Showing papers in "American Journal of Physics in 1987"
12,617 citations
1,356 citations
TL;DR: Superfluidity and Superconductivity, Third Edition as discussed by the authors introduces the low-temperature phenomena of superfluidity and superconductivity from a unified viewpoint, and stresses the existence of a macroscopic wave function as a central principle.
Abstract: Superfluidity and Superconductivity, Third Edition introduces the low-temperature phenomena of superfluidity and superconductivity from a unified viewpoint. The book stresses the existence of a macroscopic wave function as a central principle, presents an extensive discussion of macroscopic theories, and includes full descriptions of relevant experimental results throughout. This edition also features an additional chapter on high-temperature superconductors. With problems at the end of most chapters as well as the careful elaboration of basic principles, this comprehensive survey of experiment and theory provides an accessible and invaluable foundation for graduate students studying low-temperature physics as well as senior undergraduates taking specialized courses.
752 citations
TL;DR: An analysis of the conceptual structure of physics identifies essential factual and procedural knowledge which is not explicitly formulated and taught in physics courses as discussed by the authors, leading to the conclusion that mathematical modeling of the physical world should be the central theme of physics instruction.
Abstract: An analysis of the conceptual structure of physics identifies essential factual and procedural knowledge which is not explicitly formulated and taught in physics courses. It leads to the conclusion that mathematical modeling of the physical world should be the central theme of physics instruction. There are reasons to believe that traditional methods for teaching physics are inefficient and substantial improvements in instruction can be achieved by a vigorous program of pedagogical research and development.
553 citations
TL;DR: In this article, the results of a descriptive study extending over a period of several years and involving several hundred university students who were enrolled in a laboratory-based preparatory physics course were presented.
Abstract: Some common errors exhibited by students in interpreting graphs in physics are illustrated by examples from kinematics. These are taken from the results of a descriptive study extending over a period of several years and involving several hundred university students who were enrolled in a laboratory‐based preparatory physics course. Subsequent testing indicated that the graphing errors made by this group of students are not idiosyncratic, but are found in different populations and across different levels of sophistication. This paper examines two categories of difficulty identified in the investigation: difficulty in connecting graphs to physical concepts and difficulty in connecting graphs to the real world. Specific difficulties in each category are discussed in terms of student performance on written problems and laboratory experiments. A few of the instructional strategies that have been designed to address some of these difficulties are described.
529 citations
TL;DR: A simple two-stream theory, in which photons are constrained to be scattered in only two directions, forward and backward, is adequate for interpreting many observations, even quantitatively, and it paves the way for advanced study as mentioned in this paper.
Abstract: Many common observations are inexplicable by single‐scattering arguments: the variation of brightness and color of the clear sky; the brightness of clouds; the whiteness of a glass of milk; the appearance of distant objects; the blueness of light transmitted in snow and other natural ice bodies; the darkening of sand upon wetting. Yet multiple scattering is seldom mentioned in optics textbooks. It is possible to understand many observable phenomena without invoking the complete theory of multiple (incoherent) scattering. A simple two‐stream theory, in which photons are constrained to be scattered in only two directions, forward and backward, is adequate for interpreting many observations, even quantitatively, and it paves the way for advanced study.
233 citations
TL;DR: This paper found that students who had not had college instruction in geometrical optics were frequently unable to relate concepts, principles, and ray tracing techniques that had been taught in class to an actual physical system consisting of an object, a lens or a mirror, and a screen.
Abstract: Student understanding of the real images produced by converging lenses and concave mirrors was investigated both before and after instruction in geometrical optics. The primary data were gathered through interviews in which undergraduates taking introductory physics were asked to perform a set of prescribed tasks based on a simple demonstration. The criterion used to assess understanding was the ability to apply appropriate concepts and principles, including ray diagrams, to predict and explain image formation by an actual lens or mirror. Performance on the tasks, especially by students who had not had college instruction in geometrical optics, suggested the presence of certain naive conceptions. Students who had just completed the study of geometrical optics in their physics courses were frequently unable to relate the concepts, principles, and ray‐tracing techniques that had been taught in class to an actual physical system consisting of an object, a lens or a mirror, and a screen. Many students did not seem to understand the function of the lens, mirror, or screen, nor the uniqueness of the relationship among the components of the optical system. Difficulties in drawing and interpreting ray diagrams indicated inadequate understanding of the concept of a light ray and its graphical representation.
210 citations
TL;DR: In this paper, the authors investigated the thermal efficiency of a reversible heat engine with respect to two characteristic temperatures that are intermediate between the maximum and minimum cycle temperatures T+ and T−.
Abstract: What is the thermal efficiency of a heat engine producing the maximum possible work per cycle consistent with its operating‐temperature range? This question is answered here for four model reversible heat engine cycles. In each case, the work is maximized with respect to two characteristic temperatures that are intermediate between the maximum and minimum cycle temperatures T+ and T−. The maximum‐work efficiencies are found to equal or be well approximated by η*=1−(T−/T+)1/2. Because this efficiency is a function solely of the extreme cycle temperatures, it can be compared easily with the corresponding reversible Carnot cycle efficiency ηc =1−T−/T+. Here, η*, which is a much better guide to the performance of actual heat engines than ηc, is the same efficiency found by Curzon and Ahlborn [Am. J. Phys. 43, 22 (1975)] for a model irreversible heat engine operating at maximum power output. The present results show that η* is more ‘‘universal’’ than had been realized previously. If the work output per cycle i...
207 citations
TL;DR: In this paper, it was shown that the deflection angles and the intensities of the images can be expressed in terms of elliptic integrals, leading to simple approximations in the limiting case of very large deflection angle.
Abstract: We discuss the ‘‘images’’ formed when the light from a distant source suffers a large deflection in the intense gravitational field in the immediate vicinity of a Schwarzschild black hole. The light can circle around the black hole one or several times, and therefore give rise to a sequence of images. We show that the deflection angles and the intensities of the images can be expressed in terms of elliptic integrals, leading to simple approximations in the limiting case of very large deflection angles.
162 citations
TL;DR: In this article, modeling theory was used in the design of a method to teach problem solving in introductory mechanics and a pedagogical experiment to evaluate the effectiveness of the method found positive results.
Abstract: Modeling theory was used in the design of a method to teach problem solving in introductory mechanics. A pedagogical experiment to evaluate the effectiveness of the method found positive results.
149 citations
TL;DR: In this article, a simple theory of magnetic braking in a thin metal strip is proposed and the predictions of the model are compared to experiment and good agreement is obtained. But the experimental tests were conducted by spinning a thin aluminum disk of large radius between the pole pieces of an electromagnet.
Abstract: A simple theory of magnetic braking in a thin metal strip is proposed. The predictions of the model are compared to experiment and good agreement is obtained. The experimental tests were conducted by spinning a thin aluminum disk of large radius between the pole pieces of an electromagnet. A field range of 0 to 150 mT was used.
TL;DR: In this article, the lateral force on a spinning baseball in a wind tunnel has been measured and the magnitude of the force is nearly independent of the orientation of the seams of the ball.
Abstract: The lateral force on a spinning baseball in a wind tunnel has been measured. The magnitude of the force is nearly independent of the orientation of the seams of the ball. The drag coefficient appears to be at most weakly dependent on Reynolds number and to be principally a function of the ratio of the rotational speed of the equator of the ball to the wind tunnel speed. This is to be compared to the work of Briggs, which implies a strong effect of Reynolds number on the drag coefficient.
TL;DR: In this article, students were asked to compare the changes in momentum and kinetic energy of two frictionless dry-ice pucks as they moved rectilinearly under the influence of the same constant force.
Abstract: Student understanding of the impulse‐momentum and work‐energy theorems was assessed by performance on tasks requiring the application of these relationships to the analysis of an actual motion. The participants in the study were undergraduates enrolled in either the honors section of a calculus‐based introductory physics course or in the regular algebra‐based course. The students were asked to compare the changes in momentum and kinetic energy of two frictionless dry‐ice pucks as they moved rectilinearly under the influence of the same constant force. The results of the investigation revealed that most of the students were unable to relate the algebraic formalism learned in class to the simple motion that they observed.
TL;DR: In this paper, it was shown that the notion of predictive completeness is weaker than, and is implied by, the completeness criterion of Einstein, Podolsky, and Rosen.
Abstract: Special relativity demands a locality principle (no instantaneous action at a distance); locality implies Bell’s theorem; quantum mechanics violates Bell’s inequality, therefore, quantum mechanics contradicts relativity! Or so it would seem. It is shown, however, that the locality principle needed for Bell’s theorem is stronger than the simple locality that is needed to satisfy the demands of relativity and that quantum mechanics satisfies the latter. The stronger locality principle is equivalent to the conjunction of simple locality and predictive completeness, and it is the latter principle that fails. The notion of predictive completeness is weaker than, and is implied by, the completeness criterion of Einstein, Podolsky, and Rosen. But the quantum mechanical state description is not only incomplete but incompletable, for any local complete state description would satisfy Bell’s inequality and disagree with experiment.
TL;DR: Relativistic mass is discussed in both a pedagogical and historical context as mentioned in this paper, and it is pointed out that its introduction into the theory of special relativity was much in the way of a historical accident.
Abstract: Relativistic mass is discussed in both a pedagogical and historical context It is pointed out that its introduction into the theory of special relativity was much in the way of a historical accident Gaining widespread use initially in instruction, the use of relativistic mass is showing signs of progressive disfavor An analysis and criticism of the various ways relativistic mass is used in relativity is detailed and special attention is given to the frequent misuse of relativistic mass as an inertia
TL;DR: In this article, the authors describe how instruction based on the observation of actual motions can help students to develop a qualitative understanding of velocity as a continuously varying quantity and uniform acceleration as the ratio of the change in instantaneous velocity to the elapsed time, distinguish the concepts of position, velocity, change of velocity, and acceleration from one another.
Abstract: Results from research on student understanding of velocity and acceleration have been used to guide the development of a conceptual approach to teaching kinematics. This paper describes how instruction based on the observation of actual motions can help students: (1) develop a qualitative understanding of velocity as a continuously varying quantity, of instantaneous velocity as a limit, and of uniform acceleration as the ratio of the change in instantaneous velocity to the elapsed time; (2) distinguish the concepts of position, velocity, change of velocity, and acceleration from one another; and (3) make connections among the various kinematical concepts, their graphical representations, and the motions of real objects. Instructional strategies designed to address specific difficulties identified in the investigation are illustrated by example.
TL;DR: In this paper, questions based on four such research probes were included in the end-of-high-school physics examination undertaken by some 5500 students, and the results obtained give an indication of the extent to which various interpretations of some physical situations are held in a whole population.
Abstract: There has recently been a considerable growth in research probing student understanding in mechanics. Questions based on four such research probes were included in the end‐of‐high‐school physics examination undertaken by some 5500 students. The results obtained give an indication of the extent to which various interpretations of some physical situations are held in a whole population. The possibilities of using research probes as a basis for assessment questions are also illustrated.
TL;DR: In this paper, the problem of two separated, noninteracting spin − 1/2 particles in a state of zero total spin is analyzed using the consistent history interpretation of quantum mechanics and shown to behave in many respects like a classical system.
Abstract: The familiar problem of two separated, noninteracting spin‐ 1/2 particles in a state of zero total spin is analyzed using the consistent history interpretation of quantum mechanics and shown to behave in many respects like a classical system of two noninteracting objects whose individual properties are unknown but strongly correlated with each other. There is no action at a distance between the particles and a measurement on one has no effect whatsoever on the other. However, the result of a measurement of a spin component of one of the particles can be used to infer (correctly) its value prior to the measurement, and also the corresponding spin component of the other particle at all times prior to when that particle interacts with something else. In these respects the quantum system behaves like its classical counterpart. On the other hand, the paradoxical (nonclassical) aspects of the quantum situation seem to be precisely those already present in the quantum theory of a single particle.
TL;DR: In this paper, the introduction to rolling friction is studied in relation to the height that a ball attains rolling up an inclined track after rolling down a given height along another inclined track opposite from the first.
Abstract: The introduction to rolling friction is studied in relation to the height that a ball attains rolling up an inclined track after rolling down a given height along another inclined track opposite from the first. The expressions obtained for a ball rolling down a rectangular inclined track and along a horizontal track are applied to the study of the distance run along two opposed inclined tracks. Different procedures are proposed to determine the coefficient of rolling friction of the ball with the track. The values calculated from the experimental data suggest their dependence with the ball radius.
TL;DR: In this paper, a uniformly accelerated reference frame S is defined as a set of observers who remain at rest with respect to a given observer A who is accelerating at a constant rate with respect the instantaneously comoving inertial frames.
Abstract: A uniformly accelerated reference frame S is defined as a set of observers who remain at rest with respect to a given observer A who is accelerating at a constant rate with respect to the instantaneously comoving inertial frames. The one‐dimensional uniformly accelerated reference frame S is considered. The world lines of A and the other observers making up S are determined. Coordinates useful for describing events in S are carefully defined and the transformation equations between different sets of them are derived. The variation with position in S of the speed and frequency of light waves is determined. The motion of a free‐particle in S is determined. Various phenomena in S, ordinarily associated with general relativity, are considered, in particular the asymmetric aging of twins at rest at different positions and the existence of horizons.
TL;DR: A six-week non-calculus-based introductory course was designed and taught with the intention of promoting students' conceptual understanding of Newtonian mechanics as discussed by the authors, and the course was effective in promoting student crossover to the Newtonian world.
Abstract: A six‐week noncalculus‐based introductory course was designed and taught with the intention of promoting students’ conceptual understanding of Newtonian mechanics. Primary emphasis was placed on (1) laboratories structured to induce Socratic dialogue; (2) lectures stressing a qualitative approach to problem solving, and contrasting Newtonian and students’ non‐Newtonian concepts of motion; (3) videotapes from The Mechanical Universe series. That the course was effective in promoting student crossover to the Newtonian world was suggested by student performance on pre‐ and post‐course mechanics exams.
TL;DR: In this paper, the Schrodinger, Klein-Gordon, and Dirac equations for the hydrogen atom are solved in D dimensions, where D may be noninteger, and for D = 1 the non-degenerate ground state with infinite binding energy is obtained as a limit.
Abstract: The Schrodinger, Klein–Gordon, and Dirac equations for the hydrogen atom are solved in D dimensions, where D may be noninteger. For D=1 the nondegenerate ground state with infinite binding energy is obtained as a limit as D tends to 1 for the Schrodinger equation. The corresponding solution of the Klein–Gordon equation is shown to be unacceptable, contradicting previous work. Unexpectedly, no bound state solutions of the Dirac equation with D=1 are found at all. A few comments are made on the D=3 and 2 cases.
TL;DR: In this paper, the authors proposed a method to measure the conductance of a quantum field in terms of the number of particles present in the field and the amount of interference at the boundary of the field.
Abstract: 1 Introduction.- 1.1. Introduction.- 1.2. Preview of Coming Attractions.- 1.3. The Ordinary Hall Effect.- 1.4. Measuring the Conductance.- 1.5. Introduction to the Quantum Case.- 1.6. Impurity Effects.- 1.7. Gauge Arguments.- 1.8. Inversion Layers.- 1.9. Acknowledgements.- 1.10. Notes.- 1.11. Problems.- A The Integer Effect.- 2 Experimental Aspects and Metrological Applications.- 2.1. Basic Principles.- 2.2. The Devices.- 2.3. The Basic Experiment.- 2.4. Initial Experiments.- 2.5. Precision Measurement Techniques.- 2.6. Quantum Hall Resistors.- 2.7. An Absolute Resistance Standard.- 2.8. The Fine-Structure Constant.- 2.9. Temperature Dependence of ?xx.- 2.10. Temperature Dependence of ?xy.- 2.11. Current Distribution and Edge Effects.- 2.12. Current Dependence and Breakdown.- 2.13. Hall Step Widths and Shapes.- 2.14. Thermomagnetic Transport.- 2.15. Magnetic Moment.- 2.16. Magnetocapacitance.- 2.17. Magneto-Photoresponse.- 2.18. Conclusions.- 2.19. Acknowledgements.- 2.20. Notes.- 3 Effects of Imperfections and Disorder.- 3.1. Introduction.- 3.2. The Impurity Potential.- 3.3. Weak Potential.- 3.4. Scattering Potential.- 3.5. Smooth Potential.- 3.6. Continuum Percolation Model.- 3.7. General Potential.- 3.8. Numerical Studies.- 3.9. Acknowledgements.- 3.10. Notes.- 3.11. Problems.- 4 Topological Considerations.- 4.1. Topological Quantum Numbers.- 4.2. Quantum Hall Effect in a Periodic Potential.- 4.3. Generalization of the Topological Interpretation.- 4.4. Notes.- 5 Field Theory, Scaling and the Localization Problem.- 5.1. Introduction.- 5.2. Basic Notions.- 5.3. The Search for the Principle.- 5.4. Structure of the Effective Field Theory.- 5.5. Instantons and Scaling.- 5.6. Notes.- B: The Fractional Effect.- 6 Experimental Aspects.- 6.1. Introduction.- 6.2. Conditions for the Observation of the FQHE and the Choice of Semiconductor Systems.- 6.3. The Fractional Quantum Hall Effect.- 6.4. Magneto-Transport in Two Dimensions.- 6.5. Future Experiments.- 6.6. Acknowledgements.- 6.7. Notes.- 7 Elementary Theory: The Incompressible Quantum Fluid.- 7.1. Introduction.- 7.2. Quantized Motion of Small Numbers of Electrons.- 7.3. Variational Ground State.- 7.4. Computational Methods.- 7.5. Fractionally Charged Quasiparticles.- 7.6. Exactness of the Fractional Quantum Hall Effect.- 7.7. More Than One Quasiparticle.- 7.8. Conclusions.- 7.9. Acknowledgements.- 8 The Hierarchy of Fractional States and Numerical Studies.- 8.1. Introduction.- 8.2. Pseudopotential Description of Interacting Particles with the Same Landau Index.- 8.3. The Principle Incompressible States: A Non-Variational Derivation.- 8.4. Quasiparticle and Quasihole Excitations.- 8.5. The Hierarchy of Quasiparticle-Quasihole Fluids.- 8.6. Translationally Invariant Geometries for Numerical Studies.- 8.7. Ground-State Energy Studies.- 8.8. Pair Correlations and the Structure Factors.- 8.9. Quasiparticle Excitations.- 8.10. Collective Excitations.- 8.11. Acknowledgements.- 9 Collective Excitations.- 9.1. Introduction.- 9.2. Density Waves as Elementary Excitations.- 9.3. Collective Modes in the FQHE.- 9.4. Magnetophonons and Magnetorotons.- 9.5. Further Superfluid Analogies: Vortices.- 9.6. Quasi-Excitons.- 9.7. Magnetoplasmons and Cyclotron Resonance.- 9.8. Other Collective Modes.- 9.9. Role of Disorder.- 9.10. Acknowledgements.- 9.11. Notes.- 9.12. Problems.- C: The Quantum Hall Effect.- 10 Summary, Omissions and Unanswered Questions.- 10.1. Integer Effect at Zero Temperature.- 10.2. IQHE at Finite Temperatures.- 10.3. Metrology.- 10.4. Basic Picture of the Fractional Effect.- 10.5. Remarks on the Neglect of Landau Level Mixing.- 10.6. Wanted: More Experiments.- 10.7. Towards a Landau-Ginsburg Theory of the FQHE.- 10.8. Acknowledgements.- 10.9. Notes.- 10.10. Problems.- Appendix Recent Developments.- A.1. Introduction.- A.2. Off-Diagonal Long-Range Order.- A.3. Ring Exchange Theories.- A.5. Even-Denominator and Spin-Reversed States.- A.6. Spin-Reversed Hierarchy.- A.7. Summary and Conclusions.- References.
TL;DR: The Resource Letter as discussed by the authors provides a guide to the literature on the foundations of quantum mechanics over approximately the past 20 years, including Bell's theorem, interpretation of the quantum state concept, the theory of measurement, and experimental tests of fundamental aspects of quantum theory of matter and the electromagnetic field.
Abstract: This Resource Letter provides a guide to the literature on the foundations of quantum mechanics over approximately the past 20 years. Topics covered include Bell’s theorem, interpretation of the quantum state concept, the theory of measurement, and experimental tests of fundamental aspects of the quantum theory of matter and the electromagnetic field. The letter E after an item indicates elementary level of material of general interest to persons becoming informed in the field. The letter I, for intermediate level, indicates material of somewhat more specialized nature; and the letter A indicates rather specialized or advanced material. An asterisk (*) indicates those articles to be included in an accompanying Reprint Book.
TL;DR: In this paper, two concrete examples of knowledge structures in the field of electricity and magnetism are compared, and an experiment is also described, in which the actual knowledge structure of beginning students was studied.
Abstract: Problem solving in physics requires a certain quantity of knowledge of the subject matter: principles, procedures, etc. In addition, the problem solver must be able to access these principles and procedures in a given situation. Investigations have shown that failure in problem solving is often caused by lack of availability of knowledge, and also that availability is closely related to the organization of knowledge in memory. Opinions differ, however, on whether the optimal form of this organization should be centered around problem types or arranged in a hierarchical way. In this study two concrete examples of knowledge structures in the field of electricity and magnetism are compared. An experiment is also described, in which the actual knowledge structure of beginning students was studied. The outcome indicates that students with good results in problem solving organize their knowledge more in accordance with problem types than do students with poor results. The results of the experiment are discussed in the light of the two knowledge structures described. The possible role of these structures in physics teaching is treated in the final paragraph
TL;DR: In this paper, five simple nonlinear physical systems exhibiting chaotic dynamics are described, specifically designed for demonstration purposes to illustrate the ideas of period doubling, subharmonics, noisy periodicity, and intermittent and continuous chaos.
Abstract: Five simple nonlinear physical systems exhibiting chaotic dynamics are described. They are specifically designed for demonstration purposes to illustrate the ideas of period doubling, subharmonics, noisy periodicity, and intermittent and continuous chaos.
TL;DR: In this article, it was pointed out that the usual treatment of the delta function potential in the one-dimensional Dirac equation is incorrect and steps leading to such incorrect results are identified.
Abstract: It is pointed out that the usual treatment of the delta function potential in the one‐dimensional Dirac equation is incorrect. Steps leading to such incorrect results are identified. The delta function potential is also examined from the limiting case of a nonlocal potential V(x,x’). In this general case, the strength g=∫dx ∫dx’V(x,x’) is no longer a sufficient parameter to characterize a potential.
TL;DR: In this paper, the coherent states of a harmonic oscillator are introduced following Schrodinger's definition and the equivalence with other definitions is established, and the basic properties of these states are discussed in some detail.
Abstract: The coherent states of a harmonic oscillator are introduced following Schrodinger’s definition and the equivalence with other definitions is established. The basic properties of these states are discussed in some detail.
TL;DR: In the mid-1700s a debate raged between Jean d'Alembert, Leonhard Euler, and Daniel Bernoulli concerning the proper solution to the classical wave equation as mentioned in this paper.
Abstract: In the mid‐1700s a debate raged between Jean d’Alembert, Leonhard Euler, and Daniel Bernoulli concerning the proper solution to the classical wave equation. This controversy was partially solved by Lagrange and, more conclusively, by Fourier (50 years later) and it provides an interesting case study for the role of mathematics in the modeling of physical phenomena. Of particular note in this debate, was the meaning of boundary conditions. The controversy is summarized from the point of view of this mathematical physics perspective.
TL;DR: In this paper, a geometrical model of the Foucault pendulum is presented, which corrects some common misconceptions concerning the "fixed" plane in which the pendulum oscillates.
Abstract: A geometrical model of the Foucault pendulum is presented, which corrects some common misconceptions concerning the ‘‘fixed’’ plane in which the pendulum oscillates. It is shown visually, and by the use of metric geometry, that the direction of oscillation of the pendulum undergoes a parallel displacement as it moves along the Earth’s spherical surface. However, this direction of oscillation is not fixed relative to the stars.