonstration in view of these confounding factors and provide recommendations for instructors on how to maximize the educational value of the demonstration while minimizing potential confusion for students. Our analysis suggests that a stiff pivot and avoiding extreme conditions are key to obtaining results that are in good agreement with the idealized case. We also caution instructors against using the demonstration without at least mentioning the confounding factors, as this may lead to a questionable understanding of the underlying physics principles.
{"title":"On the ball on a string demonstration of angular momentum conservation","authors":"Andrea Sacchetti","doi":"10.1088/1361-6404/acf6b9","DOIUrl":"https://doi.org/10.1088/1361-6404/acf6b9","url":null,"abstract":"The ‘ball on a string’ demonstration is a common tool used in physics education to illustrate the concept of conservation of angular momentum. However, various confounding factors can cause significant deviations from the idealized case, particularly under extreme conditions or when using low-stiffness pivots or high coefficients of friction. These factors include air resistance, contact friction at the pivot point, the mass of the ball and string, the angle of the string due to gravity, and the wobbling of the pivot point due to the centrifugal forces acting on it. In this work, we critically review by means of accurate simulations the adequateness of the ‘ball on a string’ demonstration in view of these confounding factors and provide recommendations for instructors on how to maximize the educational value of the demonstration while minimizing potential confusion for students. Our analysis suggests that a stiff pivot and avoiding extreme conditions are key to obtaining results that are in good agreement with the idealized case. We also caution instructors against using the demonstration without at least mentioning the confounding factors, as this may lead to a questionable understanding of the underlying physics principles.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47438080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-31DOI: 10.1088/1361-6404/acf5b4
Niña Zambale Simon, Benjamin Jose Ambrosio, N. Hermosa
We demonstrate the use of polarization to characterize the nonlinear response of a light dependent resistor (LDR). Previous experiments use the inverse square-dependence of the irradiance to calibrate the LDR’s response. In our study, we employ cross-polarizers to vary the irradiance incident on the surface of the LDR. We integrate the LDR into a simple voltage divider circuit and measure the voltage response as we rotate one of the cross-polarizers. We derive expressions that relate the voltage measurements to the angle between the polarizers. Our analytical predictions greatly match with the results obtained from the experiments; we then apply least squares method to get the calibration constants associated with the LDR’s nonlinear response. Finally, we discuss the advantages of our technique and emphasize its pedagogical benefits for high school and undergraduate laboratory courses.
{"title":"A simple calibration experiment for light dependent resistors using Malus law","authors":"Niña Zambale Simon, Benjamin Jose Ambrosio, N. Hermosa","doi":"10.1088/1361-6404/acf5b4","DOIUrl":"https://doi.org/10.1088/1361-6404/acf5b4","url":null,"abstract":"We demonstrate the use of polarization to characterize the nonlinear response of a light dependent resistor (LDR). Previous experiments use the inverse square-dependence of the irradiance to calibrate the LDR’s response. In our study, we employ cross-polarizers to vary the irradiance incident on the surface of the LDR. We integrate the LDR into a simple voltage divider circuit and measure the voltage response as we rotate one of the cross-polarizers. We derive expressions that relate the voltage measurements to the angle between the polarizers. Our analytical predictions greatly match with the results obtained from the experiments; we then apply least squares method to get the calibration constants associated with the LDR’s nonlinear response. Finally, we discuss the advantages of our technique and emphasize its pedagogical benefits for high school and undergraduate laboratory courses.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44239306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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