bluuebunny/crossref_metadata_2025 huggingface dataset:
The bound states of a segmented potential
Authors: Kalotas T. M. , Lee A. R.
Published: September 2005

The method of potential segmentation previously developed for scattering situations, is extended to the computation of one-dimensional bound states. The energy eigenvalues are determined by the zeros of a specific transcendental function while the corresponding eigenfunctions are supplied with the aid of a series of 2×2 matrix equations.
The principle of identicality and the foundations of quantum theory. II. The role of identicality in the formation of quantum theory
Authors: Pešić Peter D.
Published: September 2005

The place of the concept of indistinguishability in the formation of quantum theory is examined, including particularly Planck’s earliest formulations of the quantum hypothesis, as well as the use of this concept in the developments surrounding the new quantum theory.
Rotating coordinates and the Ramsey separated oscillating-field resonance method
Authors: Glass-Maujean Michèle , Stroke H. Henry
Published: September 2005

Norman Ramsey has recently been awarded the Nobel Prize for the ‘‘molecular beam resonance method with separated oscillating fields’’ [Phys. Rev. 78, 695–699 (1950)]. It is shown explicitly, for pedagogical purposes, how the use of rotating-coordinate systems, introduced by Rabi et al. [Rev. Mod. Phys. 26, 167–171 (1954)] for the solution of magnetic-resonance problems can be extended to the case of Ramsey’s method with separated oscillating fields.
Externally excited semi-infinite one-dimensional models
Authors: Cannas Sergio A. , Prato Domingo
Published: September 2005

The problem of a semi-infinite harmonic chain with the first mass subject to a forced periodic motion is solved exactly. The scattering of a quantum particle by a semi-infinite Kronig–Penney chain is analyzed analytically. The behavior of extended and localized solutions is analyzed in both problems and many analogies are found between them. Special attention is paid to the asymptotic behavior of localized solutions near the band edges.
An analytical example of renormalization in two-dimensional quantum mechanics
Authors: Mead Lawrence R. , Godines John
Published: September 2005

As a concrete example of the idea of renormalization, quantum mechanical scattering of particles by a two-dimensional delta-function potential is considered. The renormalization of the scattering cross section is carried out exactly and analytically. The calculation, free from obscuring mathematical details required for realistic field theories, may aid in making the idea of renormalization more accessible.
Finite eigenfunctions in the WKB approximation
Authors: Sukhatme U. , Pagnamenta A.
Published: September 2005

A long-standing problem and major shortcoming of semiclassical (WKB) bound-state wave functions is their divergence at the classical turning points. Presently available regularization schemes are accurate but rather complicated. It is shown how finite wave functions can be simply obtained by reorganizing the WKB perturbation expansion in powers of ℏ and retaining appropriate higher-order terms. The wave functions obtained by this method are compared with exactly known ones for the harmonic-oscillator and Morse potentials.
The conic sections revisited
Authors: Foreman J. W.
Published: September 2005

When the reflecting properties of the conic sections are treated in geometrical optics, they are usually stated without proof. In some cases the reflecting property of a paraboloid of revolution is derived from geometrical arguments, but ellipsoids and hyperboloids are usually not treated explicitly. In all cases the arguments begin with the geometrical definitions of the conic sections and proceed to derive their reflecting properties. This paper deals with the inverse problem. That is, the geometrical conic sections are derived from first principles as surfaces which reflect light rays in specific ways.
Growth of large, high-quality diamond crystals at General Electric
Authors: Strong Herbert M. , Wentorf Robert H.
Published: September 2005

Diamond crystals up to about 6 mm in size which have excellent crystalline perfection can be grown at high pressures (ca. 50 kbar) and temperatures (ca. 1400 °C) by the controlled transport of carbon through a melt of a catalyst metal such as an Fe or Ni alloy, from a source of small diamond crystals to a diamond seed crystal. The temperature different driving the transport is about 30 °C and growth times are about 1 week. Finicky attention to details is essential to achieve growth at a slow, steady rate and to avoid unwanted spurious nucleation of diamond. Traces of impurities such as B or N affect the properties of the grown diamonds. Recently, the process has been used to prepare high-quality crystals having outstanding thermal conductivity which are composed almost entirely of the C-12 isotope of carbon.
Test of the adiabatic approximation in quantum mechanics: Forced harmonic oscillator
Authors: Nogami Y.
Published: September 2005

The accuracy of the adiabatic approximation in quantum mechanics is examined by applying it to the forced harmonic oscillator for which the time-dependent Schrödinger equation can be solved exactly. Nonadiabatic transitions caused by the external force that varies in time is focused on. A peculiar situation is illustrated such that, no matter how rapid and large the variation of the external force may be, all nonadiabatic transitions vanish exactly as t→∞.
A simple numerical method for solving problems in electrostatics
Authors: Lamberti Pedro W. , Prato Domingo P.
Published: September 2005

A very simple numerical method for solving boundary problems in electrostatics is presented. The approximation scheme is based on the substitution of a series expansion of the electrostatic potential by a finite sum and a discretization of the boundary where the conditions are given. These boundary conditions may be of the mixed type. In this way the original problem is reduced to the solution of a system of linear equations. As an application of the method proposed, the problem of a hollow cap of a sphere set to a constant potential is treated.
Learning quantum field theory from elementary quantum mechanics
Authors: Gosdzinsky P. , Tarrach R.
Published: September 2005

The study of the Dirac delta potentials in more than one dimension allows the introduction within the framework of elementary quantum mechanics of many of the basic concepts of modern quantum field theory: regularization, renormalization group, asymptotic freedom, dimensional transmutation, triviality, etc. It is also interesting, by itself, as a nonstandard quantum mechanical problem.
How a superconductor supports a magnet, how magnetically ‘‘soft’’ iron attracts a magnet, and eddy currents for the uninitiated
Authors: Saslow W. M.
Published: September 2005

It is shown how an infinite superconducting slab supports a permanent (‘‘hard’’) magnet against gravity. The equilibrium position is found, using the method of images and the property that superconductors expel magnetic flux, and then the supercurrents (in the approximation that they are localized at the surface) are explicitly determined, using the boundary condition associated with Ampere’s law. This calculation, which does not require the London equation (although a brief discussion of its effects is given), can be done by motivated freshmen. (Measurements by Heller on high-Tc samples yield a flotation height about half the predicted value; this is attributed to incomplete screening of the applied field, due to penetration by magnetic flux lines.) From this example two subjects can then be discussed that normally precede a discussion of superconductivity. First, these supercurrents are equal and opposite to the Amperian surface currents that attract a permanent magnet to an infinitely permeable (‘‘soft’’) magnetic slab (the image method yields equal and opposite images if the superconductor supporting the permanent magnet is replaced by an infinitely permeable material). Moreover, these supercurrents are the same as the initial eddy currents generated if a solenoid is suddenly energized or if a permanent magnet suddenly materializes above a conducting slab. Following a discussion of Maxwell’s theory of eddy currents in thin conducting sheets, the time-development of this initial eddy current distribution is obtained.
The environmental impact of vacuum decay
Authors: Crone Mary M. , Sher Marc
Published: September 2005

In the standard model of particle physics, the force laws changed discontinuously as the Universe cooled below the critical temperature for electroweak gauge symmetry breaking. In a recently proposed model, the gauge symmetry of electrodynamics, which is responsible for the photon being massless, will also be broken as the Universe cools below some critical temperature. As a result, the photon will suddenly acquire a mass that is of the order of 10−4 eV/c2, corresponding to a Compton wavelength of a centimeter. The effects of such a transition on our civilization are examined. All long-range electric and magnetic fields would vanish, as would all low-frequency electromagnetic waves. Atomic structure and solar radiation would not be appreciably affected. Effects on neural transmission might be serious, depending on the precise value of the photon mass. It is concluded that the impact on society would be severe, but probably not fatal. Life would continue, and our civilization could be restructured to accommodate the new laws of electromagnetism.
Wilberforce pendulum oscillations and normal modes
Authors: Berg Richard E. , Marshall Todd S.
Published: September 2005

This article summarizes our calculation of the normal modes and the normal coordinates for a commercially available Wilberforce pendulum. A procedure is presented by which the normal coordinates may be produced experimentally, so that the frequencies of the normal modes can be obtained both theoretically and experimentally. Where possible, results have been compared with those from previous papers. Finally, PC basic programs have been written in which the behavior of the Wilberforce pendulum has been theoretically reproduced.
A new approach to one-dimensional scattering
Authors: Kalotas T. M. , Lee A. R.
Published: September 2005

An alternative approach to the one-dimensional scattering problem is presented in which the potential is replaced by a sequence of flat barriers or wells. The resulting problem is solved exactly and the transmission coefficient obtained via multiplication of a string of 2×2 matrices.
Motion of a leaky tank car
Authors: McDonald K. T.
Published: September 2005

A solution is presented to the following problem: Describe the motion of a tank car initially at rest once an off-center drain opens. The tank car rolls without friction on a horizontal surface, and the water flows out of the drain vertically in the rest frame of the car.
A basis-independent approach to quantum optics
Authors: Deutsch Ivan H.
Published: September 2005

States of the radiation field can be defined without reference to a given basis of normal modes. In this way optical systems for which there is no natural set of orthogonal modes can be handled quantum mechanically in a more rigorous manner. In particular, coherent states and associated phase-space methods can easily be generalized to this basis-independent representation.
Motive force and centripetal force in Newton’s mechanics
Authors: Erlichson Herman
Published: September 2005

Newton’s concept of force was developed over a period of time, starting with a collisional model in his Waste Book, and culminating in his measure of the centripetal force at a point found in De Motu and again in Principia, Book I, Prop. VI. Newton kept developing his force concept, adding to it and making it many faceted. This rich concept of force has often posed difficulties for historians of science [for example, R. S. Westfall, Force in Newton’s Physics (MacDonald and American Elsevier, New York, 1971) and J. Herivel, The Background to Newton’s Principia (Oxford U.P., New York, 1965)] and others. These difficulties are related to at least six things as follows: (1) lack of understanding that Newton’s ‘‘motive force’’ is an abbreviation for ‘‘motive quantity of a force,’’ so that Newton’s ‘‘motive force’’ and his ‘‘force’’ are not two different types of force. Motive force (motive quantity) is used to quantify force; (2) lack of understanding of Newton’s model for instantaneous impulses; (3) lack of understanding that although Newton’s motive force has directionality Newton added it as a scalar in his analysis of uniform circular motion; (4) lack of understanding of Newton’s polygon model; (5) lack of understanding that Newton’s measure of the motive value of a force, the motive force, was always used to obtain a comparative measure of forces in his early mechanics; and (6) lack of understanding that Newton’s Prop. VI measure of centripetal force at a point permitted Newton to bring the time dimension into his motive force concept, thus developing it into something very close to our modern definition of force. This paper analyzes Newton’s development of his motive force concept, and discusses the difficulties that some scholars have had with various aspects of this concept.
Definitions of randomness
Authors: Compagner Aaldert
Published: September 2005

Randomness is a fundamental but elusive concept in mathematics and physics. Even for the elementary case of a random binary sequence, a generally accepted and operational definition is lacking. However, when ensembles are used for the foundation of probability theory, randomness has to be identified with uncorrelatedness, a neglected notion that yet solves many puzzles surrounding randomness. In any single sequence, a definite amount of correlation is unavoidable. At best, the remaining correlations are of high order or cover a large distance. This is the case for properly defined well-tempered pseudorandom sequences. Reliable algorithms for the generation of pseudorandom bits at rates of 1 GHz result.
Hyperfine interaction versus strong laser field-optical Back–Goudsmit (Paschen–Back) effect
Authors: Gawlik Wojciech
Published: September 2005

Strong laser perturbation of an atom with fine or hyperfine structure is analyzed in the context of a level-crossing experiment. The effect of sufficiently powerful, detuned, and/or spectrally broad light is to produce ‘‘hyperfine uncoupling,’’ which can be regarded as the optical Back–Goudsmit effect. It is easily understood in terms of an analogy between the level-crossing effect and double-slit experiment.
A toy version of the interacting boson model
Authors: Bhaumik D. , Sen Subimal , Dutta-Roy B.
Published: September 2005

For pedagogical purposes, and also to provide a simple schema wherein ideas and methods may quickly be tried out, a toy version of the interacting boson model (IBM) is developed in two dimensions.
Newton’s 1679/80 solution of the constant gravity problem
Authors: Erlichson Herman
Published: September 2005

In his letter of 6 January 1679/80 Hooke wrote to Newton ‘‘in truth I agree with You that the Explicating the Curve in which a body Descending to the Center of the Earth, would circumgyrate were a Speculation of noe Use yet’’ [The Correspondence of Isaac Newton, edited by H. W. Turnbull (Cambridge U.P., Cambridge, 1960), Vol. 2, p. 309]. In these words, Hooke referred to a hypothetical problem which he was discussing in a correspondence with Newton. The problem was that of determining the orbit of a body moving inside a narrow cut made centrally across the Earth. This was perhaps the very first inverse central force problem to be attacked by Newton. Newton seems to have used his instantaneous impulse technique to provide a drawing of a solution that was almost exact. This paper explores this fascinating early solution of an inverse central force problem.
Moments not to forget—The conditions for equating torque and rate of change of angular momentum around the instantaneous center
Authors: Tiersten Martin S.
Published: September 2005

It is shown that quick and elegant solutions of many problems in plane motion of a rigid body may be obtained by taking moments around the instantaneous center of rotation.
Zero-point energy in early quantum theory
Authors: Milonni P. W. , Shih M. -L.
Published: September 2005

In modern physics the vacuum is not a tranquil void but a quantum state with fluctuations having observable consequences. The present concept of the vacuum has its roots in the zero-point energy of harmonic oscillators and the electromagnetic field, and arose before the development of the formalism of quantum mechanics. This article discusses these roots in the blackbody research of Planck and Einstein in 1912–1913, and the relation to Bose–Einstein statistics and the first indication of wave–particle duality uncovered by Einstein’s fluctuation formula. Also considered are the Einstein–Stern theory of specific heats, which invoked zero-point energy in a way which turned out to be incorrect, and the experimental implications of zero-point energy recognized by Mulliken and Debye in vibrational spectroscopy and x-ray diffraction.
The two-slit interferometer reexamined
Authors: Sudarshan E. C. G. , Rothman Tony
Published: September 2005

It is shown that the standard exposition of the two-slit diffraction experiment is incorrect because it treats the interference as arising from the photon wave function ψ, whereas the interference is really between coherent states of the field, which do not correspond to single-photon states. Several other misconceptions are pointed out.
Quantum field theories, nuclear forces, and the cosmic rays (1934–1938)
Authors: Brown Laurie M. , Rechenberg Helmut
Published: September 2005

During the 1930s, cosmic rays were the most important source of data on the high-energy behavior of both quantum electrodynamics and nuclear forces. In the period 1934–1938, with which this article is concerned, the dominant fundamental theory of nuclear forces was that of the Fermi field. In sorting out the various cosmic-ray phenomena in the atmosphere, it was found that the less penetrating components were associated with electromagnetic cascade showers, and that the more penetrating component contained a new ‘‘elementary’’ particle, the mesotron. However, there remained puzzling features of the cosmic rays that left adequate room for other interpretations.
Why does heating water in a kettle produce sound?
Authors: Aljishi Samer , Tatarkiewicz Jakub
Published: September 2005

The question of whether it is possible to design a kettle in which water could be brought to a boil silently is addressed. In this context, acoustic phenomena associated with the heating of water in various vessels are investigated. It is shown that much of the sound emitted in the boiling process can be attributed to coupling between vapor bubble generation and collapse with the natural acoustic modes of the heating vessel utilized. Differences between the thermoacoustic characteristics of deionized and tap water heating are evaluated.
Random walks: A pedestrian approach to polymers, critical phenomena, and field theory
Authors: Raposo E. P. , de Oliveira S. M. , Nemirovsky A. M. , Coutinho-Filho M. D.
Published: September 2005

Main concepts in critical phenomena such as universality, critical dimension, analogies with the statistics of polymers and scaling theory, together with renormalization group ideas and rudimentary methods in field theory are presented through the simple and intuitive properties of random walks. This work, which requires little previous knowledge of mathematics besides elementary calculus, has served as the basis of a program to introduce undergraduate students to research in theoretical physics.
Gravitational collapse and moment of inertia of regular polyhedral configurations
Authors: Aravind P. K.
Published: September 2005

This paper proposes and solves two problems in classical mechanics that are tied closely to the geometry of the Platonic solids. The problems are: (1) to calculate the gravitational collapse time of a set of identical point masses released from rest from the vertices of a regular polyhedron; and (2) to calculate the moment of inertia (about any axis through the center) of a uniform body in the shape of one of the Platonic solids. Dimensionless figures of merit are introduced to gauge the relative performance of the Platonic solids in each of the problems studied. These figures of merit are similar to the isoperimetric quotient introduced by George Polya a long time ago. The rhombic dodecahedron and triacontahedron are also considered, and it is shown that the triacontahedron surpasses the performance of the Platonic solids in two of the problems examined.
The Doppler interpretation of Ro/mer’s method
Authors: Babović V. M. , Davidović D. M. , Aničin B. A.
Published: September 2005

Ro/mer’s method for the determination of the speed of light, based on the observation of the immersions and emersions of Jupiter’s satellites, can be interpreted in the spirit of the Doppler effect. Although this statement appears to be plausible, textbooks very seldom adopt this point of view. Granted the tabular value of the satellite’s period, this interpretation permits one to determine the speed of light in about a week, as contrasted to half a year in the original method. It is suggested to include the measurement as a student experiment in the optics curriculum. Results of actual observations are given.
On the time-dependent, generalized Coulomb and Biot–Savart laws
Authors: Ton Tran-Cong
Published: September 2005

This paper seeks to promote a wider use of the two little-known time-dependent, generalized Coulomb and Biot–Savart laws in the form given by Jefimenko’s book. For some problems, these two time-dependent laws giving the electromagnetic field from known distributions of charge and current densities without spatial differentiations provide a more convenient method of solution, but they are not well known, probably due to their difficult derivation. This paper gives an alternative derivation to these formulas using a novel ‘‘light cone transformation’’ that may be more appealing to some readers than the derivation given in the book by Jefimenko. The paper then shows that together with the law of conservation of charge these two laws can give back Maxwell’s system of four equations when the medium is infinite, homogeneous, linear, and isotropic; consequently, the time-dependent, generalized Coulomb, Biot–Savart, and charge conservation laws can be used for such a case instead of Maxwell’s four equations. Three elegant examples, which have been traditionally solved in lengthy ways, or using the postulates of the special relativity theory, are then solved using these formulas: They are the examples of a differential antenna, of an electron in a uniform motion, and in an arbitrary motion (Feynman’s formulas). The examples also highlight the necessity of using Lienard–Wiechert’s formula in typical applications of these time-dependent laws.
Physics and roller coasters—The Blue Streak at Cedar Point
Authors: Speers Robert R.
Published: September 2005

The use of a roller coaster for external classroom studies of kinematics, forces, dynamics, and energy conservation is discussed. Experimental accelerometer measurements of the vertical forces acting on riders of the Blue Streak at Cedar Point in Sandusky, Ohio are presented. Theoretically, the track profile is used to calculate/predict the vertical forces acting on a rider at the hilltops, valley bottoms, and several other points of interest along the track. Finally the experimental results and theoretical predictions are compared in the context of a rider’s experiences.
Generalized power versus efficiency characteristics of heat engines: The thermoelectric generator as an instructive illustration
Authors: Gordon J. M.
Published: September 2005

The performance of real heat engines can be characterized by their power versus efficiency curves. Real heat engines with sources of irreversibility that include friction and heat leaks exhibit fundamentally different power versus efficiency curves than those predicted by many previous studies in the finite-time thermodynamics of endoreversible heat engines, in which finite-rate heat transfer was the only irreversibility considered. It is shown that the thermoelectric generator provides an instructive illustration of a cyclic, irreversible heat engine with a power versus efficiency curve that qualitatively reproduces the key features of the corresponding curves for real heat engines. The generic sources of irreversibility are easily identifiable and analytically expressed so as to reveal more transparently the basis for the power versus efficiency characteristic.
The mean field entropy for an ensemble of identical spins with arbitrary magnitude
Authors: Tuszyński J. A. , Wierzbicki W.
Published: September 2005

This paper provides general mean field calculations of the entropy for an ensemble of N magnetic moments with an arbitrary spin value. Expressions for the case with an external magnetic field have been known for many years and have usually been calculated using the canonical ensemble partition function. Less well-known calculations in the microcanonical ensemble are also demonstrated in this paper; they involve the method of Lagrange multipliers. In addition, various special cases and relevant approximations are discussed.
Comments on ‘‘Illustration of resonances and the law of exponential decay in a simple quantum mechanical problem,’’ by Herbert Massmann [Am. J. Phys. 5
3, 679–683 (1985)]
Authors: Onley David , Kumar Anita
Published: September 2005

The time dependence of the wave packet spreading is investigated for the case of a particle confined in a one−dimensional box. (AIP)
On the evaluation of the internal energy and chemical potential of an ideal fermion system
Authors: Aguilera-Navarro V. C. , Estévez Gentil A. , Solano-Torres Wilfrido
Published: September 2005

The internal energy and chemical potential of a noninteracting Fermi gas has been evaluated in three ways: numerically (applicable to arbitrary temperatures), through an asymptotic power series expansion (suitable for low temperatures), and by means of standard Padé approximants (appropriate for low and moderate temperatures). The main conclusion of this work is that the Padé approximant, which is constructed from the asymptotic series employing only minimal labor, is far superior to the truncated series expansion.
Magnetic drag in the quasi-static limit: Experimental data and analysis
Authors: Marcuso M. , Gass R. , Jones D. , Rowlett C.
Published: September 2005

Experimental details concerning measurements of the deceleration of Al and Cu disks rotating under the influence of a localized, nonuniform magnetic field are discussed. For a specified magnetic field distribution, the deceleration of the disk is measured as a function of radial location of the field from the rotation axis and the magnetic drag coefficient at each point is calculated. The measured values of the drag coefficients are compared to theoretical predictions and excellent agreement is obtained.
Simple demonstration of storing macroscopic particles in a ‘‘Paul trap’’
Authors: Winter H. , Ortjohann H. W.
Published: September 2005

A simple experimental setup can be used to demonstrate the storage of macroscopic dust particles in a ‘‘Paul trap.’’ The trap is operated at atmospheric pressure, which results in an efficient ‘‘cooling’’ of the stored particles. Under these conditions, a single anthracene dust particle has been confined for over 2 months. The device is well suited to show the formation of ordered structures when a number of ‘‘cooled’’ species are trapped. Due to its overall simplicity, the setup can be used in lectures, student laboratories, etc.
Teaching the magnetostatic field: Problems to avoid
Authors: Herrmann F.
Published: September 2005

A widely recognized problem that physics teachers encounter is the difficulty that most students have when solving problems related to magnetic field line distributions in the presence of hard- and softmagnetic materials. Two causes of these difficulties are identified: (1) The fact that the hysteresis is introduced as the typical behavior of ferromagnetic materials; (2) the fact that the magnetic field strength H is almost absent in the electromagnetism course. Proposals to remedy the student’s problems are (a) to introduce four idealized magnetic materials, i.e., unmagnetic, hardmagnetic, softmagnetic, and superconducting materials; and (b) to use the magnetic field strength H, and not the magnetic induction B, when discussing problems of magnetostatics.
Resource Letter LS-1: Laser spectroscopy
Authors: Gupta R.
Published: September 2005

This Resource Letter provides a guide to literature on laser spectroscopy. Emphasis has been placed on various spectroscopic techniques rather than the results obtained by the laser spectroscopy. The letter E after an item indicates elementary level or material of general interest. 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 articles to be included in an accompanying Reprint Book.
A noncalculus derivation of the 1/r potential
Authors: Kurtze Douglas A.
Published: September 2005

This paper will show how to obtain the potential energy functions for some power-law forces without resort to integration by using dimensional analysis and some simple conditions which must be satisfied by any sensible definition of an ‘‘average’’ force. The Coulomb potential is actually among the simplest cases.
A novel coupled oscillation demonstration
Authors: Karioris Frank G. , Mendelson Kenneth S.
Published: September 2005

It is shown that a rigid rod, suspended horizontally by two springs, may be used to demonstrate all of the principal features of coupled harmonic oscillations. This simple system is easy to set up and analyze and has some interesting features not possessed by other coupled oscillation demonstrations. The coupling between translational motion of the center of mass (c.m.) and rotational motion about the c.m. can be easily adjusted by changing the springs and their points of attachment to the rod. The normal modes have simple interpretations as pure rotations about points away from the c.m. With proper choice of the parameters these points are located at the points of attachment of the springs. Surprisingly it is possible to measure normal mode frequencies without exciting pure normal mode motion.
Moving pointlike charges and electric and magnetic dipoles
Authors: Ribarič Marijan , Šušteršič Luka
Published: September 2005

Expansions of the volume integrals of strongly localized, continuous, differentiable electric charge and current densities are introduced in terms of the total charge, and variable and moving electric and magnetic dipoles, and conditions under which such expansions are applicable are determined. To enhance an understanding of the effects of external electromagnetic fields acting on very localized densities of electric charges and currents, the resulting Lorentz force, torque, and power are computed by using such expansions. To show how versatile variable and moving dipoles are for building physical models, the following are considered: (a) energy conversions by electric motors, by dielectric and induction heating, and by the magnetic drag force, and (b) relativistic effects in translational movements of steady electric and magnetic dipoles; in particular, the torque on a magnetic dipole moving parallel to a line carrying a steady current and uniformly distributed electric charges.
Time delay in simple one-dimensional systems
Authors: van Dijk W. , Kiers K. A.
Published: September 2005

The time delay or the time advance in the scattering of simple one-dimensional systems can be evaluated in a straightforward manner for certain potential models. It is found that when the interacting potential is attractive and has a strength such that it nearly supports an additional bound state, the time delay at small scattering energy is very large. On the other hand, if the potential supports a bound state with nearly zero binding energy, the time advance near threshold is anomalously large. The behavior of a wave packet scattering from the double delta-function potential is also investigated.
The motion of a stretched string with zero relaxed length in a gravitational field
Authors: Luke Jon C.
Published: September 2005

If a thin, perfectly flexible stretched string satisfies Hooke’s law and has the additional property of zero relaxed length, then its motion is governed exactly by the linear wave equation, even when the string is in a gravitational field. The usual smallness approximations are not needed in the derivation.
Experiments on optical fiber interferometers and laser modes
Authors: Andrés Miguel V. , Contreras Oswaldo
Published: September 2005

Three experiments on optical fiber interferometers, suitable for a teaching laboratory, are described. The guiding characteristics of single mode optical fibers enable simple interferometry experiments with large path differences to be carried out easily. These experiments show that the fringe visibility exhibits a periodic dependence on the path difference when using a multilongitudinal mode HeNe laser. A simple model can be used to explain this dependence in terms of the mode spectrum of the laser.
An intuitive introduction to dual space and some simple physical applications
Authors: Lesche B. , Alcoforado I. , Bedran M. L.
Published: September 2005

A geometric and intuitive definition of dual vectors and some simple physical applications are given. Dual vectors are used in many branches of mathematics and physics on a high and less accessible level. It is shown that dual vectors are as simple and intuitive as ordinary vectors.
Using small, rare-earth magnets to study the susceptibility of feebly magnetic metals
Authors: Davis R. S.
Published: September 2005

Small rare-earth magnets have remarkable properties that can be exploited in the construction of simple measuring devices. Examples are a torsion pendulum that measures the earth’s horizontal magnetic field and a gravimetric pendulum that responds to the small susceptibilities of various ‘‘nonmagnetic’’ materials. These preliminary demonstrations lead to the design of a practical device for measuring the susceptibilities of feebly magnetic metals in low magnetic fields. Our laboratory has used this last method to determine relatively small magnetic susceptibilities, down to 0.0003, to an uncertainty of less than 20%. A convenient feature of our apparatus is that calibration by a susceptibility standard is not required.
Upper level experimental physics resource materials
Authors: Larson Lee E.
Published: September 2005

During a 1990 NSF-sponsored workshop on improving upper level experimental physics laboratories, it was agreed that a list of resources from publishers and from institutions with strong upper level labs would be useful to the physics teaching community. This compilation is by no means exhaustive, and suggestions for additions are welcome. If you have or know of materials that should be included, please contact the compiler of this list, Lee Larson, Department of Physics, Denison University, Granville, Ohio (614-587-6468; Bitnet LARSON@DENISON).
Optical caustics in natural phenomena
Authors: Lock James A. , Andrews James H.
Published: September 2005

When observing a distant point source of light through a water droplet adhering to a pane of glass near one’s eye or the scattering of light from raindrops, one often sees optical caustics. In this paper, diffraction integrals are used to investigate these caustics. The caustic shapes are related to divergences in the stationary phase method for approximating the diffraction integrals. These divergences correspond to the coalescing of two or more geometrical light rays in ray optics or the coalescing of two or more regions of stationary phase in wave optics. The number of coalescing light rays is related to a polynomial approximation of the phase function in the diffraction integral. Also, the relation between the shape of the resulting caustic and the elementary caustic forms of the catastrophe optics classification scheme is described.
Future concentrations of atmospheric greenhouse gases CO2, CFC, and CH4: An assessment on the educational level
Authors: Hoppenau Stefan
Published: September 2005

A model on the educational level is described to estimate effective future atmospheric CO2 concentrations. The effects of chlorofluorocarbon and methane emission and deforestation are taken into account. The influence of different emission scenarios on the time evolution of greenhouse-gas concentration are illustrated. Future global energy policies are discussed both under the aspects of rising world population and the reduction in global CO2 emissions. The model can be handled on a PC or even on a pocket calculator.
Minimum engine size for optimum automobile acceleration
Authors: Haaland Carsten M.
Published: September 2005

The theoretical minimum for engine power rating required to accelerate a vehicle of mass M to velocity V in time T is shown to result from acceleration at constant maximum power. Because actual conditions do not allow infinite starting acceleration, the power per unit mass to provide optimum feasible acceleration with minimum engine power rating is given by Popt/M=a2maxTc, where amax is the maximum starting acceleration and Tc is the crossover time from maximum acceleration to the curve of acceleration at constant maximum power. Comparison with analysis of performance data for 18 automobiles reveals that 17 achieve near-optimum power usage.
A simple method of determining Debye temperatures
Authors: Deacon Christopher G. , de Bruyn John R. , Whitehead J. P.
Published: September 2005

A simple undergraduate laboratory experiment on the determination of Debye temperatures of solids is described. A sample of the solid is immersed in liquid nitrogen; from the mass of nitrogen boiled off in cooling the solid, the change in its internal energy is determined. The quantum corrections to the classical law of Dulong and Petit are calculated and the Debye temperature is obtained using a simple graphical technique.
Fourier transform construction by vector graphics
Authors: Peters Randall D.
Published: September 2005

The learning process is invariably improved by alternative, complementary views of a concept. This paper’s pictorial representation of the discrete Fourier transform (DFT) is helpful in that students can understand internal steps of development, as well as the final result, in terms of vectors. It builds upon the widely known fact that the exponential terms in the transform pair are roots of unity in the complex plane; or in alternative physics terminology, they are unit vectors. After weighting these vectors by sampled values of the function to be transformed, using a simple recipe, the DFT is obtained through vector addition.
A new angle on Compton scattering
Authors: Wilkins Dan
Published: September 2005

Generations of physicists have been inculcated with the elementary Compton formula for the wavelength change of a photon scattered from a charged particle at rest (‘‘special’’ Compton effect). It does not seem to be appreciated that by allowing the target particle to move (‘‘general’’ Compton effect), and by redefining the photon’s scattering angle, one obtains a formula just as simple but more instructive. Unlike the standard formula, it directly displays: (a) number of degrees of freedom (for general effect), (b) time-reversal invariance, (c) quadric surface of revolution—ellipsoid, etc.—for the locus of the scattered photon momenta, and (d) a criterion for occurrence of the inverse Compton effect (CE). It also: (e) facilitates interpretation of the CE as a double Doppler shift, and (f) extends the meaning of  ‘‘Compton effect’’ to arbitrary targets—massive, massless, or with imaginary mass (tachyons). It reveals a connection between the Compton scattering of a tachyon in vacuum and its Cherenkov radiation.
A laboratory course in computer interfacing and instrumentation
Authors: Kocher Carl A.
Published: September 2005

The rationale and content are described for an electronics-oriented course in computer-aided measurements. Performed on a prototyping board connected to an IBM PC-AT, the experiments emphasize digital-to-analog and analog-to-digital conversion at the chip level. Techniques are presented for parallel and serial communication; waveform generation; the acquisition, display, and analysis of data; the use of graphics; control and feedback; mechanical positioning with stepper motors; and signal averaging. Students have undertaken a wide range of original projects.
Phase measuring circuit with lead-lag indication
Authors: Clay Forrest P.
Published: September 2005

This paper deals with the design and construction of a circuit for measuring the phase difference between two coherent signals in the audio frequency range. On application of two coherent signals to the inputs of the circuit an output voltage is produced that is proportional to the phase difference between the input signals. A novel feature of the circuit is that the polarity of the output voltage indicates which of the two signals leads in phase.
On Feynman’s proof of the Maxwell equations
Authors: Hughes Richard J.
Published: September 2005

Feynman’s proof, as recounted by F. J. Dyson [Am. J. Phys. 58, 209–211 (1990)], that the Lorentz force law and two of Maxwell’s equations can apparently be deduced from minimal assumptions about the equation of motion and quantization condition for a nonrelativistic particle, is analyzed. A version of this result is found to hold in classical mechanics, and it is shown that instead of limiting interactions to electromagnetic ones, Feynman’s result is a rederivation of the constraints on the velocity-dependent generalized forces that can be accommodated in a canonical Lagrangian formalism. The generality of the result is illustrated by showing that particle motion in a noninertial frame or in a weak gravitational field also satisfies the constraints.
Why the speed of light is reduced in a transparent medium
Authors: James Mary B. , Griffiths David J.
Published: September 2005

It is well known from optics that the speed of light in a transparent medium is reduced by a factor of n (the index of refraction) as compared with vacuum. Maxwell’s electrodynamics provides a simple account of this phenomenon, and relates n to the electric susceptibility of the material. But the conventional analysis does little to illuminate the mechanism involved. This paper offers some elucidation of the ‘‘miracle’’ by which the radiation from many induced molecular dipoles conspires to produce a single wave propagating at the reduced speed.
Thomas precession: Where is the torque?
Authors: Muller Richard A.
Published: September 2005

Special relativity appears to violate the conservation of angular momentum L since it predicts that an accelerated gyroscope will precess, i.e., L will change in the absence of any applied torque. The paradox is resolved in a simple example by demonstrating that there is a torque present. The mass distribution in the gyroscope undergoes a relativistic distortion, and the center of mass is displaced away from the position of the accelerating force. The resulting torque τ=dL/dt. The model also shows the physical origins of spin-orbit coupling and of the ‘‘oscillating term.’’ A related calculation shows why a moving magnetic dipole has an electric dipole moment.
Classical Kronig–Penney model
Authors: Oseguera Urbano
Published: September 2005

Some discontinuous potentials commonly used in quantum mechanics are briefly considered in order to highlight some unusual conclusions one may draw from the solutions of the associated Schrödinger equation. Classical analogs of these potentials are given; in particular, it is shown that a boundary condition necessary for the quantum system may have physical meaning of its own in the classical counterpart. A classical example of the Kronig–Penney model displaying the appearance of frequency bands, as opposed to the energy bands found in the quantum domain, is also discussed.
Remarks on the Gaussian formula for refraction at a single spherical interface
Authors: Greco V. , Molesini G. , Quercioli F.
Published: September 2005

The derivation of the Gaussian formula for refraction at a single spherical surface is reviewed. The equivalence of different approaches is discussed, as well as the procedures along with which the first-order approximation is introduced. Critical steps in the mathematical treatment are pointed out.
Kaluza–Klein unification and the Fierz–Pauli weak-field limit
Authors: Schwarz A. J. , Doughty N. A.
Published: September 2005

An introduction to higher-dimensional unification is provided by a simple modern treatment of the original 5-D Kaluza–Klein ansatz. A demonstration is given of the way electric charge arises from momentum in the fifth dimension and an estimate of the radius of the extra dimension is obtained from simple quantum-mechanical considerations. The Fierz–Pauli weak-field approximation is applied and found to exhibit some of the essential features of Kaluza–Klein theory in a few lines without the need for a full general relativistic analysis.
The elastic constant of a rubber tube
Authors: Bruce Ian
Published: September 2005

A method is described for the evaluation of the elastic constant of a rubber automobile inner tube. The relevant theory is presented, and no expensive apparatus need be used.
Independent-particle models of the nucleus in the 1930s
Authors: Johnson Karen E.
Published: September 2005

In the early 1930s physicists developed two competing ways of describing the structure of the nucleus. One of these, the liquid-drop model as articulated by Niels Bohr, was widely regarded as preferable to Walter Elsasser’s shell model, and became the accepted nuclear model by the end of the decade. According to the conventional history of nuclear physics, independent-particle models like Elsasser’s were only revived 10 years later with the nuclear shell model of Mayer and Jensen. Throughout the period when they claimed to reject the view of nucleons as independent particles, however, nuclear physicists continued to treat nucleons mathematically as independent particles in order to calculate energy levels.
Conformal transformations and the application of complex variables in mechanics and quantum mechanics
Authors: Mittag Laurence , Stephen Michael J.
Published: September 2005

The use of complex variables and conformal mapping have long been useful tools in many branches of physics. However, these methods have not been widely applied in mechanics and elementary quantum mechanics. In this paper, it is shown that there are many useful applications of complex variables and conformal mapping in these subjects. It will be proven that central force problems in the plane have conformal duals. The inverse fifth power law force is self-dual in all dimensions. These results are extended to noncentral forces. Many of these results also apply to the quantum mechanics of a particle. For central force problems and certain noncentral force problems in the plane the Schrödinger equation preserves its form under conformal mapping and the inverse fifth power law force is again self-dual in all dimensions. The methods may also be applied in the presence of magnetic fields.
A narrow-band tunable diode laser system with grating feedback, and a saturated absorption spectrometer for Cs and Rb
Authors: MacAdam K. B. , Steinbach A. , Wieman C.
Published: September 2005

Detailed instructions for the construction and operation of a diode laser system with optical feedback are presented. This system uses feedback from a diffraction grating to provide a narrow-band continuously tuneable source of light at red or near-IR wavelengths. These instructions include machine drawings for the parts to be constructed, electronic circuit diagrams, and prices and vendors of the items to be purchased. It is also explained how to align the system and how to use it to observe saturated absorption spectra of atomic cesium or rubidium.