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Projectile motion with quadratic drag Am. J. Phys. (IF 0.9) Pub Date : 2023-03-23 John L. Bradshaw
Two-dimensional coupled nonlinear equations of projectile motion with air resistance in the form of quadratic drag are often treated as inseparable and solvable only numerically. However, when they are recast in terms of the angle between the projectile velocity and the horizontal, they become completely uncoupled and possess analytic solutions for projectile velocities as a function of that angle
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A charge analysis of non-invasive electrical brain stimulation Am. J. Phys. (IF 0.9) Pub Date : 2023-03-23 Maurice M. Klee
The brain is an electric organ. As such, for well over a hundred years, physicists, engineers, biologists, and physicians have used electromagnetic theory to try to understand how the brain works and to diagnose and treat disease. The field of electro-neuroscience is immense with thousands of papers being published each year. In this paper, we provide physics students with an introduction to the field
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Electromagnetic induction: How the “flux rule” has superseded Maxwell's general law Am. J. Phys. (IF 0.9) Pub Date : 2023-03-23 Giuseppe Giuliani
As documented by textbooks, the teaching of electromagnetic induction in university and high school courses is primarily based on what Feynman labeled as the “flux rule,” downgrading it from the status of physical law. However, Maxwell derived a “general law of electromagnetic induction” in which the vector potential plays a fundamental role. A modern reformulation of Maxwell's law can be easily obtained
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Modeling the frequency response of an acoustic cavity using the method of images Am. J. Phys. (IF 0.9) Pub Date : 2023-03-23 Frank Rice, Teresa Riedel, Isaiah Curtis
We demonstrate the ability of a simple algorithm based on the venerable method of images (MOIs), to accurately model the detailed frequency response of a multidimensional, rectangular, lossy resonant cavity. The convergence properties of the model's infinite series solution are shown to be determined by the cavity's quality factor Q. A 1D example demonstrates that the MOI series converges to the exact
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Fundamental properties of beamsplitters in classical and quantum optics Am. J. Phys. (IF 0.9) Pub Date : 2023-03-23 Masud Mansuripur, Ewan M. Wright
A lossless beamsplitter has certain (complex-valued) probability amplitudes for sending an incoming photon into one of two possible directions. We use elementary laws of classical and quantum optics to obtain general relations among the magnitudes and phases of these probability amplitudes. Proceeding to examine a pair of (nearly) single-mode wavepackets in the number-states n1 and n2 that simultaneously
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An easier-to-align Hong–Ou–Mandel interference demonstration Am. J. Phys. (IF 0.9) Pub Date : 2023-03-23 Nicholas S. DiBrita, Enrique J. Galvez
The Hong–Ou–Mandel interference experiment is a fundamental demonstration of nonclassical interference and a basis for many investigations of quantum information. This experiment involves the interference of two photons reaching a symmetric beamsplitter. When the photons are made indistinguishable in all possible ways, an interference of quantum amplitudes results in both photons always leaving the
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An economical smoke chamber and light-sheet microscope system for experiments in fluid dynamics and electrostatics Am. J. Phys. (IF 0.9) Pub Date : 2023-03-23 Karl D. Stephan
A smoke chamber and light-sheet video microscope setup is relatively easy to construct and provides opportunities for undergraduates to participate in a variety of advanced experiments, including the demonstration of Brownian motion and the interaction of induced electrostatic dipoles in aerosol particle agglomeration. We present results of these experiments along with information to allow replication
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Eccentricity and orientation of Earth's orbit from equinox and solstice times Am. J. Phys. (IF 0.9) Pub Date : 2023-03-23 B. Cameron Reed
A straightforward method of determining the eccentricity of Earth's orbit and the position of aphelion and perihelion relative to the vernal equinox from solstice and equinox times is described. The only assumption made is that the orbital eccentricity is small. Using dates for these phenomena adopted from a desk calendar gives the eccentricity to an accuracy of about 10%.
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Is contour integration essential? Alternatives for beginning physics students Am. J. Phys. (IF 0.9) Pub Date : 2023-02-17 Onuttom Narayan
The standard method to evaluate many definite integrals that are encountered in physics is contour integration. Here, we show how these can be evaluated by other means, enlarging the toolbox available to students and enabling the discussion of physical problems where these integrals arise before contour integration is introduced.
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A shorter path to some action variables Am. J. Phys. (IF 0.9) Pub Date : 2023-02-17 Juan F. Zanella Béguelin
This paper shows how to apply Leibniz's integral rule to calculate the action variables for the Kepler problem. This method offers an attractive alternative to the usual technique of complex contour integration. The method presented here to calculate definite integrals has a broad scope and is especially suitable for undergraduates who are unfamiliar with complex analysis.
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An exploration of circumbinary systems using gravitational microlensing Am. J. Phys. (IF 0.9) Pub Date : 2023-02-17 Brett C. George, Eleni-Alexandra Kontou, Patrycja Przewoznik, Eleanor Turrell
Gravitational microlensing is one of the methods to detect exoplanets–planets outside our solar system. Here, we focus on the theoretical modeling of systems with three lensing objects and in particular circumbinary systems. Circumbinary systems include two stars and at least one planet and are estimated to represent a sizeable portion of all exoplanets. Extending a method developed for binary lenses
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Producing slow light in warm alkali vapor using electromagnetically induced transparency Am. J. Phys. (IF 0.9) Pub Date : 2023-02-17 Kenneth DeRose, Kefeng Jiang, Jianqiao Li, Macbeth Julius, Linzhao Zhuo, Scott Wenner, Samir Bali
We present undergraduate-friendly instructions on how to produce light pulses propagating through warm Rubidium vapor with speeds less than 400 m/s, i.e., nearly a million times slower than c. We elucidate the role played by electromagnetically induced transparency (EIT) in producing slow light pulses and discuss how to achieve the required experimental conditions. The optical setup is presented, and
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A tabletop experiment for speed of light measurement using a Red Pitaya STEMlab board Am. J. Phys. (IF 0.9) Pub Date : 2023-02-17 Che-Chung Chou, Shi-Yu Hsaio, Jun-Zhi Feng, Tyson Lin, Sheng-Hua Lu
The speed of light is an important fundamental constant in physics, and so determining its value is a common undergraduate laboratory experiment. Methods to measure the light speed can help students practice their experimental skills and become familiar with the concepts of modern precision measurement techniques. In this paper, we demonstrate that a tabletop optical setup, comprised of an affordable
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Singular Lagrangians and the Dirac–Bergmann algorithm in classical mechanics Am. J. Phys. (IF 0.9) Pub Date : 2023-02-17 J. David Brown
Textbook treatments of classical mechanics typically assume that the Lagrangian is nonsingular; that is, the matrix of second derivatives of the Lagrangian with respect to the velocities is invertible. This assumption ensures that (i) Lagrange's equations can be solved for the accelerations as functions of coordinates and velocities, and (ii) the definitions of the conjugate momenta can be inverted
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Particle-in-cell method for plasmas in the one-dimensional electrostatic limit Am. J. Phys. (IF 0.9) Pub Date : 2023-02-17 Sara Gomez, Jaime Humberto Hoyos, Juan Alejandro Valdivia
We discuss the particle-in-cell (PIC) method, which is one of the most widely used approaches for the kinetic description of plasmas. The positions and velocities of the charged particles take continuous values in phase space, and spatial macroscopic quantities, such as the charge density and self-generated electric fields, are calculated at discrete spatial points of a grid. We discuss the computer
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Continuous fractional component Gibbs ensemble Monte Carlo Am. J. Phys. (IF 0.9) Pub Date : 2023-02-17 Niklas Mayr, Michael Haring, Thomas Wallek
A continuous fractional component (CFC) approach increases the probability of particle swaps in the context of vapor-liquid equilibrium simulations using the Gibbs ensemble Monte Carlo algorithm. Two variants of the CFC approach are compared for simulations of pure Lennard-Jones (LJ) fluids and binary LJ mixtures as examples. The details of an exemplary CFC implementation are presented. Recommendations
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From Sackur–Tetrode entropy to the ideal gas adiabatic equation in one step Am. J. Phys. (IF 0.9) Pub Date : 2023-02-17 P.-M. Binder, Ian R. Leigh
We present an alternative derivation of the relation between temperature and volume for a reversible, adiabatic process involving an ideal gas. The derivation for a monatomic gas starts with the Sackur–Tetrode equation and takes only one step. We also address the extension to diatomic gases.
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Low-energy scattering parameters: A theoretical derivation of the effective range and scattering length for arbitrary angular momentum Am. J. Phys. (IF 0.9) Pub Date : 2023-01-23 Jordi Pera, Jordi Boronat
The most important parameters in the study of low-energy scattering are the s-wave and p-wave scattering lengths and the s-wave effective range. We solve the scattering problem and find two useful formulas for the scattering length and the effective range for any angular momentum, as long as the Wigner threshold law holds. Using that formalism, we obtain a set of useful formulas for the angular-momentum
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A wave packet approach to resonant scattering Am. J. Phys. (IF 0.9) Pub Date : 2023-01-23 A. M. Michalik, F. Marsiglio
Resonant transmission occurs when constructive interference results in the complete passage of an incoming wave through an array of barriers. In this paper, we explore such a scenario with one-dimensional models. We adopt wave packets with finite width to illustrate the deterioration of resonance with decreasing wave packet width and suggest an approximate wave function for the transmitted and reflected
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“A call to action”: Schrödinger's representation of quantum mechanics via Hamilton's principle Am. J. Phys. (IF 0.9) Pub Date : 2023-01-23 Michele Marrocco
A few years ago, one of the former Editors of this journal launched “a call to action” (E. F. Taylor, Am. J. Phys. 71, 423–425 (2003)) for a revision of teaching methods in physics in order to emphasize the importance of the principle of least action. In response, we suggest the use of Hamilton's principle of stationary action to introduce the Schrödinger equation. When considering the geometric interpretation
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Science on a stick: An experimental and demonstration platform for learning several physical principles Am. J. Phys. (IF 0.9) Pub Date : 2023-01-23 Dhananjay V. Gadre, Harsh Sharma, Sangeeta D. Gadre, Smriti Srivastava
We share the design for a simple apparatus that, when paired with an Arduino processor and a computer, can be used in a wide range of laboratory measurements: observing linear kinematics, confirming Faraday's and Lenz's laws, measuring magnetic moments, and observing the effects of eddy currents. The setup is simple, inexpensive, easy to replicate, and can even be fabricated and used by students working
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Thermal infrared astronomy for the introductory laboratory Am. J. Phys. (IF 0.9) Pub Date : 2023-01-23 Clifford W. Padgett, William H. Baird, J. Spencer Coile, Wayne M. Johnson, Erin N. Groneck, Robert A. Rose
We show that infrared telescopes can be constructed at low cost using consumer-grade thermal infrared imagers and commercially available germanium lenses. Using these telescopes in the laboratory, introductory astronomy students can image nearby celestial objects to observe properties that are not seen in the visible region, in particular, variations in temperature across the surface.
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Low-cost quadrature optical interferometer Am. J. Phys. (IF 0.9) Pub Date : 2023-01-23 Tanner M. Melody, Krishna H. Patel, Peter K. Nguyen, Christopher L. Smallwood
We report on the construction and characterization of a low-cost Mach–Zehnder optical interferometer in which quadrature signal detection is achieved by means of polarization control. The device incorporates a generic green laser pointer, home-built photodetectors, 3D-printed optical mounts, a circular polarizer extracted from a pair of 3D movie glasses, and a python-enabled microcontroller for analog-to-digital
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Picometer measurements of strain coefficients by quadrature interferometry and lock-in amplification Am. J. Phys. (IF 0.9) Pub Date : 2023-01-23 Alec Nilson, Kurt Wick
Modulated strain displacements were measured with a quadrature Michelson–Morley interferometer employing polarization optics and two lock-in amplifiers to filter noise and thermal drift. The advantages of the technique, its limitations, and estimates on the accuracy are discussed, including an algorithm to correct for non-ideal components and non-linear effects. Instructions for the construction and
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Still learning about space dimensionality: From the description of hydrogen atom by a generalized wave equation for dimensions D≥3 Am. J. Phys. (IF 0.9) Pub Date : 2023-01-23 Francisco Caruso, Vitor Oguri, Felipe Silveira
A hydrogen atom is supposed to be described by a generalization of the Schrödinger equation, in which the Hamiltonian depends on an iterated Laplacian and a Coulomb-like potential r−β. Starting from previously obtained solutions for this equation using the 1/N expansion method, it is shown that new light can be shed on the problem of understanding the dimensionality of the world as proposed by Paul
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Resource Letter CP-3: Computational physics Am. J. Phys. (IF 0.9) Pub Date : 2022-12-22 Timothy J. Atherton
This Resource Letter provides information and guidance for those looking to incorporate computation into their courses or to refine their own computational practice. We begin with general resources, including policy documents and supportive organizations. We then survey efforts to integrate computation across the curriculum as well as provide information for instructors looking to teach a computational
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The drift motion of a spinning ball on carpet Am. J. Phys. (IF 0.9) Pub Date : 2022-12-22 Keith Zengel, Chris Tamer
A ball that rolls on carpet while also spinning around a vertical axis will experience a drift force that acts perpendicular to its velocity, opposite to the tangential velocity component of the front point of the ball. Here, we present a model of this motion based on three assumptions: the ball rolls without slipping around the point of contact directly below its center of mass; the ball experiences
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The mass spectrum of quarkonium using matrix mechanics Am. J. Phys. (IF 0.9) Pub Date : 2022-12-22 Aissa Belhouari
The matrix method is used to determine the mass spectrum (energy levels) of quarkonium, a composite particle comprising a quark and an anti-quark. This two-body system is similar to the hydrogen atom but at a reduced length scale. The results obtained by solving the Schrödinger equation for this system are in agreement with experimental and theoretical results obtained via other techniques, showing
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Adaptable research-based materials for teaching quantum mechanics Am. J. Phys. (IF 0.9) Pub Date : 2022-12-22 Steven Pollock, Gina Passante, Homeyra Sadaghiani
We have developed a complete collection of freely available instructional materials to assist faculty in creating a student-centered quantum mechanics (QM) class that engages students while supporting them in developing both sense-making and calculational skills. Our materials are grounded in research on students' understanding of quantum mechanics and are intended to be adaptable to a variety of instructional
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Low-cost automated spin coater and thermal annealer for additive prototyping of multilayer Bragg reflectors Am. J. Phys. (IF 0.9) Pub Date : 2022-12-22 Nathan J. Dawson, Yunli Lu, Zoe Lowther, Jacob Abell, Nicholas D. Christianson, Aaron W. Weiser, Gioia Aquino
We present and implement a design for an automated system that fabricates multilayer photonic crystal structures. The device is constructed with low-cost materials. A polystyrene/cellulose acetate multilayer Bragg reflector was fabricated to confirm the device's capability. A distributed feedback laser was also fabricated and characterized. The system has also been used to fabricate microlasers for
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Experimental realization of an additively manufactured monatomic lattice for studying wave propagation Am. J. Phys. (IF 0.9) Pub Date : 2022-12-22 Nehemiah Mork, Sai A. R. Kuchibhatla, Michael J. Leamy, Matthew D. Fronk
Increasing interest in wave propagation in phononic systems and metamaterials motivates the development of experimental designs, measurement techniques, and fabrication methods for use in basic research and classroom demonstrations. The simplest phononic system, the monatomic chain, exhibits rich physics such as dispersion and frequency-domain filtering. However, a limited number of experimental studies
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Unexpected optimal measurement protocols in Bell's inequality violation experiments Am. J. Phys. (IF 0.9) Pub Date : 2022-12-22 Alicia Negre, Renaud Mathevet, Benoit Chalopin, Sébastien Massenot
Bell's inequality violation experiments are becoming increasingly popular in the practical teaching of undergraduate and master's degree students. Bell's parameter S is obtained from 16 polarization correlation measurements performed on entangled photons pairs. We first report here a detailed analysis of the uncertainty u(S) of Bell's parameter taking into account coincidence count statistics and errors
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Concerning classical forces, energies, and potentials for accelerated point charges Am. J. Phys. (IF 0.9) Pub Date : 2022-12-22 Timothy H. Boyer
Although expressions for energy densities involving electric and magnetic fields are exactly analogous, their connections to forces and electromagnetic potentials are vastly different. For electrostatic situations, changes in the electric energy can be related directly to electric forces and to the electrostatic potential. In contrast, discussions of magnetic forces and energy changes involve two fundamentally
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The law of entropy increase for bodies in mutual thermal contact Am. J. Phys. (IF 0.9) Pub Date : 2022-12-22 Ramandeep S. Johal
The law of entropy increase for bodies in mutual thermal contact may be argued using the fact that the final temperature in the thermal process is higher than the final temperature in a reversible process for work extraction.
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Graphical analysis of an oscillator with constant magnitude sliding friction Am. J. Phys. (IF 0.9) Pub Date : 2022-11-22 V. Roitberg, Alon Drory
We treat a horizontal oscillator damped by constant-magnitude sliding friction by extending the analogy between the simple harmonic motion of a mass on a spring and the uniform circular motion of a mass attached to the end of a string. In the presence of sliding friction, the motion of the mass on a spring becomes the horizontal projection of the path of a mass attached to a string winding around two
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Charging a supercapacitor through a lamp: A power-lawRCdecay Am. J. Phys. (IF 0.9) Pub Date : 2022-11-22 Michelle L. Storms, Brad R. Trees
A circuit involving a charging supercapacitor in series with a non-Ohmic tungsten lamp displays a wealth of interesting behavior. Most notably, the current through the lamp decreases in time according to a power-law function as opposed to the exponential time dependence observed in RC circuits with Ohmic resistors. We use a combination of computational and analytical techniques to model this power-law
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Exploration of the Q factor for a parallel RLC circuit Am. J. Phys. (IF 0.9) Pub Date : 2022-11-22 J. G. Paulson, M. W. Ray
An important property of oscillating systems like RLC circuits is the Q factor, which quantifies the strength of damping in the system. The Q factor is inversely proportional to the resistance for a series RLC circuit but increases with the resistance in a parallel RLC circuit. The surprising behavior of the parallel RLC circuit makes building and modeling this circuit an interesting project for a
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A simple electronic circuit demonstrating Hopf bifurcation for an advanced undergraduate laboratory Am. J. Phys. (IF 0.9) Pub Date : 2022-11-22 Ishan Deo, Krishnacharya Khare
A nonlinear electronic circuit comprising of three nodes with a feedback loop is analyzed. The system has two stable states, a uniform state and a sinusoidal oscillating state, and it transitions from one to another by means of a Hopf bifurcation. The stability of this system is analyzed with nonlinear equations derived from a repressilator-like transistor circuit. The apparatus is simple and inexpensive
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The size of the Sun Am. J. Phys. (IF 0.9) Pub Date : 2022-11-22 M. A. Fardin, M. Hautefeuille
Why does the Sun have a radius around 696 000 km? We will see in this article that dimensional arguments can be used to understand the size of the Sun and of a few other things along the way. These arguments are not new and can be found scattered in textbooks. They are presented here in a succinct way in order to better confront the kinematic and mechanical viewpoints on size. We derive and compare
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An introduction to the Markov chain Monte Carlo method Am. J. Phys. (IF 0.9) Pub Date : 2022-11-22 Wenlong Wang
We present an intuitive, conceptual, and semi-rigorous introduction to the Markov Chain Monte Carlo method using a simple model of population dynamics and focusing on a few elementary distributions. We start from two states, then three states, and finally generalize to many states with both discrete and continuous distributions. Despite the mathematical simplicity, our examples include the essential
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Speed of light measurement with a picosecond diode laser and a voltage-controlled oscillator Am. J. Phys. (IF 0.9) Pub Date : 2022-11-22 Abdulaziz M. Aljalal
This work describes an experimental method for measuring the speed of light in air. It uses optical feedback from a visible picosecond diode laser operated below the threshold and a voltage-controlled oscillator to determine the time required for a pulse to travel a known distance. The experimental setup is compact, fitting into a space of 1 × 0.5 m2, and at the same time, can determine the speed of
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Data transmission in a multimode optical fiber using a neural network Am. J. Phys. (IF 0.9) Pub Date : 2022-11-22 Tom A. Kuusela
In digital data transmission, single mode optical fibers are commonly used since they can carry very short optical pulses without any significant distortions. In contrast, multimode fibers support many propagation modes that travel with different speeds; thus, they cannot maintain the shape of a light pulse. This feature of multiple propagation modes can be a benefit since it makes possible the transmission
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A Bose horn antenna radio telescope (BHARAT) design for 21 cm hydrogen line experiments for radio astronomy teaching Am. J. Phys. (IF 0.9) Pub Date : 2022-11-22 Ashish A. Mhaske, Joydeep Bagchi, Bhal Chandra Joshi, Joe Jacob, Paul K. T.
We have designed a low-cost radio telescope system named the Bose Horn Antenna Radio Telescope (BHARAT) to detect the 21 cm hydrogen line emission from our Galaxy. The system is being used at the Radio Physics Laboratory (RPL) (Radio Physics Lab, IUCAA NCRA-TIFR, , ), Inter-University Centre for Astronomy and Astrophysics (IUCAA), India, for laboratory sessions and training students and teachers. It
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Causality, determinism, and physics Am. J. Phys. (IF 0.9) Pub Date : 2022-10-21 Julio Gea-Banacloche
Although physical laws or theories are often invoked in debates over “causality” and “determinism,” our best current understanding of physics assigns only a limited (though still very broad) validity to these concepts. It may be, thus, helpful (particularly when having to deal with the challenges posed by quantum mechanics) to think of them as prejudices, extrapolated from our experience with a limited
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Using Hexbugs™ to model gas pressure and electrical conduction: A pandemic-inspired distance lab Am. J. Phys. (IF 0.9) Pub Date : 2022-10-21 Genevieve DiBari, Liliana Valle, Refilwe Tanah Bua, Lucas Cunningham, Eleanor Hort, Taylor Venenciano, Janice Hudgings
We describe a pandemic-inspired, modern physics distance lab course, focused both on engaging undergraduate physics majors in scientific research from their homes and on building skills in scientific paper reading and writing. To introduce the experimental and analytic tools, students are first asked to complete a traditional lab assignment in which collections of Hexbugs™, randomly moving toy automatons
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Turbulent dispersion of breath by the wind Am. J. Phys. (IF 0.9) Pub Date : 2022-10-21 Florian Poydenot, Ismael Abdourahamane, Elsa Caplain, Samuel Der, Antoine Jallon, Inés Khoutami, Amir Loucif, Emil Marinov, Bruno Andreotti
The pioneering work of Taylor on the turbulent dispersion of aerosols is one century old and provides an interesting way to introduce both diffusive processes and turbulence at an undergraduate level. Low mass particles transported by a turbulent flow exhibit a Brownian-like motion over time scales larger than the velocity correlation time. Aerosols and gases are, therefore, subjected to an effective
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Free fall of a quantum many-body system Am. J. Phys. (IF 0.9) Pub Date : 2022-10-21 A. Colcelli, G. Mussardo, G. Sierra, A. Trombettoni
The quantum version of the free fall problem is a topic often skipped in undergraduate quantum mechanics courses, because its discussion usually requires wavepackets built on the Airy functions—a difficult computation. Here, on the contrary, we show that the problem can be nicely simplified both for a single particle and for general many-body systems by making use of a gauge transformation that corresponds
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Submarine paradox softened Am. J. Phys. (IF 0.9) Pub Date : 2022-10-21 Hrvoje Nikolić
In Supplee's submarine paradox, a naive argument based on Lorentz contraction leads to a contradiction that a fast submarine should sink in the water's reference frame but float in the submarine's reference frame. Due to the submarine's rigidity constraints, it is not easy to resolve the paradox in a manifestly covariant form. To simplify the problem, we consider a version of the paradox in which one
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Long-term changes in the Earth's climate: Milankovitch cycles as an exercise in classical mechanics Am. J. Phys. (IF 0.9) Pub Date : 2022-10-21 R. C. T. Rainey
Long-term changes in the tilt of the Earth's axis, relative to the plane of its orbit, are of great significance to long-term climate change, because they control the size of the arctic and Antarctic circles. These “Milankovitch cycles” have hitherto been calculated by classical perturbation methods or by direct numerical integration of Newton's equations of motion. This paper presents an approximate
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Simple precession calculation for Mercury: A linearization approach Am. J. Phys. (IF 0.9) Pub Date : 2022-10-21 Michael J. W. Hall
The additional perihelion precession of Mercury due to general relativity can be calculated by a method that is no more difficult than solving for the Newtonian orbit. This method relies on linearizing the relativistic orbit equation, is simpler than standard textbook methods, and is closely related to Newton's theorem on revolving orbits. The main result is accurate for all values of GM/c2 for near-circular
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Surface plasmon resonance sensing in the advanced physics laboratory Am. J. Phys. (IF 0.9) Pub Date : 2022-10-21 Alaa Adel Abdelhamid, David Kerrigan, William Koopman, Andrew Werner, Zachary Givens, Eugenii U. Donev
We present a set of experiments and computations suitable for introducing upper-level undergraduate physics and engineering students to the interdisciplinary field of nanoplasmonics for periods ranging from a week-long advanced laboratory session to a summer research project. The end product is a tunable optofluidic device capable of detecting changes in a fluid medium as low as 0.002 refractive index
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Space pirates: A pursuit curve problem involving retarded time Am. J. Phys. (IF 0.9) Pub Date : 2022-09-22 Thales Azevedo, Anderson Pelluso
We revisit the classical pursuit curve problem solved by Pierre Bouguer in the 18th century, taking into account that information propagates at a finite speed. The discussion of this generalized problem of pursuit constitutes an excellent opportunity to introduce the concept of retarded time without the complications inherent to the study of electromagnetic radiation (where it is usually seen for the
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Exploring entropy by counting microstates of thep-state paramagnet Am. J. Phys. (IF 0.9) Pub Date : 2022-09-22 Steuard Jensen
Moore and Schroeder proposed an effective approach to introducing entropy and the second law through computational study of models with easily countable states at fixed energy. However, such systems are rare: the only familiar examples are the Einstein solid and the two-state paramagnet, which limits the available questions for assignment or discussion. This work considers the more general p-state
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Astronomy with Chaucer: Using an astrolabe to determine planetary orbits Am. J. Phys. (IF 0.9) Pub Date : 2022-09-22 Michael Robinson
Equipped with a home-made astrolabe and Kepler's laws, one can arrive at accurate estimates of the orbits of planets. Over the past three years, I have used an astrolabe to collect sightings of celestial bodies visible from my backyard. This paper shows that it is possible to measure one's latitude and longitude, the current time, locations of celestial bodies, and the sizes of the orbits of nearby
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Stereographic projection to and from the Bloch sphere: Visualizing solutions of the Bloch equations and the Bloch–Riccati equation Am. J. Phys. (IF 0.9) Pub Date : 2022-09-22 David J. Siminovitch
Stereographic projection mapping is typically introduced to explain the point at infinity in the complex plane. After this brief exposure in the context of complex analysis, students rarely get an opportunity to fully appreciate stereographic projection mapping as an elegant and powerful technique on its own with many fruitful applications in the physical sciences. Here, using a classical description
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Green's functions in quantum mechanics courses Am. J. Phys. (IF 0.9) Pub Date : 2022-09-22 William J. Herrera, Herbert Vinck-Posada, Shirley Gómez Páez
The use of Green's functions is valuable when solving problems in electrodynamics, solid-state physics, and many-body physics. However, its role in quantum mechanics is often limited to the context of scattering by a central force. This work shows how Green's functions can be used in other examples in quantum mechanics courses. In particular, we introduce time-independent Green's functions and the
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Efimov effect for two particles on a semi-infinite line Am. J. Phys. (IF 0.9) Pub Date : 2022-09-22 Satoshi Ohya
The Efimov effect (in a broad sense) refers to the onset of a geometric sequence of many-body bound states as a consequence of the breakdown of continuous scale invariance to discrete scale invariance. While originally discovered in three-body problems in three dimensions, the Efimov effect has now been known to appear in a wide spectrum of many-body problems in various dimensions. Here, we introduce
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Waving arms around to teach quantum mechanics Am. J. Phys. (IF 0.9) Pub Date : 2022-09-22 Kelby T. Hahn, Elizabeth Gire
Kinesthetic (or embodied) representations help students build intuition and deep understanding of concepts. This paper presents a series of kinesthetic activities for a spins-first undergraduate quantum mechanics course that supports students in reasoning and developing intuition about the complex-valued vectors of spin states. The arms representation, used in these activities, was developed as a tangible
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Maxwell's color box: Retracing the path of color matching experiments Am. J. Phys. (IF 0.9) Pub Date : 2022-09-22 Valentina Roberti, Boris Kalinic, Tiziana Cesca, Luca Bacci, Giulio Peruzzi
In his 1860 paper On the theory of compound colours, James Clerk Maxwell described an instrument used to obtain a direct comparison between daylight and a mixture of three selected spectral colors. This investigation was part of Maxwell's study of human color vision, color perception, and color representation, and it encompasses his main achievements in the field. The working principle underlying this
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A z-axis tunneling microscope for undergraduate labs Am. J. Phys. (IF 0.9) Pub Date : 2022-09-22 Randy Lindgren, Wesley Kozan, Noah Fuerst, Douglas Knapp, Joshua P. Veazey
We present the design and construction of a laboratory apparatus that provides advanced undergraduates with hands-on observations of electron quantum tunneling and the electronic density of states of various materials. The instrument is inspired by the scanning tunneling microscope (STM), but its implementation is simplified by limiting the tip motion to the single dimension along the tip-sample separation