bluuebunny/crossref_metadata_2025 huggingface dataset:
Induced electric field from a time-dependent current
Authors: Heald Mark A.
Published: March 2005

This note is an extension of the problem posed by Shakur,1 and commented on by Gauthier,2 which asks what induced electric field exists in the vicinity of a long straight wire carrying a current that increases linearly with time. While the problem appears to be elementary, it is in fact quite subtle—more for what it leaves out than what it includes. Here we pose and discuss a number of queries that might occur to someone not satisfied by Shakur’s ‘‘solution.’’
Rudolf Clausius and the road to entropy
Authors: Cropper William H.
Published: March 2005

That Rudolf Clausius invented the entropy concept is well known, but less familiar is the argument that served as his inspiration. This paper traces the development of Clausius’ ‘‘transformation theory’’ of heat, which finally persuaded him to define the measure of transformation equivalence he called entropy.
Induced current effects in Faraday’s law and introduction to flux compression theories
Authors: Namias Victor
Published: March 2005

The exact dynamical and electrical equations for a rod moving on conducting rails in a magnetic field are quite complicated and do not clearly reveal the nature of the physical processes involved, especially in regard to the electromechanical energy transfer taking place in the system. Considerable conceptual simplification is achieved by considering the two-dimensional version of the rod and rails system. The dynamics and the energy balance of the entire system can be established without difficulty in the most general conditions. The complete solution of the problem is obtained in one particular case. More importantly, such a two-dimensional model can provide a simplified but effective introduction to the field of flux compression theories, an active area of research concerned with the design and utilization of flux pumps and the generation of very intense or very weak magnetic fields. An idealized example is treated in detail. Finally, we use the simplified model to briefly discuss other new techniques and devices based on Faraday’s induction law. Among these, the electromagnetic forming of metal sheets which uses the magnetic pressure of an expanding magnetic field to swage them into a desired shape has received a number of industrial applications. Another, more speculative field of interest concerns railguns and other electromagnetic launchers, which are still in the experimental stage, but may someday surpass the traditional chemical explosives or provide a more economical alternative to conventional rocket launching.
Active and passive views of gauge invariance in quantum mechanics
Authors: Kobe Donald H.
Published: March 2005

For a quantum mechanical particle in a classical electromagnetic field, the active and passive views of gauge invariance are compared. In the active point of view, both the wavefunction and the potentials are transformed so that the Schrödinger equation is form invariant. In the passive point of view, a change in the representation of the canonical momentum is made which just cancels the change in the gauge of the potentials. The condition that a gauge-invariant operator has the same expectation value in all gauges gives a functional equation, the solution of which shows that gauge-invariant operators depend only on the kinetic momentum or coordinates.
Science and superstition: Comets and the French public in the 18th century
Authors: Stewart Philip
Published: March 2005

The confirmation in 1759 of Halley’s prediction for the return of the comet of 1682 was a triumphant scientific event, helping to convince a broad public that comets, like other celestial bodies, were knowable natural objects. Nevertheless, the frightening possibility that an unknown comet could appear at any time led to a startling degree of panic on a later occasion, when a study by Lalande on the statistical probability of a collision between earth and a comet was construed by rumor as a prophecy of imminent destruction.
Unveiling the solitons mystery: The Jacobi elliptic functions
Authors: Cervero José M.
Published: March 2005

Several examples are given in which the soliton solutions belonging to well-known nonlinear differential equations arise as simple limits of the Jacobian elliptic functions. The knowledge of the solutions of a single ordinary nonlinear differential equation is sufficient for the subsequent derivation of soliton solutions. Various explicit examples are worked out.
Constructing laboratory courses
Authors: Carlson Edward H.
Published: March 2005

I present an orderly, top-down scheme for constructing laboratory courses. Start by choosing and defining an explicit set of goals. Take special care with such higher level goals as organizational skills, work habits, communication, and ‘‘maturity.’’ Then evaluate the needed degree of coverage of the various goals, pick methods of instruction, and design the units of the course so each goal receives the appropriate relative emphasis. In all stages, be guided by recent results in the field of cognitive science.
Lagrangians for dissipative systems
Authors: Kobe Donald H. , Reali Giancarlo , Sieniutycz Stanislaw
Published: March 2005

A Lagrangian and Hamiltonian formulation can be given for a damped harmonic oscillator with damping linear in the velocity. The canonical momentum is not equal to the kinetic momentum, and the Hamiltonian is not equal to the energy. On the other hand, a pendulum accreting mass has the same Lagrangian and equation of motion. However, in this case the canonical momentum is equal to the kinetic momentum, and the Hamiltonian is equal to the energy. No ambiguity arises if the physical situation is kept in mind.
Integral approach to scattering by a surface impurity
Authors: Lessie Douglas
Published: March 2005

The integral approach to quantum mechanical scattering is exhibited heuristically in a one-dimensional context and applied to the multiple scattering problem of conduction electron scattering by a surface impurity, where the impurity is modeled as a complex delta-function potential. It is shown to provide a much more physically insightful solution than direct solution to the Schrödinger equation. The total reflection amplitude is revealed, and its behavior physically interpreted, as a multiple scattering series of impurity and barrier amplitudes coupled by appropriate phase shifts as the electron wave propagates back and forth between the impurity and surface barrier.
An improved mechanical model to demonstrate the first- and second-order phase transitions of the easy-axis Heisenberg antiferromagnet
Authors: Drumheller John E. , Raffaelle David , Baldwin Mark
Published: March 2005

A simple mechanical model is presented and analyzed which illustrates analogies to the first-order antiferromagnetic to spin–flop phase transition and the second-order phase transition from the ordered phase to the paramagnetic state in an ‘‘easy-axis’’ Heisenberg antiferromagnet.
Numerical path integration without Monte Carlo
Authors: Gerry Christopher C. , Kiefer J.
Published: March 2005

A numerical procedure for evaluating Feynman’s path integral in imaginary time without using the Monte Carlo ‘‘heat bath’’ method is discussed. The method is essentially iterative matrix multiplication and bears a close resemblance to the Feynman procedure of summing all paths by time slicing and then integrating. The procedure is used to determine ground-state energy eigenvalues for the harmonic oscillator, double-well anharmonic oscillator, and the Morse oscillator.
The one-dimensional hydrogen atom
Authors: Van Siclen Clinton
Published: March 2005

A recently found degeneracy in the energy levels of the one−dimensional hydrogen atom is attributed to a hidden O(2) symmetry. (AIP)
The energy dissipated in a switch
Authors: Harper Samuel D.
Published: March 2005

In discussions of switched circuits, the energy dissipated in the switch is usually neglected. However, this energy loss can be a substantial fraction of the energy transfer in a circuit. Here, the energy dissipated in a switch is calculated for a simple switch model. The switch is treated as a resistor, with resistance changing from infinity to zero during a switching time Ts. The model is compared with measurements of an actual transistor switch. Quantitative expressions are obtained for current, power, and energy for a specific time dependence of the resistance. In a resistively loaded circuit, it is shown that the switch dissipates an energy up to 16.7% of (V2/R)Ts, depending on the characteristics of the switch. In a capacitively loaded circuit, the switch dissipates an energy up to 100% of 1/2CV2, depending on two ratios of switch and circuit parameters. It is shown that the energy dissipated in a switch is an important consideration in high duty cycle applications, and that the nature of the switch affects noise generation.
A simple relation between bosons and fermions in angular momentum eigenstates
Authors: Sorensen Raymond A.
Published: March 2005

A correspondence is described relating many-body states of bosons and fermions. This leads to simple connections among the total angular momentum J values allowed for j shells containing several identical bosons or fermions.
Redesigning college- and university-level introductory physics
Authors: Hilborn Robert C.
Published: March 2005

The argument is made that the primary objective of an introductory course in physics should be to develop in the student an understanding of the contemporary activities of physics. To meet this objective, it is necessary to redesign the introductory course to emphasize the process of doing physics, the history of the field, as well as contemporary developments.
The general unrestrained brachistochrone
Authors: Stork David G. , Yang Ju-xing
Published: March 2005

The general unrestrained brachistochrone problem is to find the frictionless track between two points in a uniform gravitational field along which a particle with initial velocity will slide in the shortest time. Particularly important is the condition that the particle remain in contact with the track, even though it is unrestrained to the track. That is, the particle must slide along the track like a block on an inclined plane, not like a bead on a wire. Because of the unusual nature of the constraints, the techniques of Euler and Lagrange cannot be applied to this problem as it stands; a solution is presented here that does not rely on such an approach. The conditions imposed by the initial and final positions and velocities fall into our four classes, each having a unique form of solution, consisting of sections of free-fall parabolas and cycloids.
The three-dimensional hysteresis surface for nickel
Authors: Barnes George
Published: March 2005

The sizable temperature change that the ferromagnetic working substance of a Curie-point heat engine undergoes during each cycle makes the hysteresis loop lie on a three-dimensional surface in magnetic field intensity (H), intensity of magnetization (M), and temperature (T) space. The surface is on the inside of a completely enclosed cavity that contains all possible one-, two-, and three-dimensional hysteresis curves and loops for the element nickel, under normal conditions. The saturation curves are within two infinitely long ‘‘cracks’’ of finite width. Photographs of a three-dimensional scale model of half of the symmetrical cavity for the element nickel are shown. Simple theorems are developed for easy calculation of the work done and the heat transferred along a segment of any three-dimensional hysteresis curve in HMT space.
Measurement of optical absorption by calorimetry and analysis of a solar collector
Authors: Allen L. C. , Wallace J. , Deutscher G. , Lindenfeld P.
Published: March 2005

An apparatus is described for the measurement of absorptance, emittance, and selectivity. It can be used to illustrate the relative importance of heat losses by radiation, conduction, and convection in a solar collector, as well as the effects of selectivity and of full or partial evacuation on the efficiency. The apparatus can be constructed in a reasonably well-equipped departmental machine shop, and is suitable for projects or experiments by advanced undergraduate students.
A demonstration calculation of self-consistent stellar models with convective cores
Authors: Leahy D. A.
Published: March 2005

A quick procedure for calculating self-consistent stellar models is described. The procedure involves the matching of radiative stellar envelope solutions to convective core solutions. The core is assumed to have the adiabatic temperature gradient. This procedure was developed for demonstrating stellar model calculations in upper year undergraduate astrophysics courses.
Generation and experimental measurement of a one-dimensional quasi-crystal diffraction pattern
Authors: Litvin S. Y. , Romberger A. B. , Litvin D. B.
Published: March 2005

A microcomputer-generated one-dimensional quasi-crystal grating is produced on a high-resolution monitor. Photographic reproduction of the grating with about a 30× reduction in size produces an acceptable optical grating. The location of diffraction maxima and the relative intensity pattern produced by passing HeNe laser light through the grating is compared to the theoretical prediction with mixed results. The comparison of two types of film that can be used for this experiment is also discussed.
A simple physical view of the quantum electrodynamic chiral anomaly
Authors: Widom A. , Srivastava Y.
Published: March 2005

The quantum electrodynamic chiral anomaly allows for the possibility of inducing vacuum polarizations with low-energy external sources that do not actually create electron–positron pairs. A simple physical picture of such currents is first provided in one-space–one-time dimensions. The generalization to physical 3+1 dimensions is also presented.
Extending space or separating galaxies?
Authors: Aspden H.
Published: March 2005

It is suggested that the structure of space−time can be studied from the invariance of c and h with cosmic time. (AIP)
Solid-state magnetic-field transducers and Ampere’s law
Authors: Kromminga A. J. , Van Baak D. A.
Published: March 2005

This article describes the use of inexpensive Hall-effect integrated circuits to build magnetic field transducers and the use of these transducers in a sophomore-level experiment that directly illustrates Ampere’s law in its integral form. This experiment has the pedagogical advantages of permitting direct measurement of the vector components of the magnetic field and of illustrating the precise operational meaning of a line integral around a closed path.
Relaxation in resonance absorption demonstrated by the Monte Carlo method
Authors: Liljequist D.
Published: March 2005

A simple demonstration of the effect of relaxation on a resonance absorption spectrum is described. The complexities involved in a formal theoretical treatment are avoided by employing a straightforward and intuitively obvious Monte Carlo simulation. Starting from first-order perturbation theory of resonance absorption, it is noted that the absorption spectrum is related to the Fourier transform of the time dependence of the perturbation and the absorbing oscillator. A semiclassical generalization of the time dependence of the oscillator to include fluctuating resonance frequencies gives a simple expression for the absorption spectrum in the presence of adiabatic relaxation. This expression is evaluated explicitly, using the Monte Carlo method to produce the required random-nature fluctuations.
Analytical solutions for the trajectories and thermal histories of unforced particulates
Authors: Cloutman Lawrence D.
Published: March 2005

Dilute suspensions of finely dispersed particulates are found in many engineering applications. This article shows that the nonlinear equations of motion and heat transfer for the particles may be solved analytically for certain realistic drag and heat transfer functions under idealized conditions. Some applications are discussed.
The quantum mechanics of interacting electrons in a heterochannel
Authors: Wu Jin Zhong , Goodman Bernard
Published: March 2005

A semiconductor heterochannel is both a dielectric sandwich structure and a quantum-well structure. When the channel width d is sufficiently small, charge carriers in it behave like a two-dimensional electron gas. With increasing d, three-dimensional features develop. As this takes place, there is an interesting and somewhat counterintuitive interplay in determining the total interaction energy of the system, between the spreading of the wavefunctions in the third direction and the ‘‘channeling’’ of electric field lines.
Experiments with Fourier transforms at radio frequencies
Authors: Kocher Carl A.
Published: March 2005

Quantitative experiments in spectrum analysis can be performed with a radio receiver and a nonmonochromatic signal source. Construction details are given for a generator of interrupted radio-frequency oscillations in a repeated sequence of N equally spaced bursts, where N=1, 2, 3, ... . The resulting continuous spectrum is analogous to the spatial distribution of light in Fraunhofer diffraction by an N-slit grating. Variation of the burst parameters illustrates the frequency-time uncertainty relation ΔνΔt≊1 (for N=1) and, more generally, the correspondence between time-dependent signals and their Fourier transforms.
Young’s double-slit experiment using speckle photography
Authors: Bahuguna R. D. , Western Arthur B. , Lee Sean
Published: March 2005

A simple experiment on speckle photography for undergraduates is described. The magnitude of a small in-plane displacement (a few microns) of a diffuse object is calculated from an interference pattern similar to the pattern formed in Young’s double-slit interference. A specklegram, formed by a double-exposure photograph of the speckle pattern from the diffuse object, is substituted in place of the usual double slit. Apparatus, exposure details, algebraic equations for analysis of the specklegram, and typical results are presented.
Energy flow in circuits with Faraday emf
Authors: Heald Mark A.
Published: March 2005

Several elementary models are analyzed to clarify the essential features of energy flow in circuits involving electromagnetic induction.
Fraunhofer diffraction by diamond-shaped apertures: A theoretical and experimental study
Authors: Marvin Heidi Jo
Published: March 2005

The Fraunhofer diffraction pattern expected from a diamond-shaped aperture is derived and tested using etched openings in thin sheets of muscovite mica. Experiment is fully compatible with theory. The apertures are easily made and are suitable for laboratory or lecture demonstration. Measurements show the aperture growth to be proportional to etching time.
Resource Letter CPP-1:Cosmology and particle physics
Authors: Lindley David , Kolb Edward W. , Schramm David N.
Published: March 2005

This Resource Letter provides a guide to the literature on cosmology and particle physics. The letter E after an item indicates elementary level or material of general interest to persons becoming informed in the field. The letter I, for intermediate level, indicates material of somewhat more specialized nature; and the letter A indicates rather specialized or advanced material. An asterisk (*) indicates those articles to be included in an accompanying Reprint Book.
Electric field lines near an oddly shaped conductor in a uniform electric field
Authors: Spencer Ross L.
Published: March 2005

Physics textbooks almost always contain at least one picture of an oddly shaped conductor, usually in the section discussing Gauss’ law and the charged conductor. It is, however, rare to see a representation of the field lines in the neighborhood of such a conductor. This article discusses the problem of an arbitrarily shaped uncharged conductor imbedded in an otherwise uniform electric field. The method of successive overrelaxation is used to compute the electrostatic potential from which the electric field lines are computed by numerical integration.
The magnet–solenoid equivalence: A modern experiment using a personal computer
Authors: Basano L. , Ottonello P. , Pontiggia C.
Published: March 2005

The similarity of the induction field patterns generated by a solenoid and by a bar magnet is often illustrated in physics textbooks. Much less is usually said about the differences between the two fields, because it is difficult to devise an experiment, sufficiently simple and accurate, to bring these differences to light. To this end, a modern demonstration is presented here that uses a personal computer to process the recorded data; it also offers an opportunity to illustrate in a simple way the fundamentals of cross correlation and convolution.
Field versus action-at-a-distance in a static situation
Authors: Sharma N. L.
Published: March 2005

The introduction of the electromagnetic field has been a necessity only in time-varying cases. In static or steady-state cases, it has been mostly a convenience. An example is discussed where even in static situations the field is a necessity in order to conserve angular momentum. The results are used to provide a classical picture for the electron spin in terms of the angular momentum of the associated electromagnetic field.
The first spin-offs from the strategic defense initiative
Authors: Dowling John
Published: March 2005

President Reagan’s Strategic Defense Initiative (SDI) is a plan to make nuclear weapons impotent and obsolete. Physicists have a professional interest in such a program because SDI involves high-power lasers, x-ray lasers, particle beams, large astronomical mirrors, computers, increased space shuttle program, etc. SDI is of interest to physics teachers because there are many important physical problems that must be resolved before this defense system will work. In this article several problems that SDI needs to address are sketched. There is a short discussion of each problem, but no detailed solutions or answers. Physics teachers can use these problems to discuss the various aspects of SDI that are germane to ‘‘Science and Society’’ type physics courses.
Aberration and Doppler shift: An uncommon way to relativity
Authors: Blatter H. , Greber T.
Published: March 2005

Aberration, as well as the Doppler shift, are phenomena close to everyday experience. Special aspects of relativity are derived from axioms concerning the conformal celestial spheres of coinciding observers and are presented with elementary geometrical tools. One way of linking the mathematical hypotheses to physical quantities related to space-time is demonstrated. The classical formulas for aberration and Doppler shift are used as starting points for deriving the relativistic counterparts.
The harmonic oscillator via functional techniques
Authors: Donoghue John F. , Holstein Barry R.
Published: March 2005

Although functional methods are common in the research literature, they are not generally seen by students until a course in field theory. Nevertheless, it is straightforward and pedagogically useful to treat a familiar problem—the harmonic oscillator—via such techniques, as shown in the present work.
On the product of noncommuting quantum observables
Authors: Kapuscik Edward
Published: March 2005

It is shown that the symmetrized product of noncommuting quantum observables contradicts, in general, the canonical quantization procedure.
Optical heterodyne (coherent) detection
Authors: Jacobs S. F.
Published: March 2005

The optical heterodyne principle is described and its history traced. Early hopes for optical communication by this technique were frustrated by problems of wavefront degradation and laser frequency instability. However, fiber optics has recently revitalized this as an attractive possibility. In the interim, many other successful applications have been found that exploit different advantages of the heterodyne principle. Several examples are described. A number of simple optical heterodyne experiments utilizing a HeNe laser and electrical spectrum analyzer are presented. Details are furnished concerning experimental requirements and special considerations for optical heterodyne detection.
Gauge transformations in classical mechanics as canonical transformations
Authors: Kobe Donald H.
Published: March 2005

Gauge transformations for a classical charged particle are a special case of classical canonical transformations. The principle of form invariance under a gauge transformation follows as a special case of the form invariance of Hamilton’s equations under a canonical transformation.
Voltage measurements in a loop surrounding a solenoid: Some further ‘‘paradoxes’’ due to stray capacitance
Authors: Mak S. Y. , Young K.
Published: March 2005

Voltage measurements in a loop with two resistors surrounding a solenoid with a changing flux have been used to clarify concepts such as potential difference. Actual demonstrations are plagued by further paradoxes, such as the polarity dependence of the voltage measured across a resistor. These are reported and resolved in terms of stray capacitance between the loop and the solenoid producing the flux. In order to avoid these further paradoxes, it is suggested that the experiment is best performed using a standard demonstration transformer.
Temporal order in (1+1)-dimensional relativity
Authors: Aravind P. K.
Published: March 2005

Consider the following problem, restricted to relativity in one space and one time dimension: Given the space-time coordinates of n events as measured by an observer S, how can one tell if another (relatively moving) observer’s claim to seeing the events in a particular order is true? And if it is true, what are the bounds on his velocity? Both an analytical and a geometrical solution to this problem are given. The problem of enumerating all the possible time orderings that a given set of events can have in different reference frames is also solved. Ramsey’s theorem in graph theory is shown to provide some interesting temporal interconnections between members of a set of space-time events.
Precession of the perihelion of Mercury
Authors: Stump Daniel R.
Published: March 2005

The equation of motion for a test mass in the gravitational field of a spherical mass is written in a form that can be used in an undergraduate mechanics course. A simple calculation of the general relativistic precession of the perihelion of Mercury is presented.
The measurability of the kinetic momentum of a charged particle in a magnetic field
Authors: Healy W. P.
Published: March 2005

Uncertainty relations are derived for the components of the kinetic momentum (mass times velocity) of a charged particle in a magnetic field. In constrast to the components of the canonical momentum, the components of the kinetic momentum do not all commute with each other when the field is not zero. The uncertainty relations are illustrated by two Gedanken experiments in which the kinetic momentum is measured by using (a) the Doppler shift of emitted radiation and (b) the angle of deflection of the particle by the field.
Critique and correction of the textbook comparison between classical and quantum harmonic oscillator probability densities
Authors: Leubner C. , Alber Margot , Schupfer N.
Published: March 2005

This comparison, although well meant, is unsuitable for demonstrating in introductory quantum mechanics the convergence of classical and quantum predictions for large quantum numbers, for it really tries to match ‘‘classical apples’’ with ‘‘quantum pears’’! First, it compares a classical oscillatory state with a quantum stationary state, instead of comparing it to the corresponding quantum nonstationary state. Second, it compares probabilities of different quality, namely, a classical probability of the classical oscillator (which could be circumvented by specifying the initial conditions precisely) with a quantum probability of the quantum oscillator (which cannot be avoided by any means). However, it is shown that both defects can be nicely corrected, illuminating the fact that—if properly formulated— classical and quantum oscillators have more in common than the textbooks are trying to make the beginner believe. The associated quantum position probability density, because it is now truly analogous to the classical situation, agrees much better with the classical curve than the textbook one does, and its analytical form also explains why the textbook quantum curve, derived from an unwarranted comparison, nevertheless resembles the classical curve in some sense.
On electric fields produced by steady currents
Authors: Zapolsky Harold S.
Published: March 2005

It is well known that an electric (as well as a magnetic) field exists in a reference frame moving relative to a dc circuit that appears to be electrically neutral in its own rest frame. The source of this field is customarily treated as a continuous charge density, which appears in the moving frame as a consequence of the fact that charge and current densities are separate components of a four-vector, which become mixed under the operation of a Lorentz transformation. It is possible to analyze this situation in a different way, by considering the superposed Lienard–Wiechert fields of a large number of moving point charges in the limit that their spacing becomes infinitesimal. While this analysis is not as simple as the standard one, it does expose some interesting physics that is masked by the standard treatment. It is also a useful approach in resolving a paradox that appears to occur when charge and current densities are treated as static objects.
Method of images and electrostatic screening by a polarized dielectric sphere
Authors: Van Siclen Clinton DeW.
Published: March 2005

The electrostatic potential due to a point charge outside a polarized dielectric sphere is calculated by considering the analagous situation for a conducting sphere. (AIP)
A simplified proof of Bertrand’s theorem
Authors: Tikochinsky Yoel
Published: March 2005

By using a technique borrowed from the inverse problem for one-dimensional motion, the proof of Bertrand’s theorem concerning the possible central forces leading to closed orbits is considerably simplified.
Symbolic derivation of the electrodynamic Green’s tensor in an anisotropic medium
Authors: Weiglhofer Werner
Published: March 2005

A symbolic inverse operator technique is used to derive the electromagnetic Green’s tensor of an anisotropic (uniaxial) medium. By using algebraic matrix identities, the tensor differential operator of the governing field equation is inverted in a straightforward way. Thus the correct result is obtained, which has been found elsewhere with the help of a much more complicated analysis.
The classical limit of quantum mechanics from Fermat’s principle and the de Broglie relation
Authors: Rosenquist Mark , Evans James
Published: March 2005

The classical limit of quantum mechanics may be obtained, in a much simpler fashion than usual, by applying the de Broglie relation to Fermat’s principle.
Effect of discontinuities in the chopped wave state upon momentum distribution
Authors: Brenner Cathleen A. , Brill Orville L.
Published: March 2005

The effects of discontinuities in the zeroth and first derivatives of the Schrödinger wavefunction upon the momentum distribution of a particle are illustrated for the chopped wave state. Smoothing the discontinuities in the chopped wave state by use of a modulated Gaussian results in a single continuous, differentiable wavefunction which, in the corresponding limits, permits proper mathematical treatment of the uncertainty in momentum for four common cases: the chopped wave, the free particle, the Gaussian packet, and the localized particle.
The anthropic principle II
Authors: Rosen Joe
Published: March 2005

The anthropic principle proposed by the author is discussed and clarified and compared with other versions. It is applied to an explanation of space and time. A self-contained universe picture is constructed, which is richer than the unique universe picture, but allows the operation of the anthropic principle. It implies an intimate relation between space-time and the quantum.
Unbounded orbits of a swinging Atwood’s machine
Authors: Tufillaro N. , Nunes A. , Casasayas J.
Published: March 2005

The motion of a swinging Atwood’s machine is examined when the orbits are unbounded. Expressions for the asymptotic behavior of the orbits are derived that exhibit either an infinite number of oscillations or no oscillations, depending only on a critical value of the mass ratio.
A general method for treating the incidence of a plane electromagnetic wave on a plane interface between dielectrics
Authors: Navasquillo Joaquin , Such Vicente , Pomer Francisco
Published: March 2005

The fields of the reflected and refracted waves produced when a plane electromagnetic wave impinges on a plane boundary are related to the incident fields by means of a tensorial transformation. This procedure allows a unified treatment of external, internal, and total internal reflection and is suitable for general problems involving transformations of electromagnetic waves. As an application, the transmitted fields for total internal reflection of a bounded electromagnetic beam are obtained.
Direct method for measuring the speed of sound
Authors: Karshner G. B.
Published: March 2005

Using the time-of-flight method, the speed of sound is measured directly by means of an inexpensive circuit and an oscilloscope. The instantaneous nature of this method lends itself to a clear and simple demonstration of the speed of sound in air and various gases. Both a lecture demonstration and a laboratory experiment are presented.
Resource Letter ETC-1: Extraterrestrial civilization
Authors: Kuiper Thomas B. H. , Brin Glen David
Published: March 2005

This Resource Letter provides a guide to the literature about intelligent life beyond the human sphere of exploration. It offers a starting point for professionals and academics interested in participating in the debate about the existence of other technological civilizations or in the search for extraterrestrial intelligence (SETI). It can also serve as a reference for teaching. This Letter is not intended as an exhaustive bibliography, but several extensive bibliographies have been cited. The letter E after an item indicates elementary, nontechnical material of general interest to persons becoming informed in the field. Intermediate level material, of a somewhat more specialized nature, is indicated by the letter I. The annotation A indicates advanced, technical material. An asterisk (*) precedes items to be included in an accompanying Reprint Book.
Heat experiment with a microwave oven
Authors: Lonc W. P.
Published: March 2005

An experiment, suitable for an introductory laboratory course, is described in which a relatively common household item—the microwave oven—is used to do a heat experiment verifying the conservation of energy principle.
Dynamic impedance matching with a lever
Authors: Crawford Frank S.
Published: March 2005

Multiple elastic collisions are analyzed that occur between an incident mass M1, a target mass M2, and a single intermediating hinged lever of moment of inertia I that bounces back and forth between the two masses, transferring angular momentum and energy with each double collision until, if I is chosen correctly, 100% of the energy has been transferred from M1 to M2 in N double collisions, where N=1, or 2, or 3, or ... . The model was inspired by the mechanical transformer, designed and built by Ansbacher, that employs two nearly massless levers as intermediaries so as to achieve nearly complete energy transfer between two masses on an air track.
Complex analysis and quantum mechanics: A perturbative approach for the evolution operator
Authors: Moretti Paolo
Published: March 2005

A simple way of obtaining an explicit expression for the perturbative expansion of the evolution operator to any order is shown.
An introduction to generalized functions and their application to static electromagnetic point dipoles, including hyperfine interactions
Authors: Skinner Ray , Weil John A.
Published: March 2005

The Dirac δ function, the Heaviside step function, and all their derivatives are examples of generalized functions, also called distributions. The mathematical theory of generalized functions provides a useful framework for the description of the potentials and fields occurring in electromagnetic theory. It allows for greater clarity and applicability than that given by ordinary functions, especially where point charges and point dipoles are concerned. The present article provides a logical tutorial presentation of the relevant material. Maxwell’s equations for static point sources are reinterpreted in terms of potentials and fields that are generalized functions. Dipolar interactions are discussed in terms of these. Specifically, as an example, the hyperfine spin Hamiltonian for a 1-electron system is considered in some detail.
Early diamond making at General Electric
Authors: Strong H. M.
Published: March 2005

This is an account of how GE’s early interest in a new super-hard metal, cobalt cemented tungsten carbide, for drawing tungsten lamp filament wire, led to a broader interest in the realm of super pressure and to diamond synthesis. P. W. Bridgman at Harvard University had demonstrated the new metal’s (‘‘Carboloy’’) ability to generate pressures of 100 000 atm (100 kbars). Armed with this new capability, GE initiated a diamond project in 1951. In December 1954 two synthesized diamonds emerged in a marginal experiment that for a while could not be reproduced. Nevertheless, that experiment gave the critical clue to the process that now provides 90% of the world’s industrial diamond needs. The high-pressure high-temperature process (HPHT) together with the new carbon vapor deposition process (CVD) brings diamonds’ unique and valuable properties to applications requiring crystals tailored to fit specific needs.
The oscillation of the synodic period of the Moon: A ‘‘beating’’ phenomenon
Authors: Reese Ronald Lane , Chang George Y. , Dupuy David L.
Published: March 2005

The synodic period of the Moon (the period of the phases or the time from, say, full moon to full moon) exhibits oscillations about its mean value of 29.530 59 days which immediately suggest a ‘‘beating’’ between at least two frequencies. A Fourier analysis can provide some insight into the causes of the oscillation without the complexity of rigorous lunar theories. Such a Fourier approach is quite appropriate for undergraduate students of physics and astronomy, but, of course, is no substitute for more rigorous lunar theory. Fourier analysis suggests the periods of the beating frequencies to be 411 and 366 days. The 411-day period arises since this is the time it takes the Sun to return to a similar orientation along the line of apsides (the major axis) of the lunar orbit. The 366-day period is about a year or the time it takes the Earth to orbit the Sun. Since the lunar phases occur because of the relative orientation of the Earth, Moon, and Sun, an annual period might also be anticipated. The beat period of 3293 days is half the saros eclipse cycle period of 6585.3 days. Alternating lunar and solar eclipses are separated by the beat period. Higher frequency effects are apparent from the data, but not from the elementary Fourier approach. Thus this procedure must be used with caution in analyzing complex periodic data in astronomy.
Clausius–Mossotti effects: Classical and quantum mechanical approaches
Authors: Ortuño M. , Chicon R.
Published: March 2005

Clausius–Mossotti effects are a consequence of the fact that a polarizable center in a dielectric does not see its own field. A derivation of this local field correction, in which its physical origin is most evident, is performed in a classical context. It is shown how in a quantum mechanical approach the Clausius–Mossotti correction in crystalline dielectric solids is implicitly taken into account if the energy gap of the solid is used rather than the atomic energy gap.
Measuring solar luminosity with a photodiode
Authors: DuPuy David L.
Published: March 2005

This article describes a simple method suitable for an undergraduate laboratory to measure solar luminosity with a photodiode. Using an uncalibrated photodiode, the results of this method are typically accurate to about 10%. Corrections are required for the photodiode spectral response along the solar Planck curve, and for the sunlight absorbed in the Earth’s atmosphere. A value for the solar constant may also be obtained.
A generalization of the Ehrenfest urn model
Authors: Güémez J. , Velasco S. , Hernández A. Calvo
Published: March 2005

This article presents a generalization of the Ehrenfest urn model in order to obtain the time evolution of the number of molecules n(t) in any subvolume V of a vessel V0 containing N molecules of a gas. The formalism makes use of the equilibrium (stationary) probability distribution PN(n,V,V0)≡P0(n) characterizing the gas. Two cases of pedagogical value, the ideal gas (binomial distribution) and the lattice gas (hypergeometric distribution) are considered.
Solutions to time-harmonic Maxwell equations with a Hertz vector
Authors: Sein J. J.
Published: March 2005

The physical solutions to time-harmonic Maxwell equations for arbitrary sources in vacuo and for arbitrary media are formulated with a single Hertz vector. It is shown that in the special case of magnetic dielectrics the formulation is equivalent to the traditional approach with an electric and a magnetic Hertz vector. The formalism is illustrated with an integral-equation analysis of reflection from a semi-infinite conducting dielectric.
An inexpensive, versatile experiment for teaching computer-aided experimentation
Authors: Whiteley Richard V. , Luke Keung L.
Published: March 2005

In this article computer-aided experimentation means using the microcomputer as a laboratory instrument emulator, data logger, and analyzer in an experiment. Through an inexpensive, yet versatile experiment involving an RLC circuit, this article describes how to use the microcomputer as a pulse generator/voltage source, a digital oscilloscope, an ac voltmeter, a frequency meter, and a data logger and analyzer by investigating its time- and frequency-domain behavior. Excellent agreement is found between experiment and theory, which validates the measurement, hardware, and software techniques used. A new and accurate method for characterizing L and C at the natural frequencies of the RLC circuit is also presented.
Quantum-theoretic definitions of the measurement event
Authors: Dotson Allen C.
Published: March 2005

Two ways of defining measurement events in quantum mechanics are discussed in the context of spin-correlation analyses. The standard approach first leads to a reasonable model, which is now known to be unworkable, and then to a model employing superluminal connections. The alternative approach does not lead to models, but fits in well with one understanding of the Copenhagen interpretation and may help to clarify options in further developing that interpretation.
Applications of Newtonian mechanics to curve fitting
Authors: Swanson S. , Garner J.
Published: March 2005

The least-squares method of curve fitting may be posed as a problem in Newtonian mechanics for a fictitious particle. By assuming fictitious time dependence for the fitting parameters, Newtonian equations of motion (EOM) for the particle are obtained. In one technique, dynamic simulated annealing (DSA), the EOM are second order in time and, in another, steepest descents (SD), they are first order due to the presence of damping. These EOM’s are solved to perform Gaussian fits to singly peaked and doubly peaked data. Generalization to many-peaked data, as occur frequently in spectroscopy, is straightforward.
The adiabatic propagator
Authors: Holstein Barry R.
Published: March 2005

The Feynman propagator is expanded in the adiabatic limit, wherein the time scale over which the potential varies is long compared to typical quantum mechanical oscillation times in the problem. Comparison with known exact results is made for two simple models.
Time derivatives of unit vectors in orthogonal curvilinear coordinate systems
Authors: Koo W. K. , Liew Y. C.
Published: March 2005

A pedagogically pleasing and mnemonically useful method for expressing the velocity and acceleration vectors in orthogonal systems of coordinates is shown. The method relies on expressing the time derivatives of the unit vectors in matrix form. It is also noted that the spatial derivatives of the unit vectors obey a similar rule.
Magnetic lines of force and rubber bands
Authors: Cross Rodney C.
Published: March 2005

Magnetic forces are sometimes viewed as being due to tension in the field lines or mutual repulsion of field lines. The validity of these concepts is examined by considering the stresses acting on a straight, current-carrying conductor in a uniform magnetic field.
Self-similarity and long-tailed distributions in the generation of thermal light
Authors: Rockower Edward B.
Published: March 2005

Two counterintuitive phenomena are studied. (1) It is well known that a thermal electromagnetic field has a Bose–Einstein (geometric) distribution of photons within a coherence volume. This arises because of the photon clumping characteristic of a thermal Boson field. On the other hand, the distribution of the number of atoms emitting photons through spontaneous emission must be Poisson if emissions are truly independent. (2) The average time between atomic decays is finite, being just the inverse of the total decay rate of the atoms. However, it is shown that in a coherence volume or in a single mode of the resulting Gaussian electromagnetic field, the average photon interarrival time is infinite. Hence, on average, an infinite length of time must pass before 〈N〉 photons arrive in the field. These apparent paradoxes are discussed, showing how both arise from random interference of Boson fields. The infinite waiting time is seen to be one manifestation of a long-tailed distribution. Such distributions are increasingly important by virtue of their relation to self-similarity and fractals, e.g., strange attractors in the description of deterministic chaos; therefore, it is of interest to understand their counterintuitive properties and see how they arise naturally even in more traditional analyses.
Relativistic phase velocity transformation
Authors: Bachman R. A.
Published: March 2005

By utilizing the appropriate Doppler formulas, it is shown that phase velocities in both Galilean and relativistic kinematics transform according to rules different from the ordinary velocity addition laws. As corollaries, it is demonstrated that (i) phase velocities parallel to the inertial frames’ relative velocity transform according to the Lorentz velocity addition rule; (ii) regardless of its direction, the velocity of light in vacuum transforms as a relativistic particle velocity; and (iii) the relativistic phase velocity transformation rule reduces to the Galilean rule in the nonrelativistic limit.
The most tightly bound nucleus
Authors: Shurtleff Richard , Derringh Edward
Published: March 2005

An explanation is given relative cosmic abundances of Fe-56 and Ni-62. (AIP)
Errors due to average velocities
Authors: Denardo Bruce , Wong Selmer , Lo Alpha
Published: March 2005

The error caused when the average velocity over an interval is used to approximate the instantaneous velocity at either the time or spatial midpoint of the interval is calculated for one-dimensional constant acceleration and for simple harmonic motion. The results for simple harmonic motion are applied to the computed energy, which these velocity approximations cause to deviate from constancy. Also solved for are motions in which the average velocity over any interval equals the instantaneous velocity at the spatial midpoint of the interval. Finally, for a glider-and-springs system on an air track, experiment and theory are compared for the case of simple harmonic motion where time midpoints are used.
The Abramson ray-tracing method for holograms
Authors: Olson D. W.
Published: March 2005

The Abramson ray-tracing procedure for thin-transmission holograms is reviewed and extended. Example ray tracings are performed for an instructive experimental arrangement. Special effects considered are: (a) moving the viewing point source; (b) reversing the viewing light ray direction; (c) changing the viewing wavelength; and (d) pseudoscopy.