Showing papers in "American Journal of Physics in 1996"
TL;DR: The authors analyzes an excerpt of a discussion from a high school physics class from several different perspectives on students' knowledge and reasoning, illustrating a range in what an instructor might perceive in students' work and take as tasks for instruction.
Abstract: This article analyzes an excerpt of a discussion from a high school physics class from several different perspectives on students’ knowledge and reasoning, illustrating a range in what an instructor might perceive in students’ work and take as tasks for instruction. It suggests a view of current education research as providing perspectives to expand, refine, and support instructors’ perceptions and judgment, rather than as providing definitive principles or proven methods.
341 citations
TL;DR: In this paper, a generalization of calculus, namely continuous Markov process theory, in a form that should be accessible to advanced physics undergraduates is presented, which enables one to give clear, concise derivations of all the principal results of Brownian motion and Johnson noise, including fluctuation-dissipation formulas, auto-covariance transport formulas, spectral density formulas, Nyquist's formula, and an accurate numerical simulation algorithm.
Abstract: One reason why Brownian motion and Johnson noise are difficult subjects to teach is that their mathematical requirements transcend the capabilities of ordinary differential calculus. Presented here is an exposition of the needed generalization of calculus, namely continuous Markov process theory, in a form that should be accessible to advanced physics undergraduates. It is shown how this mathematical framework enables one to give clear, concise derivations of all the principal results of Brownian motion and Johnson noise, including fluctuation–dissipation formulas, auto‐covariance transport formulas, spectral density formulas, Nyquist’s formula, the notions of white and 1/f2 noise, and an accurate numerical simulation algorithm. An added benefit of this exposition is a clearer view of the mathematical connection between the two very different approaches to Brownian motion taken by Einstein and Langevin in their pioneering papers of 1905 and 1908.
269 citations
TL;DR: In this article, the casimir effect and radiative reaction in an optical cavity were discussed. But the authors did not consider the effect of the atom-photon interactions in the optical cavity.
Abstract: New aspects of the casimir effect - fluctuations and radiative reaction, G. Barton non-perturbative atom-photon interactions in an optical cavity, H.J. Carmichael et al single atom emission in an optical resonator, J.J. Childs et al one electron in a cavity, G. Gabrielse and J. Tan manipulation of non-classical field states in a cavity by atom interferometry, S. Haroche and J.M. Raimond perturbative cavity quantum electrodynamics, E.A. Hinds structure and dynamics in cavity quantum electrodynamics, H.J. Kimble spontaneous emission by moving atoms, P. Meystre and M. Wilkens quantum optics of driven atoms in coloured vacua, T.W. Mossberg and M. Lewenstein the micromaser - a proving ground for quantum physics, G. Raithel et al.
264 citations
TL;DR: In this paper, an easily reproduced experiment that allows the student to investigate the intensity and phase structure of transverse laser modes is presented. But the results are limited to the Laguerre-Gaussian modes.
Abstract: We outline an easily reproduced experiment that allows the student to investigate the intensity and phase structure of transverse laser modes. In addition to discussing the usual Hermite–Gaussian laser modes we detail how Laguerre–Gaussian laser modes can be obtained by the direct conversion of the Hermite–Gaussian output. A Mach–Zehnder interferometer allows the phase structure of the Laguerre–Gaussian modes to be compared with the phase structure of a plane wave with the same frequency. The resulting interference patterns clearly illustrate the azimuthal phase dependence of the Laguerre–Gaussian modes, which is the origin of the orbital angular momentum associated with each of them.
236 citations
234 citations
TL;DR: The authors used qualitative problem-solving strategies in teaching an introductory, calculus-based physics course as a means of highlighting the role played by conceptual knowledge in solving problems, and found that presenting strategies during lectures and in homework solutions provided an excellent opportunity to model for students the type of concept-based, qualitative reasoning that is valued in our profession, and that student-generated strategies serve a diagnostic function by providing instructors with insights on students' conceptual understanding and reasoning.
Abstract: We report on the use of qualitative problem‐solving strategies in teaching an introductory, calculus‐based physics course as a means of highlighting the role played by conceptual knowledge in solving problems. We found that presenting strategies during lectures and in homework solutions provides an excellent opportunity to model for students the type of concept‐based, qualitative reasoning that is valued in our profession, and that student‐generated strategies serve a diagnostic function by providing instructors with insights on students’ conceptual understanding and reasoning. Finally, we found strategies to be effective pedagogical tools for helping students both to identify principles that could be applied to solve specific problems, as well as to recall the major principles covered in the course months after it was over.
194 citations
TL;DR: In this paper, the authors used video motion analysis software for introductory physics students in a variety of instructional settings and found that the greater the integration of video analysis into the kinematics curriculum, the larger the educational impact.
Abstract: Video motion analysis software was used by introductory physics students in a variety of instructional settings. 368 high school and college students took part in a study where the effect of graduated variations in the use of a video analysis tool was examined. Post‐instruction assessment of student ability to interpret kinematics graphs indicates that groups using the tool generally performed better than students taught via traditional instruction. The data further establishes that the greater the integration of video analysis into the kinematics curriculum, the larger the educational impact. An additional comparison showed that graph interpretation skills were significantly better when a few traditional labs were simply replaced with video analysis experiments. Hands‐on involvement appeared to play a critical role. Limiting student experience with the video analysis technique to a single teacher‐led demonstration resulted in no improvement in performance relative to traditional instruction. Offering mor...
164 citations
TL;DR: In this paper, it was shown that an engine with a ratchet and a pawl can never achieve the efficiency of a Carnot cycle, not even in the limit of zero power (infinitely slow motion).
Abstract: The well‐known discussion on an engine consisting of a ratchet and a pawl in [R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison‐Wesley, Reading, MA, 1963), Vol. 1, pp. 46.1–46.9] is shown to contain some misguided aspects: Since the engine is simultaneously in contact with reservoirs at different temperatures, it can never work in a reversible way. As a consequence, the engine can never achieve the efficiency of a Carnot cycle, not even in the limit of zero power (infinitely slow motion), in contradiction with the conclusion reached in the Lectures.
157 citations
TL;DR: In this paper, 15 commonly held misconceptions concerning quantum mechanics, such as energy eigenstates are the only allowed states and the wave function is dimensionless, are listed and a few suggestions are offered to help combat these misconceptions.
Abstract: This paper lists 15 commonly held misconceptions concerning quantum mechanics, such as ‘‘Energy eigenstates are the only allowed states’’ and ‘‘The wave function is dimensionless.’’ A few suggestions are offered to help combat these misconceptions in teaching.
151 citations
TL;DR: The properties of the Mathieu equation are reviewed in this article in order to discuss some of the applications that have appeared in recent years, such as vibrations in an elliptic drum, the inverted pendulum, the radio frequency quadrupole, frequency modulation, stability of a floating body, alternating gradient focusing, the Paul trap for charged particles, and the mirror trap for neutral particles.
Abstract: The properties of the Mathieu equation are reviewed in order to discuss some of the applications that have appeared in recent years. Those mentioned are: vibrations in an elliptic drum, the inverted pendulum, the radio frequency quadrupole, frequency modulation, stability of a floating body, alternating gradient focusing, the Paul trap for charged particles, and the mirror trap for neutral particles.
147 citations
TL;DR: In this article, a generic treatment of wave-packet evolution is presented, and conditions under which various types of revivals occur in ideal form are provided, and explicit examples of different types of revival structure are provided.
Abstract: Localized quantum wave packets can be produced in a variety of physical systems and are the subject of much current research in atomic, molecular, chemical, and condensed‐matter physics. They are particularly well suited for studying the classical limit of a quantum‐mechanical system. The motion of a localized quantum wave packet initially follows the corresponding classical motion. However, in most cases the quantum wave packet spreads and undergoes a series of collapses and revivals. We present a generic treatment of wave‐packet evolution, and we provide conditions under which various types of revivals occur in ideal form. The discussion is at a level appropriate for an advanced undergraduate or first‐year graduate course in quantum mechanics. Explicit examples of different types of revival structure are provided, and physical applications are discussed.
TL;DR: In this paper, a simple example of a four-stroke engine operated in finite-time is analyzed subject to a fixed cycle time, and the time allocation between the hot and cold branches that maximizes the work output is considered.
Abstract: A simple example of a four‐stroke engine operated in finite‐time is analyzed. The working medium consists of noninteracting two‐level systems or harmonic oscillators. The cycle of operation is analogous to a four‐stroke Otto cycle. The only source of irreversibility is due to the finite rate of heat transfer between the working medium and the cold and hot baths. The dynamics of the working medium is governed by a master equation. The engine is shown to settle to a stable limit cycle for given contact periods with the hot and cold baths. The operation of the engine is analyzed subject to a fixed cycle time. The time allocation between the hot and cold branches that maximizes the work output is considered. Analytical results are obtained when the relaxation is very slow, very fast, or when the relaxation rates along the hot and cold branches are equal. Numerical results are presented for the general case. A maximization of the power with respect to the cycle time leads to a finite optimal cycling frequency provided the adiabatic branches are allotted finite durations.
TL;DR: A self-contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided in this article, where the theoretical basis of the method is derived and then a numerical algorithm is formulated.
Abstract: A self‐contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of the method is derived and then a numerical algorithm is formulated. The algorithm is applied to determine the ground state of the harmonic oscillator, the Morse oscillator, the hydrogen atom, and the electronic ground state of the H+2 ion and of the H2 molecule. A computer program on which the sample calculations are based is available upon request.
TL;DR: Holbrow et al. as discussed by the authors presented interesting, novel problems for use in undergraduate physics courses beyond the introductory level, such as Classical Mechanics, Electricity and Magnetism, Statistical Mechanics and Thermodynamics, Modern Physics, or Quantum Mechanics.
Abstract: The “New Problems” department presents interesting, novel problems for use in undergraduate physics courses beyond the introductory level. We will publish worked problems that convey the excitement and interest of current developments in physics and that are useful for teaching courses such as Classical Mechanics, Electricity and Magnetism, Statistical Mechanics and Thermodynamics, Modern Physics, or Quantum Mechanics. We challenge physicists everywhere to create problems that show how their various branches of physics use the central, unifying ideas of physics to advance physical understanding. We want these problems to become an important source of ideas and information for students of physics. This project is supported by the Physics Division of the National Science Foundation. Submit materials to Charles H. Holbrow, Editor.
TL;DR: In this article, the meaning and scope of a recent type of uncertainty relation of a very general character are elucidated using the notions of time-indicating dynamical variables (clock variables) and placeindicating dynamic variables (position variables), which can be successfully applied to the thought experiments that Einstein introduced into his debate with Bohr about the uncertainty principle(s) and in particular to the famous photon-box experiment.
Abstract: The meaning and scope of a recent type of uncertainty relation of a very general character are elucidated using the notions of time-indicating dynamical variables (clock variables) and place-indicating dynamical variables (position variables). It is shown that if the total energy (momentum) of a system is certain, all time-indicating (place-indicating) dynamical variables are completely uncertain. The quantum clock is discussed as an illustration of the energy–time uncertainty relation. The relations can be successfully applied to the thought experiments that Einstein introduced into his debate with Bohr about the uncertainty principle(s) and, in particular, to the famous photon-box experiment. It is shown that due to this general relation the photon box can never serve its purpose, independent of the details of the experiment.
TL;DR: In this article, the authors describe several heat engine models in which the same efficiency formula can be derived by minimizing the rate of entropy generation, including the contribution made by the components that provide a freely varying heat input to the power cycle.
Abstract: Chambadal, Novikov, Curzon and Ahlborn have shown that the efficiency of an irreversible heat engine at maximum power output is 1−(T L /T H )1/2. This article describes several heat engine models in which the same efficiency formula can be derived by minimizing the rate of entropy generation. Included in the entropy generation is the usually overlooked contribution made by the components that provide a freely varying heat input to the power cycle.
TL;DR: In this article, an interactive computer-based tutorial was developed to address the conceptual and reasoning difficulties associated with the photoelectric effect in modern physics courses, and the primary instructional strategy used in the tutorial is the drawing and interpretation of graphs of current versus voltage for the circuit in the experiment.
Abstract: An investigation conducted after standard lecture instruction in a sophomore‐level modern physics course revealed that many students were unable to interpret the photoelectric experiment in terms of the photon model for light. Findings from this research were used to guide the development of an interactive computer‐based tutorial to address the conceptual and reasoning difficulties that were identified. The primary instructional strategy used in the tutorial is the drawing and interpretation of graphs of current versus voltage for the circuit in the experiment. The program has been used both as an aid to instruction and as a probe to obtain additional information about the nature, prevalence, and persistence of specific difficulties. Analysis of student performance on examination problems on the photoelectric experiment indicates that those who have worked through the tutorial make fewer errors and give better explanations than those who have not had this experience. This result suggests that the intellectual engagement required by the program helps students improve their understanding of the photoelectric effect.
TL;DR: In this paper, the surface electric charge densities associated with current carrying circuits are analyzed in terms of the surface and interface charges present while current flows, and the authors show that the capacitance of a resistor and its adjacent elements is roughly the same as that of the adjacent elements of the open circuit.
Abstract: The significance of the surface electric charge densities associated with current‐carrying circuits is often not appreciated. In general, the conductors of a current‐carrying circuit must have nonuniform surface charge densities on them (1) to maintain the potential around the circuit, (2) to provide the electric field in the space outside the conductors, and (3) to assure the confined flow of current. The surface charges and associated electric field can vary greatly, depending on the location and orientation of other parts of the circuit. We illustrate these ideas with a circuit consisting of a resistor and a battery connected by wires and other conductors, in a geometry that permits solution with a Fourier–Bessel series, while giving flexibility in choice of wire and resistor sizes and location of the battery. Plots of the Poynting vector graphically demonstrate energy flow from the battery to the resistive elements. For a resistor with a large resistance, the potentials and surface charge densities around the current‐carrying circuit are nearly the same as for the open circuit with the resistor removed. For such resistors, the capacitance of a resistor and its adjacent elements, defined in terms of the surface and interface charges present while current flows, is roughly the same as the capacitance of the adjacent elements of the open circuit alone. The discussion is in terms of time‐independent currents and voltages, but applies also to low‐frequency ac circuits.
TL;DR: In this article, the Langevin and Fokker-planck equations of a multivariate continuous Markov process were derived for the multivariate case. But the derivations were driven by a self-consistency condition and some established theorems of random variable theory and ordinary calculus.
Abstract: A novel derivation of the Langevin equation that was recently presented in this journal for a univariate continuous Markov process is generalized here to the more widely applicable multivariate case. The companion multivariate forward and backward Fokker–Planck equations are also derived. The derivations require just a few modest assumptions, and are driven by a self‐consistency condition and some established theorems of random variable theory and ordinary calculus. The constructive nature of the derivations shows why a multivariate continuous Markov process must evolve according to equations of the canonical Langevin and Fokker–Planck forms, and also sheds new light on some uniqueness issues. The need for self‐consistency in the time‐evolution equations of both Markovian and non‐Markovian stochastic processes is emphasized, and it is pointed out that for a great many non‐Markovian processes self‐consistency can be ensured most easily through the multivariate Markov theory.
TL;DR: In this article, a simple theory using Faraday's law and the Lorentz force was proposed to analyze the effect of magnetic damping on an aluminum plate moving on a horizontal air track as it passes between the poles of a horseshoe magnet.
Abstract: A simple theory is proposed using Faraday’s law and the Lorentz force to analyze the effect of magnetic damping on an aluminum plate moving on a horizontal air track as it passes between the poles of a horseshoe magnet. The position, velocity, and acceleration of the nonmagnetic conducting plate are measured as a function of time using a motion detector. Using some simplifying assumptions, a theoretical model is obtained in which a single free parameter is used to fit the experimental data. This parameter corresponds to an effective length (LR) in which the eddy current encounters resistance as it moves around a closed path in the conductor. This leads to some interesting, but unexpected, results about the shape and magnitude of induced eddy currents.
Journal Article•
TL;DR: The authors argue that students can be taught to visualize A for simple current distributions and to see A as something with physical significance beyond its bare definition as the "thing whose curl is B".
Abstract: We collect together several ideas that we have found helpful in teaching the magnetic vector potential A. We argue that students can be taught to visualize A for simple current distributions and to see A as something with physical significance beyond its bare definition as the ‘‘thing whose curl is B.’’
TL;DR: A new approach to understand the twin paradox, based on the conventionality of simultaneity, is presented and illustrated in this paper, and the role of accelerated reference frames in explaining the twins' aging is also critically examined.
Abstract: A new approach to understanding the twin paradox, based on the conventionality of simultaneity, is presented and illustrated. The canonical version of the twin paradox is discussed with reference to its historical origins and the standard explanations given for the differential aging of the twins. It is shown that these are merely specific examples of an infinite class of possible accounts, none of which is privileged. The bounds of this class are given a novel geometrical interpretation. Nonstandard versions of the twin paradox are discussed, and the conventionality of the simultaneity approach is generalized. The role of accelerated reference frames in explaining the twins’ aging is also critically examined. The application of the conventionality of simultaneity to the twin paradox hopefully provides a way to settle the often discussed issue of the twins’ differential aging.
TL;DR: In this paper, the linear charge density on a straight segment of thin charged conducting wire was determined using several different methods, but none yields entirely convincing results and it appears that the problem itself may be ill-posed.
Abstract: We attempt to determine the linear charge density on a finite straight segment of thin charged conducting wire. Several different methods are presented, but none yields entirely convincing results, and it appears that the problem itself may be ill‐posed.
TL;DR: In this article, it was argued that in the regime of the common playground swing the driving terms dominate and the pumping of a swing in the standing position is best characterized as a driven oscillator.
Abstract: The pumping of a swing from a standing position is modeled as a rigid object forced to rotate back and forth at the lower ends of supporting ropes. This model after some approximations leads to a harmonic oscillator with driving and parametric terms. It is then argued that in the regime of the common playground swing the driving terms dominate and the pumping of a swing in the standing position is best characterized as a driven oscillator. Examination of the relative phase of the swinger and the swing also supports this conclusion. This model is compared with earlier work which claimed that the swing pumped by a standing swinger is characterized as a parametric oscillator. Simple demonstrations of both mechanisms are described. A comparison of pumping while standing and seated is also made.
TL;DR: In this paper, a new approach to thermodynamic entropy is proposed to supplement traditional coverage at the junior-senior level, which entails a model for which energy spreads throughout macroscopic matter and is shared among microscopic storage modes.
Abstract: A new approach to thermodynamic entropy is proposed to supplement traditional coverage at the junior–senior level. It entails a model for which: (i) energy spreads throughout macroscopic matter and is shared among microscopic storage modes; (ii) the amount and/or nature of energy spreading and sharing changes in a thermodynamic process; and (iii) the degree of energy spreading and sharing is maximal at thermodynamic equilibrium. A function S that represents the degree of energy spreading and sharing is defined through a set of reasonable properties. These imply that S is identical with Clausius’ thermodynamic entropy, and the principle of entropy increase is interpreted as nature’s tendency toward maximal spreading and sharing of energy. Microscopic considerations help clarify these ideas and, reciprocally, these ideas shed light on statistical entropy.
TL;DR: In this article, the survival probability of a particle diffusing within an expanding "cage" and near the edge of a receding "cliff", with death occurring when the diffuser reaches a boundary of the system, is investigated.
Abstract: The survival probabilities of a particle diffusing within an expanding ‘‘cage’’ and near the edge of a receding ‘‘cliff,’’ with death occurring when the diffuser reaches a boundary of the system, are investigated. Especially interesting behavior arises when the position of the boundary recedes from the diffuser as √At. In this case, the recession matches the rms displacement √Dt with which diffusion tends to bring the diffuser to its demise. For both the cage and cliff problems, the survival probability S(t) exhibits a nonuniversal power‐law decay in time, S(t)∼t−β, in which the value of β is dependent on the detailed properties of the boundary motion. Heuristic approaches are applied for the cases of ‘‘slow’’ (A/D≪1) and ‘‘fast’’ (A/D≫1) boundary motion which yield approximate expressions for β. An asymptotic analysis of the survival probability for the cage and cliff problems is also performed. The approximate expressions for β are in good agreement with the exact results for nearly the entire range of ...
TL;DR: In this article, the Luttinger liquid concept of fermion-boson transmutation is presented in a way which does not require a knowledge of quantum field theoretical methods, and exact results for low-temperature thermodynamics and occupation numbers in the microcanonical and the canonical ensemble are compared with the standard grand canonical results.
Abstract: The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low‐energy excitations can be described in terms of bosonic degrees of freedom. This fermion–boson transmutation (FBT) which lies at the heart of the Luttinger liquid concept is presented in a way which does not require a knowledge of quantum field theoretical methods. As the basic facts can already be introduced for noninteracting fermions they are mainly discussed. As an application we use the FBT to present exact results for the low‐temperature thermodynamics and the occupation numbers in the microcanonical and the canonical ensemble. They are compared with the standard grand canonical results.