Showing papers in "American Journal of Physics in 2002"

Optical Properties of Solids

Abstract: Preface 1. Introduction 2. Classical propagation 3. Interband absorption 4. Excitons 5. Luminescence 6. Semiconductor quantum wells 7. Free electrons 8. Molecular materials 9. Luminescence centres 10. Phonons 11. Nonlinear optics Appendix A: Electromagnetism in dielectrics Appendix B: Quantum theory of radiative absorption and emission Appendix C: Band theory Appendix D: Semiconductor p-i-n diodes

The relationship between mathematics preparation and conceptual learning gains in physics: A possible “hidden variable” in diagnostic pretest scores

Abstract: There have been many investigations into the factors that underlie variations in individual student performance in college physics courses. Numerous studies report a positive correlation between students’ mathematical skills and their exam grades in college physics. However, few studies have examined students’ learning gain resulting from physics instruction, particularly with regard to qualitative, conceptual understanding. We report on the results of our investigation into some of the factors, including mathematical skill, that might be associated with variations in students’ ability to achieve conceptual learning gains in a physics course that employs interactive-engagement methods. It was found that students’ normalized learning gains are not significantly correlated with their pretest scores on a physics concept test. In contrast, in three of the four sample populations studied it was found that there is a significant correlation between normalized learning gain and students’ preinstruction mathematics skill. In two of the samples, both males and females independently exhibited the correlation between learning gain and mathematics skill. These results suggest that students’ initial level of physics concept knowledge might be largely unrelated to their ability to make learning gains in an interactive-engagement course; students’ preinstruction algebra skills might be associated with their facility at acquiring physics conceptual knowledge in such a course; and between-class differences in normalized learning gain may reflect not only differences in instructional method, but student population differences (“hidden variables”) as well.

Classical analog of electromagnetically induced transparency

Abstract: We present a classical analog of electromagnetically induced transparency (EIT). In a system of just two coupled harmonic oscillators subject to a harmonic driving force, we reproduce the phenomenology observed in EIT. We also describe a simple experiment with two linearly coupled RLC circuits which can be incorporated into an undergraduate laboratory.

A simple model of quantum trajectories

Abstract: Quantum trajectory theory, developed largely in the quantum optics community to describe open quantum systems subjected to continuous monitoring, has applications in many areas of quantum physics. I present a simple model, using two-level quantum systems (q-bits), to illustrate the essential physics of quantum trajectories and how different monitoring schemes correspond to different “unravelings” of a mixed state master equation. I also comment briefly on the relationship of the theory to the consistent histories formalism and to spontaneous collapse models.

Synchronization of metronomes

Abstract: Synchronization is a common phenomenon in physical and biological systems. We examine the synchronization of two (and more) metronomes placed on a freely moving base. The small motion of the base couples the pendulums causing synchronization. The synchronization is generally in-phase, with antiphase synchronization occurring only under special conditions. The metronome system provides a mechanical realization of the popular Kuramoto model for synchronization of biological oscillators, and is excellent for classroom demonstrations and an undergraduate physics lab.

Nine formulations of quantum mechanics

Abstract: Nine formulations of nonrelativistic quantum mechanics are reviewed. These are the wavefunction, matrix, path integral, phase space, density matrix, second quantization, variational, pilot wave, and Hamilton–Jacobi formulations. Also mentioned are the many-worlds and transactional interpretations. The various formulations differ dramatically in mathematical and conceptual overview, yet each one makes identical predictions for all experimental results.

An experiment to measure Mie and Rayleigh total scattering cross sections

Abstract: We present an undergraduate-level experiment using a conventional absorption spectrophotometer to measure the wavelength dependence of light scattering from small dielectric spheres suspended in water. The experiment yielded total scattering cross-section values throughout the visible region that were in good agreement with theoretical values predicted by the Rayleigh and Mie theories.

Teaching quantum mechanics on an introductory level

Abstract: We present a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. In the context of virtual laboratories, the students discover from the very beginning how quantum phenomena deviate from our classical everyday experience. The results of the evaluation of the course show that most of the students acquired appropriate quantum mechanical conceptions, and that many of the common misconceptions encountered in traditional instruction have been avoided.

The effects of an interactive computer-based simulation prior to performing a laboratory inquiry-based experiment on science teachers' conceptual understanding of physics

Abstract: This paper investigated how use of an Interactive Computer-Based Simulation (ICBS) prior to performing a Laboratory Inquiry-Based Experiment (LIBE), in a conceptually oriented physics course, affects students' conceptual development of some physics ideas in Mechanics, Waves/Optics and Thermal Physics. ICBS and LIBE were selected from previous research studies, or developed to challenge students' ideas. These were integrated into a sixteen-week semester physics content class. The 13 science teachers who participated in the study were not physicists. The data collection process was based upon a self-control design where each participant alternated between treatment and control presentations. Interviews (pre-, inter-, and post-interviews) and conceptual tests (pre-, inter- and post-tests) were used, for each module presented in the class. Each one of the three physics areas had four modules, and for each module the participants responded to the three tests and participated in the three interviews. Both the tests and the interviews were statistically analyzed for (a) any significant changes in students' ability to make “scientifically accepted” predictions (a physics textbook was used as criterion) and give “scientifically accepted” explanations regarding a LIBE, after they had used an ICBS, (b) the extent to which students' experience with an ICBS, before and after the conduction of a LIBE, fostered conceptual change, and (c) investigating students' attitudes towards ICBS, LIBE, or both ICBS and LIBE, and which of them promotes more positive attitudes towards the physics areas of the study. Results indicated that students that used an ICBS before a LIBE performed significantly better than students who did not use an ICBS before a LIBE. The use of an ICBS improved students' ability to make “scientifically accepted” predictions and give “scientifically accepted” explanations regarding a LIBE, and fostered a significant conceptual change in all three physics areas that were selected for this study. Students' attitudes towards Physics, ICBS, LIBE, and both ICBS and LIBE were all found positive.

From Lorenz to Coulomb and other explicit gauge transformations

Abstract: The main purposes of this paper are (i) to illustrate explicitly by a number of examples the gauge functions χ(x,t) whose spatial and temporal derivatives transform one set of electromagnetic potentials into another equivalent set; and (ii) to show that, whatever propagation or nonpropagation characteristics are exhibited by the potentials in a particular gauge, the electric and magnetic fields are always the same and display the experimentally verified properties of causality and propagation at the speed of light. The example of the transformation from the Lorenz gauge (retarded solutions for both scalar and vector potential) to the Coulomb gauge (instantaneous, action-at-a-distance, scalar potential) is treated in detail. A transparent expression is obtained for the vector potential in the Coulomb gauge, with a finite nonlocality in time replacing the expected spatial nonlocality of the transverse current. A class of gauges (v-gauge) is described in which the scalar potential propagates at an arbitrary speed ν relative to the speed of light. The Lorenz and Coulomb gauges are special cases of the v-gauge. The last examples of gauges and explicit gauge transformation functions are the Hamiltonian or temporal gauge, the nonrelativistic Poincare or multipolar gauge, and the relativistic Fock–Schwinger gauge.

Transforming the lecture-hall environment: The fully interactive physics lecture

Abstract: Numerous reports suggest that learning gains in introductory university physics courses may be increased by “active-learning” instructional methods. These methods engender greater mental engagement and more extensive student–student and student–instructor interaction than does a typical lecture class. It is particularly challenging to transfer these methodologies to the large-enrollment lecture hall. We report on seven years of development and testing of a variant of Peer Instruction as pioneered by Mazur that aims at achieving virtually continuous instructor–student interaction through a “fully interactive” physics lecture. This method is most clearly distinguished by instructor–student dialogues that closely resemble one-on-one instruction. We present and analyze a detailed example of such classroom dialogues, and describe the format, procedures, and curricular materials required for creating the desired lecture-room environment. We also discuss a variety of assessment data that indicate strong gains in...

Students do not overcome conceptual difficulties after solving 1000 traditional problems

Abstract: The relation between traditional physics textbook problem solving and conceptual understanding was investigated. The number of problems a student solved, as estimated by students themselves, ranged from 300 to 2900 with an average of about 1500. The students did not have much difficulty in using physics formulas and mathematics. However, we found that they still had many of the well-known conceptual difficulties with basic mechanics, and there was little correlation between the number of problems solved and conceptual understanding. This result suggests that traditional problem solving has a limited effect on conceptual understanding.

Time in quantum mechanics

Abstract: Time is often said to play an essentially different role from position in quantum mechanics: whereas position is represented by a Hermitian operator, time is represented by a c-number. This difference is puzzling and has given rise to a vast literature and many efforts at a solution. It is argued that the problem is only apparent and that there is nothing in the formalism of quantum mechanics that forces us to treat position and time differently. The apparent problem is caused by the dominant role point particles play in physics and can be traced back to classical mechanics.

Neutron Interferometry: Lessons in Experimental Quantum Mechanics

Abstract: 1. Introduction 2. Neutron interferometers and apparatus 3. Neutron interactions and the coherent scattering length 4. Coherence properties 5. Spinor symmetry and spin superposition 6. Topological and geometric phases 7. Gravitational, non-inertial, and motional effects 8. Search for speculative effects 9. Solid State physics applications 10. Perfect crystal neutron optics 11. Interpretational questions 12. References

Student understanding of the first law of thermodynamics: Relating work to the adiabatic compression of an ideal gas

Abstract: We report on an investigation of student understanding of the first law of thermodynamics. The students involved were drawn from first-year university physics courses and a second-year thermal physics course. The emphasis was on the ability of the students to relate the first law to the adiabatic compression of an ideal gas. Although they had studied the first law, few students recognized its relevance. Fewer still were able to apply the concept of work to account for a change in temperature in an adiabatic process. Instead most of the students based their predictions and explanations on a misinterpretation of the ideal gas law. Even when ideas of energy and work were suggested, many students were unable to give a correct analysis. They frequently failed to differentiate the concepts of heat, temperature, work, and internal energy. Some of the difficulties that students had in applying the concept of work in a thermal process seemed to be related to difficulties with mechanics. Our findings also suggest that a misinterpretation of simple microscopic models may interfere with student ability to understand macroscopic phenomena. Implications for instruction in thermal physics and in mechanics are discussed.

Quantum mechanics for everyone: Hands-on activities integrated with technology

Abstract: Quantum mechanics is frequently taught toward the end of the first year of physics if it is taught at all. Many physics instructors believe that quantum mechanics is a very abstract subject that cannot be understood until students have learned much of classical physics. We are challenging this belief by creating instructional materials for quantum mechanics that can be integrated throughout the first physics course. In addition, we have transferred some of the materials and the basic approach to higher-level courses. The result is a hands-on approach to learning and teaching quantum mechanics for a broad spectrum of students. We describe some of our materials and the results of using these materials with students.

College Physics Students' Epistemological Self-Reflection and Its Relationship to Conceptual Learning.

Abstract: Students should develop self-reflection skills and appropriate views about knowledge and learning, both for their own sake and because these skills and views may be related to improvements in conceptual understanding. We explored the latter issue in the context of an introductory physics course for first-year engineering honors students. As part of the course, students submitted weekly reports, in which they reflected on how they learned specific physics content. The reports by 12 students were analyzed for the quality of reflection and some of the epistemological beliefs they exhibited. Students’ conceptual learning gains were measured with standard survey instruments. We found that students with high conceptual gains tend to show reflection on learning that is more articulate and epistemologically sophisticated than students with lower conceptual gains. Some implications for instruction are suggested.

Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory

Abstract: We use polarization-entangled photon pairs to demonstrate quantum nonlocality in an experiment suitable for advanced undergraduates. The photons are produced by spontaneous parametric downconversion using a violet diode laser and two nonlinear crystals. The polarization state of the photons is tunable. Using an entangled state analogous to that described in the Einstein–Podolsky–Rosen paradox, we demonstrate strong polarization correlations of the entangled photons. Bell’s idea of a hidden variable theory is presented by way of an example and compared to the quantum prediction. A test of the Clauser, Horne, Shimony, and Holt version of the Bell inequality finds S=2.307±0.035, in clear contradiction of hidden variable theories. The experiments described can be performed in an afternoon.

Anomalies in quantum mechanics: The 1/r(2) potential

Abstract: An anomaly is said to occur when a symmetry that is valid classically becomes broken as a result of quantization. Although most manifestations of this phenomenon are in the context of quantum field theory, there are at least two cases in quantum mechanics—the two-dimensional delta function interaction and the 1/r2 potential. The former has been treated in this journal; in this article we discuss the physics of the latter together with experimental consequences.

Testing the development of student conceptual and visualization understanding in quantum mechanics through the undergraduate career

Abstract: In order to probe various aspects of student understanding of some of the core ideas of quantum mechanics, and especially how they develop over the undergraduate curriculum, we have developed an assessment instrument designed to test conceptual and visualization understanding in quantum theory. We report data obtained from students ranging from sophomore-level modern physics courses, through junior–senior level quantum theory classes, to first year graduate quantum mechanics courses in what may be the first such study of the development of student understanding in this important core subject of physics through the undergraduate career. We discuss the results and their possible relevance to the standard curriculum as well as to the development of new curricular materials.

When physical intuition fails

Abstract: We analyze the problem-solving strategies of physics professors in a case where their physical intuition fails. A nonintuitive introductory-level problem was identified and posed to twenty physics professors. The problem placed the professors in a situation often encountered by students, and their response highlights the importance of intuition and experience in problem solving. Although professors had difficulty in solving the problem under the time constraint, they initially employed a systematic approach, for example, visualizing the problem, considering various conservation laws, and examining limiting cases. After finding that familiar techniques were not fruitful, they made incorrect predictions based on one of two equally important factors. In contrast, other more familiar problems that require the consideration of two important principles (for example, conservation of both energy and momentum for a ballistic pendulum) were quickly solved by the same professors. The responses of students who were given the same problem reflected no overarching strategies or systematic approaches, and a much wider variety of incorrect responses were given. This investigation highlights the importance of teaching effective problem-solving heuristics, and suggests that instructors assess the difficulty of a problem from the perspective of beginning students.

Grip-slip behavior of a bouncing ball

Abstract: Measurements of the normal reaction force and the friction force acting on an obliquely bouncing ball were made to determine whether the friction force acting on the ball is due to sliding, rolling, or static friction. At low angles of incidence to the horizontal, a ball incident without spin will slide throughout the bounce. At higher angles of incidence, elementary bounce models predict that the ball will start to slide, but will then commence to roll if the point of contact on the circumference of the ball momentarily comes to rest on the surface. Measurements of the friction force and ball spin show that real balls do not roll when they bounce. Instead, the deformation of the contact region allows a ball to grip the surface when the bottom of the ball comes to rest on the surface. As a result the ball vibrates in the horizontal direction causing the friction force to reverse direction during the bounce. The spin of the ball was found to be larger than that due to the friction force alone, a result that can be explained if the normal reaction force acts vertically through a point behind the center of the ball.

Deformation quantization in the teaching of quantum mechanics

Abstract: We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages that make its consideration worthwhile. In particular, it sheds new light on the relation between classical and quantum mechanics. We demonstrate how it can be used to solve specific problems and clarify its relation to conventional quantization and path integral techniques. We also discuss its recent applications in relativistic quantum field theory.

Model analysis of fine structures of student models: An example with Newton’s third law

Abstract: In problem-solving situations, the contextual features of the problems affect student reasoning. Using Newton’s third law as an example, we study the role of context in students’ uses of alternative conceptual models. We have identified four contextual features that are frequently used by students in their reasoning. Using these results, a multiple-choice survey was developed to probe the effects of the specific contextual features on student reasoning. Measurements with this instrument show that different contextual features can affect students’ conceptual learning in different ways. We compare student data from different populations and instructions and discuss the implications.

Measurements of the horizontal coefficient of restitution for a superball and a tennis ball

Abstract: When a ball is incident obliquely on a flat surface, the rebound spin, speed, and angle generally differ from the corresponding incident values. Measurements of all three quantities were made using a digital video camera to film the bounce of a tennis ball incident with zero spin at various angles on several different surfaces. The maximum spin rate of a spherical ball is determined by the condition that the ball commences to roll at the end of the impact. Under some conditions, the ball was found to spin faster than this limit. This result can be explained if the ball or the surface stores energy elastically due to deformation in a direction parallel to the surface. The latter effect was investigated by comparing the bounce of a tennis ball with that of a superball. Ideally, the coefficient of restitution (COR) of a superball is 1.0 in both the vertical and horizontal directions. The COR for the superball studied was found to be 0.76 in the horizontal direction, and the corresponding COR for a tennis ball was found to vary from −0.51 to +0.24 depending on the incident angle and the coefficient of sliding friction.

Investigating Student Understanding of Quantum Physics: Spontaneous Models of Conductivity.

Abstract: Students are taught several models of conductivity, both at the introductory and the advanced level. From early macroscopic models of current flow in circuits, through the discussion of microscopic particle descriptions of electrons flowing in an atomic lattice, to the development of microscopic nonlocalized band diagram descriptions in advanced physics courses, they need to be able to distinguish between commonly used, though sometimes contradictory, physical models. In investigations of student reasoning about models of conduction, we find that students often are unable to account for the existence of free electrons in a conductor and create models that lead to incorrect predictions and responses contradictory to expert descriptions of the physics. We have used these findings as a guide to creating curriculum materials that we show can be effective helping students to apply the different conduction models more effectively.

Demonstration of negative group delays in a simple electronic circuit

Abstract: We present a simple electronic circuit that produces negative delays. When a pulse is sent to the circuit as input, the output is a pulse with a similar wave form that is shifted forward in time. The advance time or negative delay can be increased to the order of seconds so that we can observe the advance with the naked eye by observing two light emitting diodes that are connected to the input and the output. The negative group delay in the electronic circuit shares the same mechanism with superluminal light propagation, where the group velocity exceeds the speed of light or even becomes negative.

Resource Letter: FMMLS-1: Friction at macroscopic and microscopic length scales

Abstract: This Resource Letter provides a guide to the literature on the fundamental origins of friction. Books, reviews, and journal articles are cited for the following topics: History of friction and tribology, the adhesion theory of macroscopic friction, first principles’ treatments of frictional energy dissipation at the atomic level, experimental methods for studying friction at the atomic-scale, stick-slip phenomena and lattice commensurability effects.

Understanding Probabilistic Interpretations of Physical Systems: A Prerequisite to Learning Quantum Physics.

Abstract: Probability plays a critical role in making sense of quantum physics, but most science and engineering undergraduates have very little experience with the topic. A probabilistic interpretation of a physical system, even at a classical level, is often completely new to them, and the relevant fundamental concepts such as the probability distribution and probability density are rarely understood. To address these difficulties and to help students build a model of how to think about probability in physical systems, we have developed a set of hands-on tutorial activities appropriate for use in a modern physics course for engineers. We discuss some student difficulties with probability concepts and an instructional approach that uses a random picture metaphor and digital video technology.