bluuebunny/crossref_metadata_2025 huggingface dataset:
Bow and arrow dynamics
Authors: Marlow W. C.
Published: March 2005

Past analyses of bow and arrow dynamics have assumed the string to be inextensible. This results in predictions of efficiencies that are significantly higher than measured values (efficiencies over 90% are predicted versus 70% to 85% for measurements, circa 1960). The present analysis allows for an elastic string. It is found that arrow exit then takes place when the string and bow limbs still have substantial kinetic energy, and therefore this energy is unavailable for kinetic energy of the arrow. Moreover, the potential energy remaining in the string and bow limb system can also reduce the amount of energy available for the arrow. For the Hickman model of a long bow used in this study, the elastic string prediction of efficiency is 78%, whereas the inelastic prediction is 92%. The analysis utilizes a Lagrangian distributed mass formulation to develop the governing equations of motion and to generate an equivalent point mass model. The equations of motion were numerically integrated to obtain efficiency, arrow velocity, virtual masses, string tension, string extension, arrow exit time, string and limb potential energies, system momentum, and the dynamic force required to hold the bow handle stationary. Estimates of the effect of air resistance were made and found to be less than 2% of the total system energy. The vibratory dynamics of the string and bow limbs subsequent to arrow exit was analyzed. The results of the elastic string considerations are in reasonable agreement with experimental data and negate the usual explanation for the long-standing discrepancy between theory and experiment as due to air resistance and hysteresis losses in the string and bow limbs.
Augmenting course quality through the use of videotapes
Authors: Shult Donald
Published: March 2005

Several ways of easily producing and using videotapes to improve general physics classes have been developed. These take a minimum of equipment and have been shown to be highly successful.
Elementary derivation of the radiation field from an accelerated charge
Authors: Holstein Barry R. , Swift Arthur R.
Published: March 2005

Using only the equivalence principle and elementary electrodynamics we calculate the radiation from an accelerating charge in a direction perpendicular to its motion.
Atomism from Newton to Dalton
Authors: Schofield Robert E.
Published: March 2005

Newton’s achievements, both in the Principia and the Opticks, were firmly rooted in an atomistic theory of matter, resembling aspects of modern nuclear physics in its emphasis on fundamental particles held in differing arrays by short and long-range forces. Marred by premature sophistication, its parameters of particle size and shape and interparticulate forces could not be quantified. Although it inspired many scientists of the eighteenth century and was further developed into a qualitative theory which intrigued scientists into the twentieth century, Newtonian unitary corpuscular (or atomistic) matter theory was replaced for most investigators by a variety of substances for which the particulate nature was of less concern than the character of their gross behavior. It was on this basis that Dalton developed his new (chemical) atomism, reifying the multiplicity of substances with separate atoms for each, distinguished by operational differences in their chemical atomic weights.
Mechanical resonance of a plastic strip
Authors: Ayers R. Dean
Published: March 2005

An experiment to illustrate mechanical resonance has been designed for use in lower division laboratories. The apparatus and procedure have deliberately been kept as simple as possible. The basic experiment yields measurements of amplitude versus driving frequency, but a fairly simple elaboration allows for measurements of the phase lag as well.
Science for elementary school teachers: A quantitative approach
Authors: Goldberg H. S. , Boulanger F. D.
Published: March 2005

A quantitative hands-on approach for teaching science to elementary school teachers is described. The materials has been presented to students in undergraduate elementary teacher education and to teachers in the Chicago metropolitan area, the latter with NSF support. The program has been successful not only in stimulating interest in science teaching but was resulted in measured imporvement in the science skills of elementary school children.
Topological physics illustrated in the laboratory
Authors: Rosenbaum T. F. , Stein D. L.
Published: March 2005

Topological ideas can be used to predict a variety of textures and defects in condensed matter systems under certain conditions. Liquid crystals exhibit a rich variety of such textures, and provide an accessible system on which to perform tabletop experiments. One means of creating and observing various liquid crystal textures is described, and results of these observations are presented.
Using simulation on programmable pocket calculators in computer- assisted instruction
Authors: Riggi F.
Published: March 2005

Different programs have been developed for the simulation of physics experiments by using TI-57 programmable calculators. Two of these programs, describing the simulation of a successive radioactive decay and the random motion of a gas molecule, are presented.
Microcomputer listens to the coefficient of restitution
Authors: Smith P. A. , Spencer C. D. , Jones D. E.
Published: March 2005

A previous article in this Journal titled ’’Listening to the coefficient of restitution,’’ describes a procedure for determining the coefficient by measuring the times between bounces for a ball dropped onto a hard surface. The procedure has been completely computerized. A microcomputer collects and sends data to a large computer where analysis is done and graphical output is generated. The data collection hardware and software are described. Results are illustrated.
Bohlin’s and other integrals for the damped harmonic oscillator
Authors: Gettys W. Edward , Ray John R. , Breitenberger Ernst
Published: March 2005

We discuss several little known and interesting integrals of the motion for the damped harmonic oscillator.
Quantum mechanics of the Einstein–Hopf model
Authors: Milonni P. W.
Published: March 2005

The Einstein–Hopf model for the thermodynamic equilibrium between the electromagnetic field and dipole oscillators is considered within the framework of quantum mechanics. Essential to the consistency of the theory is the fluctuation–dissipation theorem connecting the radiation reaction with the zero-point electromagnetic field. The well-known ’’particle’’ term in the Einstein fluctuation formula is shown to be aconsequence of the quantum-mechanical zero-point oscillations of the field and the dipole radiators. Both the wave and particle aspects of the fluctuation formula are interpreted in terms of the fundamental absorption and emission processes.
1981 Robert A. Millikan Lecture, Steven’s Point, Wisconsin, 17 June 1981 ’’Are we overlooking something?’’
Authors: Bartlett Albert A.
Published: March 2005

In recent decades great strides have been made in advancing the analytical level and content of introductory college physics for scientists and engineers. In order to accomodate these advances, ’’nonessential’’ or ’’less essential’’ materials may be sidetracked, de-emphasized, or omitted. Perhaps the most common candidates for characterization as nonessential are the elementary examples and applications of physics from the world of everyday experience. Although mature physicists see great beauty and understanding in analysis, a heavy classroom emphasis on mathematical analysis may give students the impression that the sole goal of elementary physics is the development of the skills of abstract analysis. Analysis is essential! But if our students are to become more than mere analysts, we must share with them some of the fun, fascination, and understanding that can be found in the physics of everyday phenomena, in the applications of physics in other disciplines, and in the interface between science and society. Examples the author has found to be useful are given.
High-sensitivity microwave optics
Authors: Nunn W. M.
Published: March 2005

Microwave optics experiments operating at a 3.33-cm wavelength (9 GHz) are described that have an overall signal gain of 58 dB, which is achieved by using a 1000-Hz square-wave modulated reflex klystron and a high-gain, narrowband amplifier following a point-contact detector. A metal-plate electromagnetic lens is employed that has a gain of 22.5 dB relative to an isotropic radiator, produces a beam collimated to within 12 deg between half-power points, and has a 3.7% bandwidth around a center frequency of 9 GHz. This basic system was used to developed microwave versions of the Michelson interferometer, Bragg reflection, Brewter’s law and total internal reflection, and Young’s interference experiment. Measured radiation intensities for four signal sources are shown to lie well within Federal performance regulations established in 1971.
Generation of conical beams of light for smoke-chamber demonstrations
Authors: Stanley Eric
Published: March 2005

Various mirror arrangements are discovered for the generation of conical light beams. Ellipticity problems are considered. (AIP)
Course on the nature of physical science
Authors: Derr Patrick G. , Andersen Roy S.
Published: March 2005

There is increasing student and administrative demand for courses in the natural sciences that are accessible to undergraduates who are not majoring in a science. As the current trend to reimpose academic distribution requirements continues, the demand will increase still further. This paper describes a course that legitimately serves such a demand, and provides the nonscience student with an understanding of the methods and nature of natural science. The course is a seminar organized around a detailed examination of the Copernican revolution, in part through Copernicus’s original writings and in part through contemporary historical and philosophical analyses. The authors conclude that the course provides a successful model for achieving the aim of deepening the nonscientist’s understanding of what science is and how it proceeds.
A simple model for inelastic scattering
Authors: Loeser J. G. , Rabitz H. , DePristo A. E. , Rohlfing E. A.
Published: March 2005

A simple model for inelastic scattering may be obtained by suitably generalizing scattering from a square well. The generalization introduces matrices into the quantum-mechanical scattering equations. These equations may be solved exactly to give an explicit expression for the scattering matrix. In this paper we first describe and solve the model, and then discuss the results it predicts for a simple example. We will see that even a simple inelastic system can exhibit rich scattering behavior.
Resource Letter L-1: Lasers
Authors: O’Shea Donald C. , Peckham Donald C.
Published: March 2005

This Resource Letter provides a source of information on lasers and some applications revised and updated from Resource Letter MOP-1 issued more than 16 years ago. It is intended for the use of high school and college teachers both in courses and in guiding students to a broad range of appropriate literature. Articles marked with an asterisk (*) have been selected for publication in an accompanying reprint book. As will be noted the emphasis has been divided between laser history and classroom demonstrations with lasers, since we feel these will be the most valuable articles for readers of this Journal.
Interaction-free quantum measurements: A paradox?
Authors: Dicke R. H.
Published: March 2005

In Heisenberg’s famous discussion of the measurement of a particle’s position using a microscope, the momentum transferred to the particle by the scattered photon makes the particle’s momentum uncertain. It is shown that momentum is also transferred when the lack of a scattered photon is used to discover that the particle is absent from the field of view of the microscope (i.e., located outside the light beam). This apparent paradox, a transfer of momentum and/or energy to a missing particle by a light beam (without the scattering of a photon), is discussed and ’’resolved’’ using quantum measurement theory.
Bringing home the atomic world: Quantum mysteries for anybody
Authors: Mermin N. D.
Published: March 2005

A simple device is described, based on a version of Bell’s inequality, whose operation directly demonstrates some of the most peculiar behavior to be found in the atomic world. To understand the design of the device one has to know some physics, but the extraordinary implications of its behavior should be evident to anyone. Except for a preface and appendix for physicists, the paper is addressed to the general reader.
Origins of Dirac’s electron, 1925–1928
Authors: Moyer Donald Franklin
Published: March 2005

This is the first of a three-part series. This essay describes Dirac’s generalizations of quantum mechanics leading to his theory of the electron.
Hadron spectra and quarks
Authors: Gasiorowicz Stephen , Rosner Jonathan L.
Published: March 2005

An extensive review of the quark model and its implications is given. Among the topics considered are gauge invariance, QCD, charm particles, QED, flavor, conservation laws, and mass formulas. (AIP)
Landau diamagnetism: A simple calculation
Authors: Dupré A.
Published: March 2005

Starting from the energy and degeneracy of the Landau levels of a free-electron gas in a magnetic field, the nonoscillatory term of the Landau diamagnetism is derived for T=0, using elementary algebra only.
Poincaré group as reflections in straight lines
Authors: Dunn K. A.
Published: March 2005

The Poincaré group, the group of transformations of the plane which preserve the Minkowski distance between points, is derived as compositions of suitably defined reflections in straight lines. It is shown that any such transformation must be one of four types.
Decay of a compound particle and the Einstein–Podolsky–Rosen argument
Authors: Flores J. , Henestroza E. , Mello P. A. , Moshinsky M.
Published: March 2005

By analyzing the decay of a compound system into two praticles, we show that measurements on particle 1 will define with an arbitrary degree of precision the coordinate and momenta of particle 2 at times large compared with the lifetime of the compound system, i.e., when the two particles no longer interact. Thus we have an example of the Einstein–Podolsky–Rosen argument in which all the requirements of quantum mechanics are met. Criticism of the point of view they present should then center on their epistemological position (such as their definition of physical reality) rather than on their use of the quantum-mechanical formalism.
Evaluations of Dirac’s electron, 1928–1932
Authors: Moyer Donald Franklin
Published: March 2005

This the second of a three-part series. This essay surveys evaluations of Dirac’s theory by other physicists, especially by Bohr who used Dirac’s speculations about negative energy electrons as evidence for the failure of quantum mechanics at nuclear dimensions.
Generalized Lagrangian and conservation law for the damped harmonic oscillator
Authors: Bahar Leon Y. , Kwatny Harry G.
Published: March 2005

An explicit construction of the time-dependent Lagrangian for a damped harmonic oscillator is given. The connection between this Lagrangian with the time-independent one developed by Morse and Feshbach is established. Various methods of deriving a first integral for the equation of motion are given. It is shown that the results developed in this paper by direct means are in agreement with those obtained through the use of group-theoretic methods, such as invariance principles and Noether’s theorem, which are mathematically more advanced approaches.
Elementary approach to separable potentials of exponential form
Authors: Chalk Jeff
Published: March 2005

By differentiating the radial equation with separable potentials of exponential form, a differential equation with constant coefficients is obtained. The Yamaguchi potential is used as the principal example in deriving bound-state and scattering solutions in a simple approach that elucidates the correspondence between the poles of the scattering amplitude and the roots of the bound-state problem.
Large-scale spring experiment
Authors: Fyfe F. M. , Stroink G. , March R. H. , Calkin M. G.
Published: March 2005

The authors present a way of performing the spring experiment that requires more personal involvement on the part of the student.(AIP)
Short Foucault pendulum: A way to eliminate the precession due to ellipticity
Authors: Crane H. Richard
Published: March 2005

The problem of ellipticity in the motion of the ordinary Foucault pendulum and the error caused by it are discussed. A simple method of slightly modifying the force–displacement relation in such a way that precession does not result from ellipticity is presented. The practical range of length of the Foucault pendulum is extended downward substantially. As experimental verification, results from a 70-cm pendulum, mounted as a ’’wall clock’’ are given. Rates of turning from daily readings show a 2% rms deviation from the mean, and the long-term average is within 2% of the rate calculated for the local latitude.
Early history of physics laboratories for students at the college level
Authors: Phillips Melba
Published: March 2005

Student laboratories became an integral part of the study of physics around 1870, some forty years later than those in chemistry. The motivation was both cultural and utilitarian, and the situation that produced the innovation was the growth of manufacturing industry in the mid-19th century. The first published and most influential laboratory manual was that prepared by E. C. Pickering for use at the Massachusetts Institute of Technology.
Abbe’s sine theorem from a thermodynamic and Fourier transform argument
Authors: Higbie Jack
Published: March 2005

Abbe’s sine theorem of geometrical theory of lens aberrations is considered by thermodynamics and Fourier transform arguments.(AIP)
Diffraction grating as a model of the incommensurate phase
Authors: Rutar V. , Seliger J.
Published: March 2005

The author shows a special diffraction grating can be used as a model of the incommensurate phase of a crystal. (AIP)
Simplified version of Dirac’s extensible model of the electron
Authors: Fliessbach T.
Published: March 2005

Dirac’s extensible model of the electron is presented on an elementary level retaining the basic physical idea.
Proposal regarding a new general physics program for geologists
Authors: Conforto A. M. , Menzinger F.
Published: March 2005

This paper describes a proposal for a new physics program for geology majors at the University of Rome. The course is based on a problem-oriented approach and extends the range of physics concepts covered by more traditional courses. Emphasis is put on the need to apply to geological problems the physical concepts usually only discussed in the case of simple but too-idealized physical phenomena. The preliminary results of the first two years of the program experimentation discussed here seem to be quite satisfactory. This study may be seen within the broader framework of the increasing attention on the role and methods of physics education for nonphysics majors within university curricula.
Guided electromagnetic waves: A geometrical development
Authors: Cleveland J. R.
Published: March 2005

Plane wave propagation is used in geometrical arguments of high visualization to obtain essential characteristics and quantities of guided electromagnetic waves. Diagrams are obtained illustrating field intensity maxima for different propagation modes, phase and group velocities, and guide and cutoff wavelengths.
Reliable and economical circuit I
V characterization solar cells
Authors: Muoy Y. H. , Charles J. P. , Adbelkrim M.
Published: March 2005

A transistorized circuit for solar cells which is easy to assemble and use for undergraduate teaching laboratories is described.(AIP)
Suggestions on the construction of multiple-choice tests
Authors: Hudson H. T. , Hudson Carolyn K.
Published: March 2005

Multiple-choice tests are becoming more and more common in physics classes. In the construction of such tests, attention to certain details will minimize the effects of random guessing. In addition, it has been found that for the majority of students, when a reasonable number of tests are given on a schedule throughout the semester the cumulative grade from such tests can provide essentially the same information as would hand-graded problems.
Alternative choice for the energy flow vector of the electromagnetic field
Authors: Lai C. S.
Published: March 2005

An alternative choice for the energy flow vector of the electromagnetic field is proposed by discarding a term ∇×(φ H) from the Poynting vector. This new choice for the energy flow vector is in harmony with our ordinary intuitions, and yields Larmor’s radiation formula for an accelerated charge.
Paradox in the classical treatment of the Stern–Gerlach experiment
Authors: Alstro/m Preben , Hjorth Poul , Mattuck Richard
Published: March 2005

Most textbook authors assume that the force on a magnetic moment sent into a Stern–Gerlach apparatus, is exclusively in the direction of the magnetic field. Hence they conclude that classically one should expect a continuous distribution of particles along a line in the field direction, on a screen placed behind the apparatus. However, it is easily shown that, because the divergence of the field is zero, there is in fact an equally large force transverse to the field direction. This would lead to an isotropic distribution of particles on the screen, in contradiction to the above conclusion. The paradox is resolved by taking into account the torque on the magnetic moment. This produces a rapid precession about the field direction, causing the transverse force to average out and thus giving the usual textbook result.
Nuclear spins in the Earth’s magnetic field
Authors: Callaghan P. T. , Le Gros M.
Published: March 2005

Details are given of a simple apparatus for the observation of nuclear precession in the Earth’s magnetic field. Spin echos are generated using a pulse of oscillatory magnetic field resonant at the Larmor frequency. Students can use the system to measure a nuclear magnetic moment, nuclear relaxation times, and the local strength and orientation of the Earth’s magnetic field.
The connection between the charged-particle current and the displacement current
Authors: Terry William K.
Published: March 2005

In Ampère’s circuital law, two separate terms are required to describe the contributions to the magnetic field of the charged-particle current and the ’’displacement current.’’ In this paper, it is shown how both terms arise by applying the Biot–Savart law to a calculation of the displacement current resulting from the motion of a single charged particle. The conclusions drawn from this calculation are applied to the case of a steady straight current filament.
How good are the common approximations used in physics?
Authors: Feller Steven A. , Kasper Joseph E.
Published: March 2005

The qualities (relative errors) of several of the common approximations used in undergraduate physics are studied. Some novel features of the approximations are discussed. In some cases it is found that the approximations are substantially better than is usually thought to be the case.
Angular momentum structure of the scattering phase shift
Authors: Leacock Robert A.
Published: March 2005

The partial-wave analysis of the quantum-mechanical scattering of a particle by a spherically symmetric potential is considered for continuous angular momentum, in contrast to the usual treatment where the angular momentum is discrete. Numerical illustrations of the scattering phase shift as a function of real, continuous angular momentum are presented. The scattering phase shift is calculated for Yukawa and exponential potentials of various strengths and ranges, and the properties of the phase shift (considered as a function of real, continuous angular momentum) are linked to the bound states and resonances of the quantum-mechanical system. Considering the phase shift as a function of continuous angular momentum eliminates the need to consider an infinite number of individual phase shifts and thus significantly simplifies the partial- wave description of the particle motion.
Two-band model of itinerant magnetism
Authors: Testa James , Falicov L. M.
Published: March 2005

A simple model of ferromagnetism and antiferromagnetism is presented and is solved analytically in the mean-field approximation. Full use is made of symmetry and the problem is reduced to an easily interpreted geometrical picture. Regions of various phase stabilities as functions of the dynamical parameters—bandwidths and electron–electron interactions—are described in detail. The model and its solutions are a good introduction to the theory of itinerant magnetism.
Quantized angular momenta in the laser gyro
Authors: Wolf E. L.
Published: March 2005

A brief discussion is presented of the operation of the traveling-wave ring laser as a sensor of rotation. The description, based on the azimuthal probability function P(φ) associated with a linear combination of oppositely directed and conserved angular momenta Lz = ±mh/, is free of certain restrictions inherent in the conventional treatment, as well as providing a simple and transparent picture of the physical origin of gyroscopic action.(AIP)
Resonance scattering from a double δ-function potential
Authors: Lapidus I. Richard
Published: March 2005

The transmission coefficient and total cross section as functions of energy are obtained for scattering of particles by a double δ-function potential in one dimension. This example may be useful for the discussion of resonance scattering in an introductory quantum mechanics course. (AIP)
Trouble with the method of images
Authors: Newcomb William A.
Published: March 2005

By a seemingly straightforward application of the method of images, we are led to the absurd result that if a point charge q is placed between two conducting plates, then all of the electric flux originating in q will terminate on one of the two plates, and none of it on the other. The error is traced to its source in an improper operation of termwise integration of infinite series and is corrected.
Evaluation of some averages for the hydrogen atom
Authors: Sánchez del Río C.
Published: March 2005

The Hellman-Feynman theorem is used to calculate 〈r−1〉, 〈r−2〉, and 〈r−3〉 for the hydrogen atom. (AIP)
Even honors students have conceptual difficulties with physics
Authors: Peters P. C.
Published: March 2005

Honors students in an introductory physics course are shown to exhibit some of the same kinds of misconceptions as do students in the usual standard introductory courses. Examples are given of exercises and written exam questions that probe for conceptual understanding, and student responses to these questions are used to identify conceptual difficulties common to many students. Because these misconceptions were found in a very select group of students, the implication may be drawn that conceptual difficulties of the same kind are present in students in all levels of introductory physics.
Heuristic extension of the Schwarzschild metric
Authors: Espinosa James M.
Published: March 2005

The Schwarzschild solution of Einstein’s equations of gravitation has several singularities. It is known that the singularity at r = 2Gm/c2 is only apparent, a result of the coordinates in which the solution was found. Paradoxical results occuring near the singularity show the system of coordinates is incomplete. We introduce a simple, two-dimensional metric with an apparent singularity that makes it incomplete. By a straightforward, heuristic procedure we extend and complete this simple metric. We then use the same procedure to give a heuristic derivation of the Kruskal system of coordinates, which is known to extend the Schwarzschild manifold past its apparent singularity and produce a complete manifold.
Iterative solutions of transcendental equations of mathematical physics with the programmable pocket calculator
Authors: Krane K. S.
Published: March 2005

A method is outlined that permits the solution of transcendental equations, such as often arise in mathematical physics, using short iterative routines ideally suited to the programmable pocket calculator. The method is outlined, conditions for convergence are discussed, and examples are given.
Gravitational deflection of fast particles and of light
Authors: Koltun Daniel S.
Published: March 2005

The gravitational deflection of relativistic particles and of light is discussed from a simple point of view, in terms of velocity-dependent forces in flat space. This picture is shown to be equivalent to that of general relativity, and some of its metric extensions, in the limit of weak gravitational effects. The deflection can then be predicted, up to one free parameter. The relation of that parameter to the spin of gravitational radiation is considered, giving a simple discussion of the known connection between general relativity and a theory with spin-two fields.
One-dimensional muonic helium atom
Authors: Lapidus I. Richard
Published: March 2005

Wave functions are found for the one-dimensional muonic He atom in which the Coulomb interaction is replaced by a δ-function interaction between all particles. (AIP)
Simple nitrogen laser
Authors: Kunabenchi R. S. , Gorbal M. R. , Savadatti M. I.
Published: March 2005

The design of a modified N2 laser is presented which utilizes strips of glass plates glued on top of each other.(AIP)
Can one measure the one-way velocity of light?
Authors: Nissim-Sabat Charles
Published: March 2005

As Fung and Hsieh maintain, one can readily measure the speed of light in one direction if it is different from c/(1−α cos ϑ) 0?α?1. On the other hand, if the velocity of light is c/(1−α cos ϑ), the properties observed upon reflection from a plane mirror do not allow one to conclude α = 0 (as they claim) but rather that α cannot be close to unity. Finally, it is shown that if the one-way velocity is c/(1−α cos ϑ), a wide variety of experiments fail to yield a value for α.
Continuum eigenfunction expansions and resonances: A simple model
Authors: Dean Cleon E. , Fulling S. A.
Published: March 2005

A one-dimensional square-well model of an atom in an electric field is solved exactly. This problem is instructive for two reasons: (1) The Hamiltonian has a continuous spectrum, but the eigenfunctions do not reduce asymptotically to plane waves. Therefore the general Titchmarsh–Kodaira theory of eigenfunction expansions is needed to normalize the eigenfunctions properly. The normalization is expressed by a spectral density function, ρ(E). (2) ρ(E) exhibits ’’bumps’’ at values of the energy at which the electron wave function’s amplitude inside the well is particularly large. These are resonant states of the system. The gradual sharpening of the resonances into discrete bound states as the electric field is turned off is demonstrated.
Discontinuity in the first derivative of the Schrödinger wave function
Authors: Home D. , Sengupta S.
Published: March 2005

Bound state problems in quantum mechanics are considered for the edge of a square well potential and singular points of a Coulomb and a δ-function potential. (AIP)
Discussion of ’’vorticity and rotation’’
Authors: Tritton D. J.
Published: March 2005

The suggestion by Lindgren that the vorticity vector may be expressed as the sum of a ’’microscopic’’ and a ’’macroscopic’’ rotation is shown to apply in such restricted circumstances that it is not a useful concept. This comment is expanded to include a discussion of the most effective way of giving students an understanding of vorticity. The Appendix indicates some flows that exemplify these points.
Energy waste in a university building
Authors: Numark Neil J. , Bartlett Albert A.
Published: March 2005

Interesting physics problems that can be used as examples in introductory physics courses relating to the waste of thermal energy can be found in the mechanical systems of campus buildings. The design of these wasteful systems may represent the ‘‘state of the art’’ as it existed just a few years ago, so such examples are probably abundant. Our Student Recreation Center was opened in 1973. It has an ice skating rink with the associated large refrigeration system. Simple calculations using elementary thermodynamics applied to this system show that the heat rejected by the system is roughly a quarter of a megawatt, which is approximately the average thermal power needed to heat water for the showers in the building. An outcome of this student project is the recommendation that the rejected heat be used to heat (or preheat) the shower water at an estimated annual saving of $40 000 in current energy costs.
Radiant energy transfer
Authors: Coulter Byron L. , Adler Carl G.
Published: March 2005

The fraction of a light pulse’s energy that can be transformed to kinetic energy of a moving body is found to depend on the body’s speed as well as color. At low speeds a white object will receive about twice as much kinetic energy as a black object. At speeds approaching the speed of light almost all of the pulse’s energy will be transformed into kinetic energy by either a black or a white body.
Adapted Wigner–Eckart theorem
Authors: Raboy Sol
Published: March 2005

A derivation of a special case of the Wigner–Eckart theorem suitable for use in an undergraduate course in quantum mechanics is presented. This presentation is restricted to the wave mechanical formalism of quantum mechanics.
Physicist’s proof of Fermat’s theorem of primes
Authors: Gutfreund H. , Little W. A.
Published: March 2005

The prime numbers play a central role in the theory of numbers. We show that Fermat’s theorem on primes may be proved using symmetry properties of Ising-spin configurations; and that similarly this may be extended to certain composite numbers. Our method of proof suggests a ’’physical’’ interpretation of the primes.
Cosmology of Nordström’s first theory of gravitation
Authors: Willenbrock Scott S. D.
Published: March 2005

Nordström’s first theory of gravitation, which is a Lorentz covariant scalar theory, is discussed, and the cosmological solution to the field equation is derived. It is shown that there are two physically equivalent representations of the theory that differ in the system of units with which measurements are made. The cosmological solution is found to be an infinite, Euclidean universe with a big bang and a big crunch.
Uniformly accelerated reference frame and twin paradox
Authors: Good R. H.
Published: March 2005

Some simple concepts of general relativity are presented via two animated films and an elementary treatment that emphasizes the event horizon and the gravitational frequency shift. The twin paradox is illustrated from the standpoint of each twin.
Chladni’s law for vibrating plates
Authors: Rossing Thomas D.
Published: March 2005

The normal vibrational modes of free circular plates can be classified according to the number of nodal diameters m and the number of nodal circles n. Chladni observed that the addition of one nodal circle raised the frequency f about the same amount as adding two nodal diameters, and Rayleigh pointed out that f is proportional to (m+2n)2 for large f. Waller, however, concluded that the number of nodal diameters necessary to raise the frequency as much as a nodal circle varies from two to five. We have examined data on the vibrations of flat and non-flat circular plates and fitted their vibration frequencies to the relationship f = c(m+bn)k. By proper choice of c it is possible to satisfy Chladni’s law (b = 2, k = 2) over quite a wide range of frequency in flat plates. Non-flat plates such as cymbals and bells, require different choices of b and k. A brief history of Chladni patterns, and suggestions for observing and demonstrating the vibrational modes of plates are included (AIP).
The stability of bicycles
Authors: Lowell J. , McKell H. D.
Published: March 2005

We review previous ideas on why a bicycle is stable and analyze a somewhat simplified model. We show that a bicycle is almost, though not quite, self-stable; the most important parameter governing the stability is the ‘‘castor’’ of the front wheel, as was suggested by Jones [Phys. Today 23, 34 (1970)]. The almost stable behavior explains why a bicycle is so easy to ride at speed.
Constant power equations of motion
Authors: Stephenson Roger
Published: March 2005

Correct solutions for the common problems associated with bodies accelerating under the application of constant power are generally missing from physics textbooks. The kinematic equations for this motion are not overly difficult to derive and bear strong similarities to their familiar constant force counterparts. The concept of ‘‘zip’’ is here defined as the square root of the power to mass ratio, and is shown to be a useful parameter of this kind of motion. Several specific problems are solved and the results compared with available real data.
Relativistic addition of velocities
Authors: Takahashi Y.
Published: March 2005

A simplified kinematical diagram of velocity addition is shown in this paper, as an application of the special Lorentz transformation. In this method, two component vectors derived from a velocity vector u′(u′x′,uy′) in one of two inertial frames are added to the realtive velocity vector v between the two inertial frames. The above component vectors of u′ are u′x′ex′ +[1−(v/c)2]1/2u′y′e′y′ and u′y′ey′ +[1−(v/c)2]1/2u′x′e′x′ where e′x′ and ey′ are unit vectors parallel to and perpendicular to v, respectively, and v stands for the value of v and c for the velocity of light in free space.
Motion in a time-dependent, uniform electric field
Authors: Fallieros S. , Friar J. L.
Published: March 2005

The quantal motion of a charged nonrelativistic particle in a uniform but time-varying electric field is discussed. It is pointed out that states of definite but variable momentum exist in this case and are, in a way, the analog of the coherent states of the harmonic oscillator. The gauge invariance of the theory is illustrated, and the results are related to the description of the motion in an accelerated reference frame. A brief discussion of the propagation function and of the evolution operator is also presented.
Force measurement and force transformation in special relativity
Authors: Martins Roberto de A.
Published: March 2005

Relativistic dynamics has been historically built without an immediate connection to empirical operations. In order to test dynamic laws by experiment, it is necessary that at least one dynamic parameter be made measurable for moving systems. A method of force measurements applicable to moving systems is proposed. It is shown with the aid of thought experiments that the method leads to the accepted relativistic force transformations.
Stimulated emission, absorption, and interference
Authors: Cray Melissa , Shih Mei-Li , Milonni Peter W.
Published: March 2005

It is shown how stimulated emission and absorption may be viewed in terms of the interference of the incoming field and the field radiated by the atom.
Communication in industrial research laboratories
Authors: Jamerson Frank E.
Published: March 2005

Industrial physicists publish their research results in internal company reports as well as in physics journals. In internal reports, research findings are communicated primarily to engineering and management groups. Because of the specific needs and preferences of these groups, the criteria for internal reports are different from those usually considered best for an ’’outside’’ publication. For the same reason, oral presentations in a company differ from those for a professional society meeting. The criteria for communications inside and outside a company are compared since physics graduates entering industry must be made aware of these differences—preferably before they graduate.
Electrostatics of systems of parallel plates
Authors: Scholten P. D.
Published: March 2005

Expressions are derived for the surface charge density on each surface of any member of a system of N infinite, parallel, charged, conducting plates. Various special cases are considered to show that this problem is suitable for independent investigation by undergraduates. A particular example discussed is that of a 10-plate system, each plate of which possesses the same total surface charge density. Assuming that an electric breakdown occurs in the gap between two plates when a certain critical electric field value is reached, the breakdown pattern for the entire system is studied as additional charge is added to particular plates. Such examples show how this problem can illustrate symmetries in nature and how they are affected by perturbations.
Measuring relativistic electrons in the undergraduate laboratory
Authors: Couch Jack G. , Dorries Terry K.
Published: March 2005

An experiment is described for measuring the momentum and energy of relativistic electrons from a radioactive beta source. Electrons are momentum-selected in a simple beta-ray spectrometer and then measured for energy with a surface barrier detector. The results illustrate to students a clear confirmation of the relativistic energy–momentum relationship, and provide an accurate measure of the rest mass of electrons and the speed of light. The apparatus we describe also can be used in experiments for measuring beta spectra.
Science and society test VI: Energy economics
Authors: Hafemeister David W.
Published: March 2005

Simple numerical estimates are developed in order to quantify a variety of energy economics issues. The Verhulst equation, which considers the effect of finite resources on petroleum production, is modified to take into account supply and demand economics. Numerical and analytical solutions to these differential equations are presented in terms of supply and demand elasticity functions, various finite resources, and the rate of increase in fuel costs. The indirect cost per barrel of imported oil from OPEC is shown to be about the same as the direct cost. These effects, as well as those of discounted benefits and deregulation, are used in a calculation of payback periods for various energy conserving devices. A phenomenological model for market penetration is developed along with the factors for future energy growth rates. A brief analysis of the economic returns of the ’’house doctor’’ program to reprofit houses for energy conservation is presented.
Fundamentals of zoological scaling
Authors: Lin Herbert
Published: March 2005

Most introductory physics courses emphasize highly idealized problems with unique well-defined answers. Though many textbooks complement these problems with estimation problems, few books present anything more than an elementary discussion of scaling. This paper presents some fundamentals of scaling in the zoological domain—a domain complex by any standard, but one also well suited to illustrate the power of very simple physical ideas. We consider the following animal characteristics: skeletal weight, speed of running, height and range of jumping, food consumption, heart rate, lifetime, locomotive efficiency, frequency of wing flapping, and maximum sizes of animals that fly and hover. These relationships are compared to zoological data and everyday experience, and match reasonably well.
Induction transducer for recording the velocity of a glider on an air track
Authors: Rochon P. , Gauthier N.
Published: March 2005

A simple electromagnic method using an induction transducer for recording directly and automatically velocity-time curves of a glider on an air track (AIP).
Magnetic and electric fields of rotating charge distributions
Authors: Marsh James S.
Published: March 2005

A charge distribution with axial symmetry is allowed to rotate with constant angular velocity around the axis of symmetry. The magnetic field of the resultant current density is calculated in terms of the electrostatic field of the charge distribution. The relation is of greatest utility in the calculation of the magnetic field of a rotating spherically symmetric charge distribution in terms of its electrostatic potential.
Automatic measurement of the mean lifetime of the muon
Authors: Lewis Roger J.
Published: March 2005

This paper describes a microcomputer-based apparatus for the measurement of the mean lifetime of the muon. The equipment exposes the student to many modern experimental techniques and is suitable for an advanced undergraduate physics laboratory.
Generation of simple harmonic motions
Authors: Yan C. C.
Published: March 2005

Simple harmonic motion is examined from the viewpoint of how such motion can be generated. It is shown that a family of plane curves including circles as its subfamily generate simple harmonic motions by projection. The idea of dynamic force constants is introduced. Employing such an idea, one may conclude that any force field that generates a simple harmonic motion is equivalent to the force field obeying Hooke’s law with the force constant replaced by the appropriately generalized dynamic force constant.
Gauge transformations and the electric dipole approximation
Authors: Kobe Donald H.
Published: March 2005

Some subtle aspects of the electric dipole approximation (EDA) are discussed, and some persistent criticisms answered. The usual form of the EDA is that the scalar potential is −E⋅r and the vector potential is zero. The EDA does not describe the electromagnetic wave, but only the effect of the electromagnetic wave in the long-wavelength limit on a nonrelativistic electron bound in an atom. The EDA is the first term in the multipole expansion of the scalar potential in the multipolar gauge, in which the potentials are expressed as integrals over the electric and magnetic fields.
Demonstrations of beats as moving interference patterns
Authors: Stein T. S. , Dishman L. G.
Published: March 2005

A ripple tank demonstration is described that displays the dynamic interference patterns responsible for producing beats. Photographs are provided of a computer simulation of various beat interference patterns. Young’s two-slit interference pattern is presented as a special case (the zero-beat case) of the more general beat interference pattern. Equations for the constructive interference paths of beat interference patterns are derived.
Simple experiment to illustrate the functional form of air resistance
Authors: Lewis J. C. , Kiefte H.
Published: March 2005

A simple experiment is described to obtain the functional form of air resistance, for a spherical body, from uniform circular motion. The experiment is effective, fun to carry out, and very instructive for a first university mechanics course.
One-body and two-body operators on systems of identical particles
Authors: Greenberg N. I. , Raboy S.
Published: March 2005

The form of one-particle and two-particle operators is obtained in the notation of second quantization. These forms are applied to many-particle states of identical particles where the appropriate symmetry with respect to exchange of particles is invoked from the start. The form in the wave-mechanical formalism of operators suggested by classical analog is derived in a matter suitable for inclusion in courses in quantum mechanics.
Electron interaction with matter
Authors: Ouseph P. J. , Hoskins K. D. , Wadsworth M. , Miller J.S. , Merriam S.
Published: March 2005

An undergraduate laboratory experiment to study the interaction of monoenergetic electrons is discussed in this paper. In this experiment it is possible to study several aspects of electron interaction such as variation of intensity, most probable energy loss, and full width at half maximum of the energy distribution as a function of absorber thickness. This experiment along with similar experiments on gamma and alpha absorption will enable the students to understand the differences in the interactions of these radiations with matter.
Approximate bandwidth and diffraction efficiency in thick holograms
Authors: Ludman Jacques E.
Published: March 2005

The approximate bandwidth and diffraction efficiency (DE) for thick holograms are derived in an extremely simplified fashion from considerations of the geometry of the holograms alone. The results agree with the exact expressions derived from coupled wave theory and afford a far more direct insight into the effect of the various geometric and material parameters with the hologram performance.