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Solving time-independent Schrödinger equation variationally using random numbers 求解时间无关的Schrödinger方程变分使用随机数
IF 0.7 4区 教育学
European Journal of Physics Pub Date : 2023-08-31 DOI: 10.1088/1361-6404/acf5b5
Pranjal Praneel, Ashish Kumar, M. Harbola
{"title":"Solving time-independent Schrödinger equation variationally using random numbers","authors":"Pranjal Praneel, Ashish Kumar, M. Harbola","doi":"10.1088/1361-6404/acf5b5","DOIUrl":"https://doi.org/10.1088/1361-6404/acf5b5","url":null,"abstract":"\u0000 Finding wavefunctions for even the simplest of interacting particle systems consisting of two particles is extremely difficult. It is therefore highly desirable that an accurate and easily implementable method be available to instructors and students of quantum-mechanics for obtaining wavefunctions for these particles. The usual approach taken to do this is to use parametrized functional form for the wavefunction in conjunction with the variational method to find approximate wavefunction and energy for the ground-state of such systems. In this paper, we employ random numbers to obtain ground-state wavefunctions and energies of two interacting particles in different one-dimensional potentials. The idea behind using random numbers is to search freely for functions that lead to lower and lower energy, converging eventually to its lowest value. The method presented is easily applicable numerically using a simple algorithm, and the wavefunctions obtained are highly accurate. Thus, the method presented makes study of two interacting particles accessible to instructors and students alike in a transparent manner.","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":"45955767","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}
引用次数: 0
Challenges in addressing student difficulties with basics and change of basis for two-state quantum systems using a multiple-choice question sequence in online and in-person classes 在网上和面对面课堂上使用多项选择题序列解决学生基础困难的挑战以及两国量子系统基础的改变
IF 0.7 4区 教育学
European Journal of Physics Pub Date : 2023-08-31 DOI: 10.1088/1361-6404/acf5b3
Peter Hu, Yangqiuting Li, Chandralekha Singh
{"title":"Challenges in addressing student difficulties with basics and change of basis for two-state quantum systems using a multiple-choice question sequence in online and in-person classes","authors":"Peter Hu, Yangqiuting Li, Chandralekha Singh","doi":"10.1088/1361-6404/acf5b3","DOIUrl":"https://doi.org/10.1088/1361-6404/acf5b3","url":null,"abstract":"Research-validated multiple-choice questions comprise an easy-to-implement instructional tool for scaffolding student learning and providing formative assessment of students’ knowledge. We present findings from the implementation of a research-validated multiple-choice question sequence on the basics of two-state quantum systems, including inner products, outer products, translation between Dirac notation and matrix representation in a particular basis, and change of basis. This study was conducted in an advanced undergraduate quantum mechanics course, in both online and in-person learning environments, across three years. For each cohort, students had their learning assessed after traditional lecture-based instruction in relevant concepts before engaging with the multiple-choice question sequence. Their performance was evaluated again afterward with a similar assessment and compared to their earlier performance. We analyze, compare, and discuss the trends observed in the three implementations.","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":"43152838","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}
引用次数: 0
Visualization of cylindrical resonances 圆柱形谐振的可视化
IF 0.7 4区 教育学
European Journal of Physics Pub Date : 2023-08-31 DOI: 10.1088/1361-6404/acf5b6
Brais Vila
{"title":"Visualization of cylindrical resonances","authors":"Brais Vila","doi":"10.1088/1361-6404/acf5b6","DOIUrl":"https://doi.org/10.1088/1361-6404/acf5b6","url":null,"abstract":"The analysis of cylindrical resonators is part of standard physics curricula but, unlike for their rectangular counterpart, their mode structure is hardly ever visualized. The aim of this work is to show a way of doing it, providing a set of interactive web applications and citing potential use cases in the form of both academic courses and published research. These cover several branches of physics and engineering, showing that these materials can be useful for a broad audience.","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":"49606056","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}
引用次数: 0
The electric flux through a square of a point charge near one corner 通过一个角附近的正方形点电荷的电通量
IF 0.7 4区 教育学
European Journal of Physics Pub Date : 2023-08-31 DOI: 10.1088/1361-6404/acf5b2
Elisabeth Atems
{"title":"The electric flux through a square of a point charge near one corner","authors":"Elisabeth Atems","doi":"10.1088/1361-6404/acf5b2","DOIUrl":"https://doi.org/10.1088/1361-6404/acf5b2","url":null,"abstract":"This paper presents two geometric models that can be used by students studying electrostatics to explore the electric flux of a point charge through a square in the limit of infinitesimal displacement from one corner. We first use qualitative reasoning to show that the limit is not a single value, but depends on the direction of displacement, and has significant discontinuities at the plane inside the square and along its sides. In the first model, the square is treated as one face of a cube. With this model, we discuss how to use Gauss’s law to determine the limiting flux through the square for displacements along symmetry lines of the cube, and their reflections through the planes of the faces. The second model treats the square as the base of a square pyramid and enables derivation of the limiting flux for displacements in an arbitrary direction. The result is verified against that obtained analytically, by integrating the definition of electric flux over the area of the square, in the limit of infinitesimal displacement from the corner. Both models require and facilitate an intuitive understanding of Gauss’s law and the limit concept, and the quantitative reasoning involves a minimum of algebra and no calculus. The first model, especially, is suitable for use in a guided-inquiry tutorial or problem-solving workshop for undergraduate physics students.","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":"45897489","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}
引用次数: 0
A modular experimental system for teaching fluid dynamics with Faraday waves 用法拉第波教授流体动力学的模块化实验系统
IF 0.7 4区 教育学
European Journal of Physics Pub Date : 2023-08-18 DOI: 10.1088/1361-6404/acf1df
Henrik B Pedersen, Albert Freud Abildgaard, Morten Søtang Jacobsen, H. Juul
{"title":"A modular experimental system for teaching fluid dynamics with Faraday waves","authors":"Henrik B Pedersen, Albert Freud Abildgaard, Morten Søtang Jacobsen, H. Juul","doi":"10.1088/1361-6404/acf1df","DOIUrl":"https://doi.org/10.1088/1361-6404/acf1df","url":null,"abstract":"We describe a modular setup for the observation of Faraday waves on a vibrating bath. The setup will be used as a project exercise on fluid dynamics in a first-year course on experimental physics at Aarhus University as well as for future research on fluids. As a demonstration of the setup, the acceleration threshold for the onset of Faraday waves on a silicone oil bath as a function of the driving frequency is measured and compared to thresholds calculated using different existing models. The possibility to characterize surface waves with the system is demonstrated by recording and analyzing images of Faraday waves, e.g. showing explicitly that the Faraday waves in the present case are subharmonic and establishing the dispersion relation for the waves.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44064945","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}
引用次数: 0
Computing the gravitational acceleration within the World Pendulum Alliance as an application of the remote laboratory methodology 作为远程实验室方法的应用，计算世界钟摆联盟内的重力加速度
IF 0.7 4区 教育学
European Journal of Physics Pub Date : 2023-08-17 DOI: 10.1088/1361-6404/acf173
Freddy Torres-Payoma, D. Herrera, Karla Triana, Laura Neira-Quintero, J. D. Castaño-Yepes
{"title":"Computing the gravitational acceleration within the World Pendulum Alliance as an application of the remote laboratory methodology","authors":"Freddy Torres-Payoma, D. Herrera, Karla Triana, Laura Neira-Quintero, J. D. Castaño-Yepes","doi":"10.1088/1361-6404/acf173","DOIUrl":"https://doi.org/10.1088/1361-6404/acf173","url":null,"abstract":"This paper describes a method for calculating gravitational acceleration using simple pendulums available through the World Pendulum Alliance. This network comprises fourteen institutions across eight countries, each providing a pendulum that can be accessed remotely via the Internet. We demonstrate how to measure the pendulum's period for N oscillations, discussing the importance of repetitions and samples in minimizing experimental uncertainty. We then use the averaged period value to compute the local gravitational acceleration, accounting for corrections due to the moment of inertia of the system. Finally, we analyze the geographical location of each pendulum to explore the dependence of gravity on latitude, longitude, and altitude and discuss its implications for the Earth's shape. We believe this tool will be useful for physics courses at the introductory and university levels due to its remote access features and its relevance to fundamental concepts.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45132703","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}
引用次数: 0
A graduate laboratory experiment to study the dynamics of an acoustically levitated particle 研究声学悬浮粒子动力学的研究生实验室实验
IF 0.7 4区 教育学
European Journal of Physics Pub Date : 2023-08-15 DOI: 10.1088/1361-6404/acf0a4
A. Dolev, Lorenzo Noseda, B. Yalcin, M. Sakar
{"title":"A graduate laboratory experiment to study the dynamics of an acoustically levitated particle","authors":"A. Dolev, Lorenzo Noseda, B. Yalcin, M. Sakar","doi":"10.1088/1361-6404/acf0a4","DOIUrl":"https://doi.org/10.1088/1361-6404/acf0a4","url":null,"abstract":"The comprehension of physical wave phenomena is imperative for students in the fields of engineering and basic sciences. Laboratory experiments that involve generation of acoustic waves can be used to explain advanced nonlinear wave phenomena. Acoustic levitation is a method for stably suspending and trapping objects in mid-air using acoustic radiation forces. This paper discusses an experimental apparatus that offers an economical means to demonstrate the acoustic levitation of polystyrene particles while enabling the investigation of stability and nonlinear dynamics of the trapped particles. Additionally, this platform offers the potential to examine other phenomena, such as the interaction forces between multiple acoustically levitated particles. The mechanical design of the system along with the data acquisition and control techniques are thoroughly explained.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46671628","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}
引用次数: 0
Some remarks on projectile motion with a linear resistance force 关于有线性阻力的抛物运动的几点看法
IF 0.7 4区 教育学
European Journal of Physics Pub Date : 2023-08-15 DOI: 10.1088/1361-6404/acf0a5
C. A. Morales, J. Muñoz, C. E. Vera
{"title":"Some remarks on projectile motion with a linear resistance force","authors":"C. A. Morales, J. Muñoz, C. E. Vera","doi":"10.1088/1361-6404/acf0a5","DOIUrl":"https://doi.org/10.1088/1361-6404/acf0a5","url":null,"abstract":"In this article, we revisit projectile motion assuming a retarding force proportional to the velocity, Fr⃗=−mkV⃗ . We obtain an analytical expression for the set of maxima of the trajectories, in Cartesian coordinates, without using the Lambert W function. Also, we investigate the effect of parameter k on the radial distance of the projectile showing that the radial distance oscillates from a certain critical launch angle and find an approximate expression for it. In our analysis, we consider the impact of parameter k in the kinetic energy, the potential energy, the total energy, the rate of energy loss, and the phase space. Our results can be included in an intermediate-level classical mechanics course.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42398802","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}
引用次数: 0
Irreversibility of sudden processes: compression versus expansion in perfect gases 突发过程的不可逆性：理想气体中的压缩与膨胀
IF 0.7 4区 教育学
European Journal of Physics Pub Date : 2023-08-15 DOI: 10.1088/1361-6404/acf0a6
Andrés Vallejo, Matías Osorio
{"title":"Irreversibility of sudden processes: compression versus expansion in perfect gases","authors":"Andrés Vallejo, Matías Osorio","doi":"10.1088/1361-6404/acf0a6","DOIUrl":"https://doi.org/10.1088/1361-6404/acf0a6","url":null,"abstract":"We focus on the study of the processes undergone by a perfect gas when the external pressure is suddenly modified. The analysis shows that, from the second law perspective, there is a non-evident asymmetry between the processes of compression and expansion between the same pressures, which is manifested through different levels of entropy production. If the system remains in contact with a thermal reservoir during the processes this asymmetry is remarkable, since while entropy grows linearly with the relative change of pressure during the compression, the relation between those variables is logarithmic during the expansion.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49297520","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}
引用次数: 0
Seeing the unseen—enhancing and evaluating undergraduate polarization experiments with interactive Mixed-Reality technology 基于交互式混合现实技术的大学生极化实验观察与评价
IF 0.7 4区 教育学
European Journal of Physics Pub Date : 2023-08-15 DOI: 10.1088/1361-6404/acf0a7
Paul Schlummer, Adrian Abazi, Rasmus Borkamp, Jonas Lauströer, Reinhard Schulz-Schaeffer, Carsten Schuck, W. Pernice, S. Heusler, D. Laumann
{"title":"Seeing the unseen—enhancing and evaluating undergraduate polarization experiments with interactive Mixed-Reality technology","authors":"Paul Schlummer, Adrian Abazi, Rasmus Borkamp, Jonas Lauströer, Reinhard Schulz-Schaeffer, Carsten Schuck, W. Pernice, S. Heusler, D. Laumann","doi":"10.1088/1361-6404/acf0a7","DOIUrl":"https://doi.org/10.1088/1361-6404/acf0a7","url":null,"abstract":"Learning from hands-on experiments requires learners to interpret their concrete interactions with the setup in terms of abstract physical concepts. To facilitate conceptual learning and close the gap between abstract physical models and the haptic interaction with the pertinent experimental setup, we developed an interactive Mixed-Reality learning environment centred around an undergraduate lab experiment dealing with light polarization. The use of Smartglasses (Microsoft HoloLens II) enables real-time visualization of data measured in the setup and ensures a high degree of spatial and temporal contiguity between functional components and model-based representations. A pilot study with N = 73 undergraduate students was conducted in a pre/post design to evaluate the learning environment with respect to learning outcome and learners’ affection towards the experiment. The results show that students’ knowledge had significantly increased after working with the learning environment with a large effect size (t(72) = 8.50, p ≤ 0.001, d = 1.03), and the activities are perceived as interesting and enjoyable. This proves the effectiveness of the environment with regard to learning about polarization and opens the pathway for an extension of our approach to other topics in science education.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42938062","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}
引用次数: 0
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