Arutunian, S. G., Aginian, M. A., Margaryan, A. V., Lazareva, E. G., Chung, M.
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.
{"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":"395 ","pages":"0"},"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}
Livia A. J. Guttieres, Marko D. Petrović, James K. Freericks
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.
{"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":"403 7","pages":"0"},"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}
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.
{"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":"403 5","pages":"0"},"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}
Charles Barclay, Tonis Eenmae, Taavet Kalda, Hara Papathanassiou, Nikita Poljakov, Gustavo A. Rojas, Tiit Sepp, Greg Stachowski, Aniket Sule, Ioana A. Zelko
The first global e-competition on astronomy and astrophysics was held online in September–October 2020 as a replacement for the International Olympiad on Astronomy and Astrophysics, which was postponed due to the COVID-19 pandemic. Despite the short time available for organization, 8 weeks, the competition was run successfully, with 325 students from over 42 countries participating with no major issues. The feedback from the participants was positive and reflects the ways in which such events can boost interest in astronomy and astronomy education. With online activities set to become more prevalent in the future, we present an overview of the competition process, the challenges faced, and some of the lessons learned, aiming to contribute to the development of best practices for organizing online competitions.
{"title":"The first Global e-Competition on Astronomy and Astrophysics","authors":"Charles Barclay, Tonis Eenmae, Taavet Kalda, Hara Papathanassiou, Nikita Poljakov, Gustavo A. Rojas, Tiit Sepp, Greg Stachowski, Aniket Sule, Ioana A. Zelko","doi":"10.1119/5.0121242","DOIUrl":"https://doi.org/10.1119/5.0121242","url":null,"abstract":"The first global e-competition on astronomy and astrophysics was held online in September–October 2020 as a replacement for the International Olympiad on Astronomy and Astrophysics, which was postponed due to the COVID-19 pandemic. Despite the short time available for organization, 8 weeks, the competition was run successfully, with 325 students from over 42 countries participating with no major issues. The feedback from the participants was positive and reflects the ways in which such events can boost interest in astronomy and astronomy education. With online activities set to become more prevalent in the future, we present an overview of the competition process, the challenges faced, and some of the lessons learned, aiming to contribute to the development of best practices for organizing online competitions.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136103250","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}
We consider a heavy external object moving in an ideal gas of light particles. Collisions with the gas particles transfer momentum to the object, leading to a force that is proportional to the object's velocity but in the opposite direction. In an ideal classical gas at temperature T, the force acting on the object is proportional to T. Quantum statistics causes a deviation from the T-dependence and shows that the force scales with T2 at low temperatures. At T = 0, the force vanishes in a Bose gas but is finite in a Fermi gas.
{"title":"Force on a moving object in an ideal quantum gas","authors":"Wittaya Kanchanapusakit, Pattarapon Tanalikhit","doi":"10.1119/5.0127334","DOIUrl":"https://doi.org/10.1119/5.0127334","url":null,"abstract":"We consider a heavy external object moving in an ideal gas of light particles. Collisions with the gas particles transfer momentum to the object, leading to a force that is proportional to the object's velocity but in the opposite direction. In an ideal classical gas at temperature T, the force acting on the object is proportional to T. Quantum statistics causes a deviation from the T-dependence and shows that the force scales with T2 at low temperatures. At T = 0, the force vanishes in a Bose gas but is finite in a Fermi gas.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"404 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135112048","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}
John Essick, Jesse Kinder, Beth Parks, Donald Salisbury, Todd Springer, Keith Zengel
{"title":"In this issue: November 2023","authors":"John Essick, Jesse Kinder, Beth Parks, Donald Salisbury, Todd Springer, Keith Zengel","doi":"10.1119/5.0177701","DOIUrl":"https://doi.org/10.1119/5.0177701","url":null,"abstract":"","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"403 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135112049","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}
The quantum free energy of a system governed by a standard Hamiltonian is larger than its classical counterpart. The lowest-order correction, first calculated by Wigner, is proportional to ℏ2 and involves the sum of the mean squared forces. We present an elementary derivation of this result by drawing upon the Zassenhaus formula, an operator-generalization for the main functional relation of the exponential map. Our approach highlights the central role of non-commutativity between kinetic and potential energy and is more direct than Wigner's original calculation, or even streamlined variations thereof found in modern textbooks. We illustrate the quality of the correction for the simple harmonic oscillator (analytically) and the purely quartic oscillator (numerically) in the limit of high temperature. We also demonstrate that the Wigner correction fails in situations with sufficiently rapidly changing potentials, for instance, the particle in a box.
{"title":"Leading quantum correction to the classical free energy","authors":"Markus Deserno, O. Teoman Turgut","doi":"10.1119/5.0106687","DOIUrl":"https://doi.org/10.1119/5.0106687","url":null,"abstract":"The quantum free energy of a system governed by a standard Hamiltonian is larger than its classical counterpart. The lowest-order correction, first calculated by Wigner, is proportional to ℏ2 and involves the sum of the mean squared forces. We present an elementary derivation of this result by drawing upon the Zassenhaus formula, an operator-generalization for the main functional relation of the exponential map. Our approach highlights the central role of non-commutativity between kinetic and potential energy and is more direct than Wigner's original calculation, or even streamlined variations thereof found in modern textbooks. We illustrate the quality of the correction for the simple harmonic oscillator (analytically) and the purely quartic oscillator (numerically) in the limit of high temperature. We also demonstrate that the Wigner correction fails in situations with sufficiently rapidly changing potentials, for instance, the particle in a box.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"404 6-7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135112045","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}
Flynn B. Darby, Michael Y. Hua, Oskari V. Pakari, Shaun D. Clarke, Sara A. Pozzi
In this advanced instructional laboratory, students explore complex detection systems and nondestructive assay techniques used in the field of nuclear physics. After setting up and calibrating a neutron detection system, students carry out timing and energy deposition analyses of radiation signals. Through the timing of prompt fission neutron signals, multiplicity counting is used to carry out a special nuclear material (SNM) nondestructive assay. Our experimental setup is comprised of eight trans-stilbene organic scintillation detectors in a well-counter configuration, and measurements are taken on a spontaneous fission source as well as two (α,n) sources. By comparing each source's measured multiplicity distribution, the resulting measurements of the (α,n) sources can be distinguished from that of the spontaneous fission source. Such comparisons prevent the spoofing, i.e., intentional imitation, of a fission source by an (α,n) neutron source. This instructional laboratory is designed for nuclear engineering and physics students interested in organic scintillators, neutron sources, and nonproliferation radiation measurement techniques.
{"title":"Multiplicity counting using organic scintillators to distinguish neutron sources: An advanced teaching laboratory","authors":"Flynn B. Darby, Michael Y. Hua, Oskari V. Pakari, Shaun D. Clarke, Sara A. Pozzi","doi":"10.1119/5.0139531","DOIUrl":"https://doi.org/10.1119/5.0139531","url":null,"abstract":"In this advanced instructional laboratory, students explore complex detection systems and nondestructive assay techniques used in the field of nuclear physics. After setting up and calibrating a neutron detection system, students carry out timing and energy deposition analyses of radiation signals. Through the timing of prompt fission neutron signals, multiplicity counting is used to carry out a special nuclear material (SNM) nondestructive assay. Our experimental setup is comprised of eight trans-stilbene organic scintillation detectors in a well-counter configuration, and measurements are taken on a spontaneous fission source as well as two (α,n) sources. By comparing each source's measured multiplicity distribution, the resulting measurements of the (α,n) sources can be distinguished from that of the spontaneous fission source. Such comparisons prevent the spoofing, i.e., intentional imitation, of a fission source by an (α,n) neutron source. This instructional laboratory is designed for nuclear engineering and physics students interested in organic scintillators, neutron sources, and nonproliferation radiation measurement techniques.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"404 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135112044","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}
{"title":"An alternative derivation of propagator for a linear potential","authors":"Xi-Jun Ren","doi":"10.1119/5.0103857","DOIUrl":"https://doi.org/10.1119/5.0103857","url":null,"abstract":"","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"404 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135112046","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}
The Wilberforce pendulum illustrates important properties of coupled oscillators including normal modes and beat phenomena. When helical spring is attached to a mass to create the Wilberforce pendulum, the longitudinal and torsional oscillations are coupled. A Wilberforce can be constructed simply from a standard laboratory spring, and a smartphone's accelerometer and gyroscope can be used to monitor the oscillations. We show that the resulting time-series data match theoretical predictions, and we share the procedures for observing both normal modes and beats.
{"title":"Coupled oscillations of the Wilberforce pendulum unveiled by smartphones","authors":"Thomas Gallot, Daniel Gau, Rodrigo García-Tejera","doi":"10.1119/5.0138680","DOIUrl":"https://doi.org/10.1119/5.0138680","url":null,"abstract":"The Wilberforce pendulum illustrates important properties of coupled oscillators including normal modes and beat phenomena. When helical spring is attached to a mass to create the Wilberforce pendulum, the longitudinal and torsional oscillations are coupled. A Wilberforce can be constructed simply from a standard laboratory spring, and a smartphone's accelerometer and gyroscope can be used to monitor the oscillations. We show that the resulting time-series data match theoretical predictions, and we share the procedures for observing both normal modes and beats.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":"403 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135112050","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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