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Metastable states in a 1D quantum system 一维量子系统中的嬗变态
IF 0.9 4区 教育学
American Journal of Physics Pub Date : 2023-12-01 DOI: 10.1119/5.0124407
J. Goff, Don C. Colladay
{"title":"Metastable states in a 1D quantum system","authors":"J. Goff, Don C. Colladay","doi":"10.1119/5.0124407","DOIUrl":"https://doi.org/10.1119/5.0124407","url":null,"abstract":"One-dimensional (1D) systems in which metastable states exist are physically important, but they are usually not discussed quantitatively in textbooks. This paper presents a relatively simple 1D system involving a piecewise-constant potential for which metastable states can be easily calculated using a computer algebraic system. The metastable-state wave functions are computed and plotted for various particle energies. The Breit–Wigner approximation is used to fit the resulting resonant structure in the transmission coefficient. Connections are made between the initial analysis and poles of the scattering matrix that corresponds to the potential.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138608374","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
Pendulum waves: A model of Thomae's function 钟摆波托马函数模型
IF 0.9 4区 教育学
American Journal of Physics Pub Date : 2023-12-01 DOI: 10.1119/5.0131936
Xiangdong Feng, Changhong Lu, Jurgen Schulte, Zengxu Shan, Gentong Liu
{"title":"Pendulum waves: A model of Thomae's function","authors":"Xiangdong Feng, Changhong Lu, Jurgen Schulte, Zengxu Shan, Gentong Liu","doi":"10.1119/5.0131936","DOIUrl":"https://doi.org/10.1119/5.0131936","url":null,"abstract":"The pendulum wave apparatus exhibits cyclic pendulum patterns, including wave-like motion and pendulums alignments. This work presents a complete analytical solution to the times and numbers of pendulum alignment, which is shown to be a subset of Thomae's function. Based on the properties of this function and basic number theory, a comprehensive analysis of pendulum patterns is presented.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138620240","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
Using lock-in detection to build a barcode scanner 使用锁定检测构建条形码扫描器
IF 0.9 4区 教育学
American Journal of Physics Pub Date : 2023-12-01 DOI: 10.1119/5.0151621
Riley E. Alexander, Maya M. DiFrischia, Margaret J. Doubman, Stefany Fabian Dubon, Lily Goltz, Yuqian Li, Rebecca A. Long, Genevieve Love, Nina Martinez Diers, Matangi Melpakkam, Catie Robinson, Elizabeth M. Tompkins, Avalon L. B. Vanis, Xinrui Wang, Mallory Yu, Sarah E. Spielman, Michael W. Noel
{"title":"Using lock-in detection to build a barcode scanner","authors":"Riley E. Alexander, Maya M. DiFrischia, Margaret J. Doubman, Stefany Fabian Dubon, Lily Goltz, Yuqian Li, Rebecca A. Long, Genevieve Love, Nina Martinez Diers, Matangi Melpakkam, Catie Robinson, Elizabeth M. Tompkins, Avalon L. B. Vanis, Xinrui Wang, Mallory Yu, Sarah E. Spielman, Michael W. Noel","doi":"10.1119/5.0151621","DOIUrl":"https://doi.org/10.1119/5.0151621","url":null,"abstract":"Lock-in detection is a widely used experimental technique in which a weak signal is measured by modulating it at a particular frequency. Then, by detecting an experimental output at that frequency, the desired signal can be isolated from much larger-amplitude noise. Here, we report on the implementation and optimization of a homemade laser barcode scanner based on the lock-in technique. Our setup is comprised of components that are readily available in an undergraduate instructional laboratory. The successful transcription of the barcode into a digital signal was achieved, and this digital signal was collected with a simple computer and processed to reveal the encoded number.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138622985","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
Nonlinear oscillator acceleration and period variation with amplitude 非线性振荡器加速度和周期随振幅的变化
IF 0.9 4区 教育学
American Journal of Physics Pub Date : 2023-12-01 DOI: 10.1119/5.0139124
Peter F. Hinrichsen
{"title":"Nonlinear oscillator acceleration and period variation with amplitude","authors":"Peter F. Hinrichsen","doi":"10.1119/5.0139124","DOIUrl":"https://doi.org/10.1119/5.0139124","url":null,"abstract":"A classic nonlinear spring mass oscillator, the nonlinearity of which could be varied by changing the initial stretching of the spring, was used to investigate how the amplitude dependence of the period and the harmonic content depended on the nonlinearity. The oscillations were measured with a photogate and a MEMS accelerometer, allowing both the oscillation period and the Fourier components of the motion to be precisely determined. The results were in good agreement with theory.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138621113","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
Comment on “Avoid propagation of typos with numerical methods” [Am. J. Phys. 89(1), 9 (2021)] 关于 "用数值方法避免错别字传播 "的评论 [Am. J. Phys. 89(1), 9 (2021)]
IF 0.9 4区 教育学
American Journal of Physics Pub Date : 2023-12-01 DOI: 10.1119/5.0167881
B. C. Reed
{"title":"Comment on “Avoid propagation of typos with numerical methods” [Am. J. Phys. 89(1), 9 (2021)]","authors":"B. C. Reed","doi":"10.1119/5.0167881","DOIUrl":"https://doi.org/10.1119/5.0167881","url":null,"abstract":"","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138625488","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
S-matrices for simple quantum systems 简单量子系统的s矩阵
4区 教育学
American Journal of Physics Pub Date : 2023-11-01 DOI: 10.1119/5.0078607
Leo de Wit
{"title":"<i>S</i>-matrices for simple quantum systems","authors":"Leo de Wit","doi":"10.1119/5.0078607","DOIUrl":"https://doi.org/10.1119/5.0078607","url":null,"abstract":"Scattering processes are a standard topic covered in introductory courses on quantum mechanics and particle physics. Unfortunately, a full mathematical treatment tends to be overwhelming for undergraduate students. This article introduces some toy models that are easy to comprehend but still contain the essential features of quantum theory. We define a Hilbert space with state vectors and use creation/annihilation operators to construct transition matrices and S-matrices. We show how perturbation theory gives rise to Feynman diagrams and Feynman rules. We also discuss how we can use symmetry and group theory to restrict what interactions are possible.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135112052","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
Oblique angle collisions between three or more billiard balls 三个或更多台球之间的斜角碰撞
4区 教育学
American Journal of Physics Pub Date : 2023-11-01 DOI: 10.1119/5.0119656
Rod Cross
{"title":"Oblique angle collisions between three or more billiard balls","authors":"Rod Cross","doi":"10.1119/5.0119656","DOIUrl":"https://doi.org/10.1119/5.0119656","url":null,"abstract":"Oblique angle collisions between two balls or two disks have been addressed by many authors. This paper describes oblique angle collisions between three or four billiard balls. Measurements and calculations are presented for cases where one ball is incident obliquely on two or three identical balls, which are in contact and initially at rest. Conservation laws alone are not sufficient to predict the outcome. Adding information about the impact forces on each ball (and ignoring friction forces) provides good theoretical agreement with experimental results.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135112047","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
Electric field lines of an arbitrarily moving charged particle 任意移动的带电粒子的电场线
4区 教育学
American Journal of Physics Pub Date : 2023-11-01 DOI: 10.1119/5.0124544
Arutunian, S. G., Aginian, M. A., Margaryan, A. V., Lazareva, E. G., Chung, M.
{"title":"Electric field lines of an arbitrarily moving charged particle","authors":"Arutunian, S. G., Aginian, M. A., Margaryan, A. V., Lazareva, E. G., Chung, M.","doi":"10.1119/5.0124544","DOIUrl":"https://doi.org/10.1119/5.0124544","url":null,"abstract":"Electromagnetic fields of relativistic charged particles have a broad frequency spectrum and a sophisticated spatial structure. Field lines offer a visual representation of this spatial structure. In this article, we derive a general set of equations for the field lines of any moving charged particle. The electric field lines are completely determined by the unit vector from the retarding point to the observation point. After proper transformations, the field line equations describe the rotation of this vector with an angular velocity coinciding with Thomas precession. In some cases, including all planar trajectories, the field line equations reduce to linear differential equations with constant coefficients. We present a detailed derivation of these equations and their general analytical solution. We then illustrate this method by constructing field lines for the “figure eight” motion of an electric charge moving under the influence of a plane wave, including complex field lines in three dimensions.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136103067","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
Computational projects with the Landau–Zener problem in the quantum mechanics classroom 量子力学课堂中朗道-齐纳问题的计算项目
4区 教育学
American Journal of Physics Pub Date : 2023-11-01 DOI: 10.1119/5.0139717
Livia A. J. Guttieres, Marko D. Petrović, James K. Freericks
{"title":"Computational projects with the Landau–Zener problem in the quantum mechanics classroom","authors":"Livia A. J. Guttieres, Marko D. Petrović, James K. Freericks","doi":"10.1119/5.0139717","DOIUrl":"https://doi.org/10.1119/5.0139717","url":null,"abstract":"The Landau–Zener problem, where a minimum energy separation is passed with constant rate in a two-state quantum-mechanical system, is an excellent model quantum system for a computational project. It requires a low-level computational effort, but has a number of complex numerical and algorithmic issues that can be resolved through dedicated work. It can be used to teach computational concepts, such as accuracy, discretization, and extrapolation, and it reinforces quantum concepts of time-evolution via a time-ordered product and of extrapolation to infinite time via time-dependent perturbation theory. In addition, we discuss the concept of compression algorithms, which are employed in many advanced quantum computing strategies, and easy to illustrate with the Landau–Zener problem.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135112051","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
Galilean relativity and the path integral formalism in quantum mechanics 伽利略相对论与量子力学中的路径积分形式
4区 教育学
American Journal of Physics Pub Date : 2023-11-01 DOI: 10.1119/5.0140018
Charles Torre
{"title":"Galilean relativity and the path integral formalism in quantum mechanics","authors":"Charles Torre","doi":"10.1119/5.0140018","DOIUrl":"https://doi.org/10.1119/5.0140018","url":null,"abstract":"Closed systems in Newtonian mechanics obey the principle of Galilean relativity. However, the usual Lagrangian for Newtonian mechanics, formed from the difference of kinetic and potential energies, is not invariant under the full group of Galilean transformations. In quantum mechanics, Galilean boosts require a non-trivial transformation rule for the wave function and a concomitant “projective representation” of the Galilean symmetry group. Using Feynman's path integral formalism, this latter result can be shown to be equivalent to the non-invariance of the Lagrangian. Thus, using path integral methods, the representation of certain symmetry groups in quantum mechanics can be simply understood in terms of the transformation properties of the classical Lagrangian and conversely. The main results reported here should be accessible to students and teachers of physics—particularly classical mechanics, quantum mechanics, and mathematical physics—at the advanced undergraduate and beginning graduate levels, providing a useful exposition for those wanting to explore topics such as the path integral formalism for quantum mechanics, relativity principles, Lagrangian mechanics, and representations of symmetries in classical and quantum mechanics.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135112053","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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