bluuebunny/crossref_metadata_2025 huggingface dataset:
The American Physical Society: A survey of its first 50 years
Authors: Phillips Melba
Published: September 2005

As the distinct scientific professions arose in the 19th century, the need for professional societies was felt. Spurred by the momentous discoveries of its last decade (x rays, radioactivity, the electron), the American Physical Society was organized in 1899. The initiative was taken by Arthur Gordon Webster; Rowland and Michelson, the most prestigious physicists in the country, accepted positions as president and vice president. The chief and almost exclusive concern of APS was the encouragement of research in pure physics. This single-minded behavior resulted in the formation of other societies of physicists: the Optical Society of America in 1916, the Acoustical Society of America and the Society of Rheologists in 1929, and the American Association of Physics Teachers in 1930, with talk of associations for applied physics and mathematical physics. That fragmentation coupled with the financial difficulties of the APS led to the formation of the American Institute of Physics in 1931. AIP played a more active role during the war years than did APS, but after the war the Physical Society grew rapidly. Its 50th anniversary celebration, held at Harvard, was characterized by optimism despite the existence of many new problems.
The physics of fly casting
Authors: Robson John M.
Published: September 2005

The physics of the forward motion of the flyline during a fly cast is discussed, and a computer model of this motion is proposed which reproduces the main features of this part of the cast.
Lise Meitner’s escape from Germany
Authors: Sime Ruth Lewin
Published: September 2005

Lise Meitner (1878–1968) achieved prominence as a nuclear physicist in Germany; although of Jewish origin, her Austrian citizenship exempted her from Nazi racial laws until the annexation of Austria in 1938 precipitated her dismissal. Forbidden to emigrate, she narrowly escaped to the Netherlands with the help of concerned friends in the international physics community.
Resource Letter QHE-1: The integral and fractional quantum Hall effects
Authors: Van Degrift C. T. , Cage M. E. , Girvin S. M.
Published: September 2005

This Resource Letter provides a guide to the literature on the integral and fractional quantum Hall effects. 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 articles that are especially useful or interesting; a double asterisk (**) indicates those articles to be included in an accompanying reprint book.
The effects of coefficient of restitution variations on long fly balls
Authors: Kagan David T.
Published: September 2005

The coefficient of restitution of major league baseballs is required to be 0.546±0.032. These allowed variations affect the launch velocity and ultimately the range of fly balls. The variations in the range for well-hit balls are calculated here to be on the order of 15 ft. These calculations provide an interesting collection of mechanics problems that might be of interest for undergraduate students.
Did the Big Bang begin?
Authors: Lévy-Leblond Jean-Marc
Published: September 2005

It is argued that the age of the universe may well be numerically finite (20 billion years or so) and conceptually infinite. A new and natural time scale is defined on a physical basis using group-theoretical arguments. An additive notion of time is obtained according to which the age of the universe is indeed infinite. In other words, never did the Big Bang begin. This new time scale is not supposed to replace the ordinary cosmic time scale, but to supplement it (in the same way as rapidity has taken a place by the side of velocity in Einsteinian relativity). The question is discussed within the framework of conventional (big-bang) and classical (nonquantum) cosmology, but could easily be extended to more elaborate views, as the purpose is not so much to modify present theories as to reach a deeper understanding of their meaning.
An exotic harmonic oscillator: The frequency depends on initial conditions
Authors: Sztrajman Jorge B.
Published: September 2005

A simple mechanical system formed by two bodies joined by means of a rigid bar and constrained to move in orthogonal directions is presented. The behavior is analogous to that of a special type of simple harmonic oscillator: The frequency depends on the initial conditions whereas the amplitude always turns out to be the same.
Conduction current and the magnetic field in a circular capacitor
Authors: Bartlett D. F.
Published: September 2005

From the perspective of Ampere’s circuital law, either displacement current or conduction current can be viewed as the source for the magnetic field inside a circular capacitor that is slowly being charged. The Biot–Savart law is more selective. How it can be used with conduction current alone is shown. Also considered is the ‘‘leaky capacitor. Here it is shown that an isolated charged capacitor which discharges slowly in a homogeneous Ohmic dielectric produces no magnetic field anywhere. Alternatively, a field is produced if the conducting material is confined to a limited region. This field is calculated for a circular capacitor when only the material in the gap is conducting.
Fractal dimension: Limit capacity or Hausdorff dimension?
Authors: Essex Christopher , Nerenberg M. A. H.
Published: September 2005

It is shown that for often encountered nonpathological sets the limit capacity and the Hausdorff dimension differ. This raises the question in the context of physics as to which of these should be called the ‘‘fractal’’ dimension.
Tangent law of refraction for heat conduction through an interface and underlying variational principle
Authors: Tan A. , Holland L. R.
Published: September 2005

By considering heat flux as ‘‘rays,’’ a law of refraction for heat conduction through an interface is obtained from the boundary conditions. This law is analogous to but different from Snell’s law, with the tangents of the angles of incidence and refraction replacing the sines and the reciprocal of the thermal conductivity taking the place of the refractive index. The deviation of the refracted ray departs from that predicted by Snell’s law as the angle of incidence increases and is zero for both normal and grazing incidences. The tangent law of refraction is also derived from a minimal principle similar to Fermat’s. Finally, a variational principle of heat conduction is postulated and illustrated with a simple example.
Optical bistability experimentation with liquid dyes
Authors: Zhang H. Y. , He X. H. , Tang S. H. , Kuok M. H.
Published: September 2005

A practical method for the observation of nonlinearity in refractive index using only low-cost equipment is described. The system is simple to operate and yet didactic, and has the aesthetic appeal of myriad variations of etalon fringes and hysteresis loops. It is also suitable for mass duplication as a standard classroom experiment in the undergraduate laboratory. Exemplary results are shown.
Physical cause of group velocity in normally dispersive, nondissipative media
Authors: Johnson Francis S.
Published: September 2005

A physical explanation for group velocity is given for the very common case of group velocity less than the phase velocity with negligible absorption. The underlying physics is that a nonpropagating or immobilized energy density must be present in the medium associated with the presence of the wave field. The individual waves carry energy forward in a wave packet and energize the medium in the forward portion of the packet. In the rear portion of the packet, the individual waves grow at the expense of the energy immobilized in the medium, the particle motions in the medium being in phase with the wave field and therefore capable of generating new waves in phase with the group of waves that produced them. The physics is conveniently described in terms of deep water waves, but the principles involved apply equally well to other dispersive, nonabsorbing media, including plasmas, dielectrics, and waveguides. The flux of energy can be expressed as the phase velocity times that part of the energy density that propagates with the individual waves or, averaged over a wave period, as the total energy density (including the energy immobilized in the medium) times the group velocity. This eliminates the confusion commonly present when an attempt is made to interpret the Poynting flux for electromagnetic waves in terms of the product of an energy density and the group velocity. The group velocity is just the weighted average velocity.
Verification of fundamental principles of mechanics in the computerized student laboratory
Authors: Eckstein Shulamith G.
Published: September 2005

The new high standard of precision made possible by computerized data acquisition and analysis enables students to investigate many principles of mechanics that have heretofore not been feasible. In collision experiments on an air track, the motion of gliders can be followed in detail throughout the collision. The motion of the gliders may then be analyzed in order to study center-of-mass motion, action and reaction forces, force and the energy gradient, impulse and momentum change, and work and energy change. In addition, the force law between two magnets may be measured statically, and the result compared with that obtained by dynamic measurements.
Interference between spontaneous emission in different directions
Authors: Lai Ming , Diels J.-C.
Published: September 2005

Is there coherence between the two beams spontaneously emitted in opposite directions by a thin plane of radiating atoms? A simple interference experiment gives a positive answer to this question.
Perturbation of Uranus by Neptune: A modern perspective
Authors: Lai H. M. , Lam C. C. , Young K.
Published: September 2005

The perturbation of Uranus by Neptune is analyzed in a simple model, in which the unperturbed orbits are regarded as circular and coplanar. Both the forward problem of calculating the deviation in the position of Uranus and the inverse problem of using the observed deviations to infer the elements of Neptune are attempted. The model accounts for the data quite well, offering a simple understanding of its features. Because the perturbation is nearly resonant, the effect of Neptune is actually an order of magnitude larger than the historically reported remaining deviation and the inverse problem also admits a fairly good solution that places Neptune in a diametrically opposite position.
The contracting square quantum well
Authors: Pinder D. N.
Published: September 2005

The one-dimensional square quantum well of varying width is shown to be an instructive example for testing the appropriateness of approximate solutions in quantum mechanics. The range of wall speeds over which the adiabatic approximation is applicable is investigated and related to the initial energy of the quantum system for both expanding and contracting wells. However, of more interest is the applicability of the sudden approximation to these systems. It is shown that this approximation is appropriate for expanding wells at quite modest wall speeds, whereas the approximation cannot be applied for contracting wells no matter how rapidly the well width contracts. The physical reasons for the inapplicability of the sudden approximation for contracting wells is investigated.
Generalization of the Hagen–Poiseuille velocity profile to non-Newtonian fluids and measurement of their viscosity
Authors: Eu Byung Chan
Published: September 2005

By using the constitutive equation for the stress tensor that yields a viscosity formula similar to the Eyring formula for non-Newtonian fluids and solving the hydrodynamic equation for a tube flow of such fluids, a generalization is obtained of the Hagen–Poiseuille formula for velocity profile in tube flow under pressure. The volume flow rate is calculated with the velocity profile, and a method of measuring zero shear rate viscosity is suggested. As the pressure difference increases, the calculated velocity profiles become increasingly flatter in the midportion of the tube than that predicted by the Hagen–Poiseuille formula, which remains parabolic for all values of the pressure difference.
Expansion coefficients of a squeezed coherent state in the number state basis
Authors: Gong J. J. , Aravind P. K.
Published: September 2005

An analytic expression is obtained for the expansion coefficients of a single-mode squeezed coherent state in the number state (or Fock) basis. This is done by deriving a set of coupled recursion relations for the coefficients that are solved in closed form. The result coincides with that of Stoler and Yuen but the present method has the advantage (for neophytes) that it does not involve any sophisticated operator ordering techniques. Thus the present approach is suitable for inclusion in a course on quantum mechanics dealing with squeezed states.
Force-free magnetic fields
Authors: Zaghloul H. , Barajas O.
Published: September 2005

This article reviews the subject of force-free magnetic fields. It critically analyzes the force-free condition, explaining that it behaves properly under Lorentz, parity, rotational, and time-reversal transformations. It refutes the proof that it is impossible to have completely force-free magnetic fields. It shows how general solutions of the force-free condition in rectangular, cylindrical, and spherical coordinate systems are obtained. It explains how these fields have been applied in different areas of physics.
The field strength and the Lagrangian of a gauge theory
Authors: Pal Palash B. , Sateesh K. S.
Published: September 2005

A modified method of obtaining gauge field Lagrangians is presented based on extending the rule of converting ordinary derivatives to covariant derivatives. (AIP)
Poetry for physicists
Authors: Tobias Sheila , Abel Lynne S.
Published: September 2005

In an effort to discover what makes the humanities difficult and unpopular with some science and engineering students, 14 Cornell faculty from the disciplines of chemistry, physics, applied mathematics, geology, materials science, and engineering were invited to become ‘‘surrogate learners’’ in a junior/senior level poetry seminar designed expressly for them. Their encounter with humanistic pedagogy and scholarship was meant to be an extension of ‘‘Peer Perspectives on Science’’ [see S. Tobias and R. R. Hake, ‘‘Professors as physics students: What can they teach us?’’ Am. J. Phys. 56, 786 (1988)]. The results challenge certain assumptions about differences between scholarship and pedagogy in the humanities and science (as regards ‘‘certainty’’ and models). But the experiment uncovered other problems that affect ‘‘marketing’’ the humanities to science and engineering students. Results are some additional insights into what makes science ‘‘hard’’ for humanities students and why physical science and engineering students have difficulty with and tend to avoid courses in literature, as well as into what can make humanities courses valuable for science students.
The twin paradox revisited
Authors: Dray Tevian
Published: September 2005

The twin paradox of special relativity results from failing to recognize the fundamental asymmetry between the two twins: One and only one twin changes direction and thus undergoes acceleration. What happens if the universe is closed, so that the twin in the rocket can return to Earth without changing direction? The twin paradox is reformulated in a closed universe (a cylinder) and then resolved by showing that there is still a (much more subtle!) asymmetry between the two twins.
Models of baseball bats
Authors: Brody Howard
Published: September 2005

By observing the vibrations of a hand-held baseball bat, it is possible to show that the bat behaves as if it were a free body at the impact of the bat and the ball. The hand-held bat shows none of the behavior of a bat with one end firmly clamped in a vise.
Physical holonomy, Thomas precession, and Clifford algebra
Authors: Urbantke H.
Published: September 2005

After a general discussion of the physical significance of holonomy group transformations, a relation between the transports of Fermi–Walker and Levi–Cività in special relativity is pointed out. A well-known example—the Thomas–Wigner angle—is rederived in a completely frame-independent manner using Clifford algebra.
The influence of distant boundaries on quantum mechanical energy levels
Authors: Barton G. , Bray A. J. , McKane A. J.
Published: September 2005

Change in the energy of bound states of the one-dimensional Schrödinger equation is investigated when distant boundaries are introduced where previously none existed. The argument covers the truly one-dimensional equation and, also, the radial equation for central potentials with spherically symmetric boundaries. A simple, explicit formula for this energy change is derived and is illustrated with specific examples, including the harmonic oscillator and the ground state of the hydrogen atom.
Fractal gases of zero momentum with respect to all inertial frames
Authors: Moore Guy S. M.
Published: September 2005

Unlike gases containing molecules obeying Maxwell–Boltzmann statistics, ‘‘fractal gases’’ obey the fundamental axiom that their linear momentum is zero when resolved in any direction with respect to all inertial frames of reference. In contrast to speculation, the properties of fractal gases obeying Newtonian mechanics, or special or general relativity can be investigated in a way similar to the logic of geometry. They have the following properties: (1) An entire fractal gas cannot decay into a Maxwell–Boltzmann distribution, but is in a state of overall equilibrium. (2) Localities tend toward localized equilibrium, upset later by collision with other localities. (3) Fractal gases contain temperature differences that are a source of temporary order. (4) The appearance of a fractal gas to a hypothetical observer would suggest creation in an initial discontinuity.
Correlated wavefunction of two particles in an infinite well with a delta repulsion
Authors: Mohallem J. R. , Oliveira L. M.
Published: September 2005

The generator coordinate method is applied to the one-dimensional model problem of two particles in an infinite potential well with a delta-function repulsion potential between them. The aim is to produce a simple example involving correlated wavefunctions, accessible to undergraduate and graduate students in the area of quantum mechanics.
Dielectric screening by cavities and the method of images
Authors: Saslow W. M.
Published: September 2005

A bare multipole potential Φ(r)=(A/rl+1)Pl(cos θ), concentric with a spherical cavity embedded within a dielectric, has its potential within the dielectric changed, not by the factor ε−1, but rather by the factor F(l)=(2l+1)/[l+(l+1)ε]. Moreover, a multipole source potential in the dielectric Φ(r)=(Arl)Pl(cos θ) has its potential within a concentric spherical cavity changed by a factor εF(l). The result is that the interaction between two multipoles in widely separated cavities is modified by a factor ε−1 times a factor εF(l) for each multipole. By decomposing the bare potential of a point monopole source into its cavity multipole components, screening each component separately, and then resumming, it is shown why the method of images works both for point charges with semi-infinite dielectrics and for line charges with dielectric circular cylinders—but not for point changes with dielectric spheres.
Quasiequilibrium determination of high-T
c superconductor transition temperatures
Authors: Pechan Michael J. , Horvath Jonathan A.
Published: September 2005

A fast and inexpensive method for making accurate determinations of transition temperatures above 77 K in superconducting oxides is presented. The technique is based upon cooling in liquid nitrogen, then warming the sample in the vapors above the liquid level inside a standard glass or stainless steel vacuum bottle. Proper sample support and placement of the thermocouple, key elements in this technique, are discussed. Once pads have been placed on the sample, Tc can be determined, to an accuracy of ±1 K, within 15 min. Due to its speed, accuracy, and low cost, this technique is well suited for application in an advanced undergraduate laboratory experiment.
Relativistic aspects of nonrelativistic quantum mechanics
Authors: Dieks Dennis , Nienhuis Gerard
Published: September 2005

It is argued that nonrelativistic quantum mechanics does not in all respects behave as a fully Galilean invariant theory. The difference is empirically significant, as is illustrated by the Sagnac effect. The conclusion of this article sheds some new light on a recent discussion concerning the status of de Broglie’s theory of matter waves.
Light scattering by fibers: An analysis using the partial wave phase-shift formalism of quantum mechanics
Authors: Cumpson Peter J.
Published: September 2005

The scattering of laser light by a glass fiber is easy to observe experimentally, though the scattering pattern will usually be rather complex. By applying the partial wave method familiar from quantum mechanical scattering, it is possible to calculate the pattern exactly.
Faraday rotation in the undergraduate advanced laboratory
Authors: Pedrotti Frank L. , Bandettini Peter
Published: September 2005

A Faraday rotation experiment is described for laser beams of two wavelengths in moderate magnetic fields, using flint glasses of large rotary birefringence and (liquid) carbon disulfide. Results show a linear relation between angle of rotation and field strength, and indicate a strong dependence on wavelength, attributable to the dispersion, which is determined from a measurement of the Verdet constant. The theoretical treatment and experimental technique are recommended for the advanced undergraduate laboratory.
A computing laboratory for introductory quantum mechanics
Authors: Kinderman Jesusa V.
Published: September 2005

This article discusses a computing laboratory developed to reinforce concepts presented in a junior level quantum mechanics class. The problems of this laboratory were designed to be solved on a microcomputer by using a commercial spreadsheet or by writing a computer program. They included plotting probability densities, numerically solving the Schrödinger equation, numerically solving for the eigenvalues and eigenvectors of matrix operators, and applying the variational method to the deuteron in a Yukawa potential.
Resource Letter MM-1: Magnetic monopoles
Authors: Goldhaber Alfred S. , Trower W. Peter
Published: September 2005

This Resource Letter provides a guide to the literature on magnetic monopoles. 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. The letter A indicates more specialized or advanced material. An asterisk (*) indicates those articles included in the accompanying Reprint Book.
The pumping of a swing from the seated position
Authors: Case William B. , Swanson Mark A.
Published: September 2005

The pumping of a playground swing from the seated position is modeled using a dumbbell consisting of three masses. The equation of motion of the system when the dumbbell is forced to rock back and forth is obtained. When reasonable approximations for amplitudes are made, the equation of a linear harmonic oscillator with a driving and three parametric terms is obtained. Based on an analysis of this equation using numerical values of the parameters, it is concluded that the pumped swing is a driven harmonic oscillator for small-to-moderate amplitudes. Growth rates and relative phase of pumping and swing motion are determined and discussed. The source of the driving term is traced to the conservation of total angular momentum (motion of the center of mass and motion about the center of mass) about the point of support of the swing.
An undergraduate experiment on the vibration of a cantilever and its application to the determination of Young’s modulus
Authors: Turvey Keith
Published: September 2005

An experiment is described to test the theory for the frequencies of lateral vibrations of a uniform cantilever. Good agreement between experiment and theory is obtained. Young’s modulus for the cantilever material (steel) is determined from the observed frequencies of the fundamental mode for a series of different lengths, and the result is compared with that obtained from static deflection of the cantilever. The agreement between the dynamic and static determinations is satisfactory.
Electromagnetic plane waves with parallel electric and magnetic fields E∥H in free space
Authors: Shimoda Koichi , Kawai Toshio , Uehara Kiyoji
Published: September 2005

Maxwell’s equations for electromagnetic waves in free space, with parallel electric and magnetic fields, are solved under the condition that the fields are functions of z and t, independent of either x or y. A number of interesting examples of plane waves obtained from the general solution are shown. Their properties and the vanishing Poynting vector are discussed.
A video technique to facilitate the visualization of physical phenomena
Authors: Cadmus Robert R.
Published: September 2005

A specialized image-processing device, the video peak store, can be used to enhance significantly a variety of physics lecture demonstrations by combining information from many video frames into a single composite frame. The use of this technology allows students to observe more clearly the details of processes and therefore understand more clearly the underlying physical principles. The characteristics and advantages of this technique are discussed and specific examples are presented.
Quantum mysteries revisited
Authors: Mermin N. David
Published: September 2005

A gedanken gadget is described, based on an idea of Greenberger, Horne, and Zeilinger, that provides a more powerful demonstration of quantum nonlocality than Bell’s analysis of the Einstein–Podolsky–Rosen experiment.
Investigation of driven harmonic oscillations in the computerized student laboratory
Authors: Eckstein Shulamith G. , Fekete Dan
Published: September 2005

The study of driven mechanical harmonic oscillations in the undergraduate student laboratory is greatly enhanced by the new high standard of precision achieved by computerized data acquisition and analysis. In this paper, two experiments are described that investigate transient behavior. In one experiment, beats are observed when the driving frequency is not equal to the resonant frequency; and in the other experiment, oscillations are observed to grow linearly with time at the resonant frequency. Steady-state behavior is also investigated. Both amplitude and phase are measured as functions of frequency.
Illustrating phase transitions with soap films
Authors: Lovett David R. , Tilley John
Published: September 2005

First-order and second-order phase transitions are demonstrated using soap-film models. The models consist of two-dimensional parallel plates or three-dimensional frameworks in which film patterns are maintained. By making the sizes of the frameworks variable, it is possible to induce switching between film patterns analogous to transitions between phases. These phase changes are discussed thermodynamically and using a catastrophe theory model.
Null-length springs: Some curious properties
Authors: Jagla Eduardo A. , Dalvit Diego A. R.
Published: September 2005

Null-length springs, in spite of being apparently simple, reveal several unexpected properties. All of these stem from the fact that these springs, lacking a characteristic length, show no differences between longitudinal and transverse vibrations. Some of these qualities are demonstrated in an elementary way so as to show the underlying physics. The properties proved are used to obtain certain well-known results of introductory physics. Finally, an experimental setup is described briefly to simulate null-length springs.
Wave-optical experiments with very cold neutrons
Authors: Gähler Roland , Zeilinger Anton
Published: September 2005

A series of experiments is reviewed on precision measurements of the diffraction of slow neutrons paralleling those with light: diffraction at an absorbing edge, at an absorbing wire, and at single- and double-slit assemblies. Besides their educational value, the experimental results also provide precise confirmations of the theoretical predictions as calculated via a Fresnel–Kirchhoff approach. The intensity in all these experiments was so low that the formation of the interference patterns individual neutron by individual neutron could easily be observed. The experiments are presented and analyzed in a way suitable for undergraduate teaching.
Newton’s zero-order rainbow: Unobservable or nonexistent?
Authors: Bohren Craig F. , Fraser Alistair B.
Published: September 2005

Newton asserted without proof that a zero-order rainbow exists, one associated with two refractions and no reflection. Subsequent authors also postulated such a rainbow but argued that it is not seen because its angular position (26 deg) is too close to the Sun. But it is not seen because it does not exist. Newton’s erroneous 26-deg rainbow appears to have resulted from his failure to account for the dependence on angle of incidence of the solid angle of twice-refracted rays corresponding to a given bundle of incident rays.
Analysis of a four-level laser system: Investigations of the output power characteristics of a He–Ne laser
Authors: Döhner H. -J. , Elsässer W.
Published: September 2005

The output power characteristics of a He–Ne laser are studied as an illustration of a four-level gas laser excitation scheme. A linear dependence of the output power on the pumping rate is deduced from measurements of the output power as a function of the excitation current for various cavity lifetimes. These investigations are suitable for a laboratory course for advanced physics students.
A note on the Blackburn pendulum
Authors: Whitaker Robert J.
Published: September 2005

The invention of the ‘‘Y-suspended’’ pendulum in 1815 by James Dean and analyzed in the same year by Nathaniel Bowditch has been discussed by Crowell [Am. J. Phys. 49, 452–454 (1981)]. It was reinvented by Hugh Blackburn in approximately 1844 while he was a student at Cambridge and is frequently referred to as the ‘‘Blackburn pendulum’’ in the literature. The history of this device for demonstrating harmonic motion is traced. Blackburn was professor of mathematics at the University of Glasgow for 30 years, and a biographical sketch of him is included.
The probability distribution for a lattice gas: A simple characterization of the liquid–vapor phase transition
Authors: Güémez J. , Velasco S.
Published: September 2005

The equilibrium probability distribution of a lattice gas with short-range binary interaction is obtained. Numerical analysis shows the appearance of two peaks of such distribution for sufficiently low temperatures. This implies the onset of a first-order phase transition. From the possible behaviors of the distribution (one peak, two peaks, or a ‘‘plateau’’), a splitting of the thermodynamic space of the system is reported. This splitting is macroscopically (thermodynamically) interpreted in the light of the behavior of the isotherms obtained from the thermal equation of state.
The solution of the Dirac equation for a high square barrier
Authors: Thomson Mark J. , McKellar Bruce H. J.
Published: September 2005

The transmission of a Dirac particle through a high (V0>E+m) square electrostatic potential barrier is investigated further. As is well known, the transmission coefficient is nonzero even as V0 goes to infinity. As well as reproducing the usual wave mechanics approach, a detailed fermion–antifermion multiple scattering calculation and an S-matrix calculation are examined to provide additional insight into the problem. The origin of the curious behavior is found to be the result of pair creation and annihilation events.
The Feynman inverse sprinkler problem: A detailed kinematic study
Authors: Collier Michael R. , Berg Richard E. , Ferrell Richard A.
Published: September 2005

This paper represents an extension of the results of an original paper on the subject [Am. J. Phys. 57, 654–657 (1989)]. Here an experiment, originally performed by Titcomb et al., to demonstrate the inverse sprinkler effect is described and analyzed. It is shown that, in a water reservoir, the angular momentum of the sprinkler head is approximately equal and opposite that of the fluid in the sprinkler arms. However, in an air reservoir, one must consider the effects of both turbulence and the motion of the reservoir. Both effects result in a steady-state acceleration of the inverse sprinkler in a direction opposite that of the normal sprinkler. Also presented is a more detailed analysis than the one given in the original paper to explain the steady-state behavior of the inverse sprinkler.
Error analysis by simulation
Authors: Peterson Mark A.
Published: September 2005

It is suggested that error analysis in elementary laboratories be carried out by computer simulation of repeated measurements. Results should be represented as histograms. This procedure is concrete and correct, and makes definite and graphic what is meant by ‘‘error analysis.’’
Relativistic solutions to the falling body in a uniform gravitation field
Authors: Adler Carl G. , Brehme Robert W.
Published: September 2005

Many different solutions to the problem of the relativistic particle in a uniform gravitational field have been offered. The fact that different, apparently correct, solutions to the same problem exist is in itself a puzzle. A resolution to this puzzle is found by exploiting the equivalence principle to reduce the problem to the observations made by an accelerated observer of objects moving inertially in a background inertial frame. It is shown that some solutions, those arising from a truly curved space-time, cannot be treated in this manner. It is found that differences in the remaining solutions arise because the authors use coordinate displacement to describe the motion rather than proper distance. The coordinate systems of these different accelerated frames are distorted and produce different apparent motions of objects in the background frame. When the ‘‘right’’ variables are used all motions are identical.
The physics of the drive in golf
Authors: MacDonald William M. , Hanzely Stephen
Published: September 2005

With the personal computer the undergraduate physics student can investigate interesting physical systems. This is illustrated with a study of golf drives predicted from experimentally measured lift and drag coefficients which give forces nearly proportional to the square of the velocity of the ball. Their interplay gives a surprising linear dependence of range on initial velocity, in good agreement with empirical formulas but in contrast with the quadratic dependence discussed in introductory physics courses. Spin damping is easily introduced and found to decrease the range for a given launch angle. The exploration of quantitative and qualitative differences between the trajectories produced by measured drag and lift forces and those predicted by a model with a linear velocity dependence illustrates the scientific method at work.
Exact partial wave analysis for scattering by a segmented potential
Authors: Kalotas T. M. , Lee A. R. , Howard V. E.
Published: September 2005

By approximating the scattering potential in the lth partial wave equation with a series of constant segments, an exact solution in terms of spherical Bessel and Neumann functions becomes available. Continuity at the segment boundaries is achieved with the aid of a simple 2×2 matrix formalism and leads to exact expressions for the scattering phase shifts.
Time-dependent generalizations of the Biot–Savart and Coulomb laws
Authors: Griffiths David J. , Heald Mark A.
Published: September 2005

Strictly, Coulomb’s law and the Biot–Savart law determine the electric and magnetic fields for static sources only. Time-dependent generalizations of these two laws, introduced by Jefimenko, are used here to explore the applicability of Coulomb and Biot–Savart outside the static domain. The fact that Biot–Savart holds for some classes of time-dependent currents has led to much confusion in the literature, which this paper endeavors to dispel. To illustrate Jefimenko’s equations, the standard Liénard–Wiechert fields of a point charge are derived.
Resonance, Tacoma Narrows bridge failure, and undergraduate physics textbooks
Authors: Billah K. Yusuf , Scanlan Robert H.
Published: September 2005

The dramatic Tacoma Narrows bridge disaster of 1940 is still very much in the public eye today. Notably, in many undergraduate physics texts the disaster is presented as an example of elementary forced resonance of a mechanical oscillator, with the wind providing an external periodic frequency that matched the natural structural frequency. This oversimplified explanation has existed in numerous texts for a long time and continues to this day, with even more detailed presentation in some new and updated texts. Engineers, on the other hand, have studied the phenomenon over the past half-century, and their current understanding differs fundamentally from the viewpoint expressed in most physics texts. In the present article the engineers’ viewpoint is presented to the physics community to make it clear where substantial disagreement exists. First it is pointed out that one misleading identification of forced resonance arises from the notion that the periodic natural vortex shedding of the wind over the structure was the source of the damaging external excitation. It is then demonstrated that the ultimate failure of the bridge was in fact related to an aerodynamically induced condition of self-excitation or ‘‘negative damping’’ in a torsional degree of freedom. The aeroelastic phenomenon involved was an interactive one in which developed wind forces were strongly linked to structural motion. This paper emphasizes the fact that, physically as well as mathematically, forced resonance and self-excitation are fundamentally different phenomena. The paper closes with a quantitative assessment of the Tacoma Narrows phenomenon that is in full agreement with the documented action of both the bridge itself in its final moments and a full, dynamically scaled model of it studied in the 1950s.
Breit–Rabi Zeeman states of atomic hydrogen
Authors: Dickson R. S. , Weil J. A.
Published: September 2005

The magnetic field dependence of the isotropic nonrelativistic one-electron atom with nuclear spin-1/2, in its electronic ground state, is reviewed. Attention is called to the little-known fact that a level crossing exists (at field B∼17 T for 1H) between the two members of the upper spin (MS=1/2) doublet. Anisotropy of such a hydrogenic atom, due to the presence of a suitable external electric field (for instance, 1H trapped in crystalline SiO2) causes anticrossing of these levels and causes previously forbidden magnetic-dipole transitions to attain appreciable intensity in that B region.
Novel method for WKB analysis of multidimensional systems
Authors: Meyer S. A. , Morgenstern M. A. , Knudson S. K. , Noid D. W.
Published: September 2005

The availability of powerful microcomputers with graphics capabilities expands the range of numerical procedures that can be employed for undergraduate use. The use of simple software packages for the evaluation of multidimensional WKB approximate eigenvalues is discussed. Introductory courses in quantum mechanics rarely make use of semiclassical theories, such as WKB, to relate quantum mechanics to classical mechanics. This relationship can be helpful for the student’s understanding of quantum mechanics, and a computer experiment can provide a useful avenue for making the concepts concrete. The major components of the approach involve the use of a package for the integration of differential equations, to treat the classical equations of motion, and a computer-aided design package to determine the phase integral areas. The codes are not expensive, and all exploit the graphical capabilities of microcomputers, which are critical for visualizing the relationship between classical and quantum ideas.
An operator solution for the Hulthén potential
Authors: de Lange O. L.
Published: September 2005

Shift operators are derived for s states of the Hulthén potential. These operators are used to obtain energy eigenvalues and normalized coordinate-space wave functions for bound s states. The condition for the existence of these states is deduced from the Hellmann–Feynman theorem, and this theorem together with the hypervirial theorem are used to calculate certain expectation values.
Resource Letter AP-1: The anthropic principle
Authors: Balashov Yuri V.
Published: September 2005

This Resource Letter provides a guide to the literature on the anthropic principle. 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. The annotation A indicates rather specialized or advanced material.
Variations on the Aharonov–Bohm effect
Authors: Holstein Barry R.
Published: September 2005

Three variations of the usual two-slit electron diffraction experiment—insertion of a solenoid, of a rotating superconductor, and of an electric line charge in a neutron diffraction experiment—are examined. Each is shown to lead to a shift in the interference pattern.
A surprising optical property of Plexiglas rods—An unusual approach to birefringence
Authors: Schneider Werner B.
Published: September 2005

Plexiglas (Lucite) is optically anisotropic, it scatters laser light, it has a high transparency for light, and it is economical and easy to cut and polish. Combining these properties, a lot of interesting applications are possible, which are very useful for teaching optics. The demonstration of elliptically polarized light in a direct and impressive way or the easy construction of quarter-wave or half-wave retardation plates with exceptional performance are a few examples.
Generalized Gantmacher formulas through functions of matrices
Authors: Bahar Leon Y.
Published: September 2005

Gantmacher formulas are generalized by including the effect of the centripetal and angular accelerations in addition to the usual Coriolis term. The integration is accomplished by using a method based on functions of matrices, which permits the summation of an infinite series in closed form through the use of the Cayley–Hamilton theorem. The problem is further extended by allowing arbitrary matrix coefficients in the vector equation of motion, provided they obey a certain commutativity condition. In addition to standard examples, the problem of a particle moving on a plane rotating with variable angular velocity is considered. This example differs from the ones considered in the literature because neither the centripetal nor the angular acceleration terms can be neglected. Solutions of various orders are developed by truncating the exact solution when appropriate.
On variational problems in parametric form
Authors: Forbes G. W.
Published: September 2005

An important class of variational problems concerns properties of geometric curves (such as length, curvature, etc.) that are independent of the parametrization. When formulated in terms of an arbitrary parameter, many of the familiar tools appear to fail for these problems. For example, the associated Euler–Lagrange equations are not independent, the process of solving for the Hamiltonian breaks down, and, as a consequence, the form of the Hamilton–Jacobi equation is obscured. Several alternative methods have previously been developed specifically for the solution of problems of this form, but these relatively sophisticated techniques have no direct links to the methods familiar from the context of classical mechanics. It is shown here that it is possible to solve such problems by using the conventional tools of mechanics. In particular, the integration of the Euler–Lagrange equations is realized in terms of a specific parameter that is completely determined save for a crucial, arbitrary scale factor. By considering an unusual Legendre transform, a direct analogue of Hamilton’s canonical equations is shown to emerge. More importantly, a unique form for the analogue of the Hamilton–Jacobi equation is derived from the conventional Hamilton–Jacobi equations for members of a family of auxiliary variational problems. Fermat’s principle is discussed in some detail to illustrate the methods introduced here.
The rotational analog for Faraday’s magnetic induction law: Experiments
Authors: Dempsey Daniel F.
Published: September 2005

An induced emf appears if magnetic flux through a circuit varies as a result of a change in the magnetic field, the circuit’s shape, or the circuit’s orientation. The effect is enhanced if the circuit contains a number of turns. Behavior analogous to the above occurs if fluid confined to tubing takes the place of charge confined to wiring, while the role of the magnetic field is assumed by an angular velocity field. Various experiments are presented whose results confirm the analogy.
Molecular-dynamics simulator for optimal control of molecular motion
Authors: Husman M. , Schwieters C. , Littman M. , Rabitz H.
Published: September 2005

In recognition of recent interest in developing optimal control techniques for manipulating molecular motion, this paper introduces a computer-driven electromechanical analog of this process. The resultant molecular-dynamics simulator (MDS) is centered around a linear air track for which the atoms of the controlled molecule are simulated as nearly frictionless carts on the track. Bonds in the simulated molecule are described by precision springs, and the interaction with an external optical field is simulated through a computer-based linear driver. When the MDS is operated in the harmonic regime, it can be used as an exact analog of molecular-scale quantum systems through Ehrenfest’s theorem or, equivalently, as a classical set of coupled oscillators. The tools of optimal control theory currently being applied at the molecular scale are used to design the forcing function for the MDS. Optical encoders are used to measure bond distances for graphic representation of the MDS behavior. Bond breaking can also be simulated by bond-length-sensitive trigger-release mechanisms. The MDS is especially useful as a modeling tool to bridge theoretical studies and eventual laboratory experiments at the true molecular scale.
Digital pendulum damping: The single-oscillation approach
Authors: Basano Lorenzo , Ottonello Pasquale
Published: September 2005

The motion of a hydrodynamically damped pendulum is analyzed experimentally and theoretically. The present approach is complementary to the traditional one (based on the analysis of a long sequence of periods) in the sense that the equation of motion is numerically solved within the domain of a single half-oscillation. This method allows one to obtain information about the influence of an oscillation onto the next one, a memory effect that would be considerably weakened by a multiple-oscillation analysis.
In defense of relativistic mass
Authors: Sandin T. R.
Published: September 2005

The concept of relativistic mass brings a consistency and simplicity to the teaching of special relativity to introductory students. For example, E=mc2 then expresses the beautifully simplifying equivalence of mass and energy. Those who claim not to use relativistic mass actually do so—if not by name—when considering systems of particles or photons. Relativistic mass does not depend on the angle between force and velocity—this supposed dependence results from incorrect use of Newton’s second law of motion.