bluuebunny/crossref_metadata_2025 huggingface dataset:
Vacuum gravity
Authors: Stefanski Bogdan , Bedford Donald
Published: March 2005

We show that the Heisenberg relations, in addition to allowing vacuum fluctuations to occur, effectively prevent detection of their associated gravitational fields. The role of the Schwartzschild radius in this demonstration is remarkable.
Multiloop dc circuits by source conversion and nodal analysis
Authors: Giltinan David A.
Published: March 2005

A supplemental method for teaching multiloop dc circuits is presented. The use of source conversion and nodal analysis results in algebraically simpler equations than the conventional approach of most introductory calculus based physics texts.
Spectroscopic measurement of the semiconductor energy gap
Authors: Sconza A. , Torzo G.
Published: March 2005

A homemade grating spectrometer and simple electronics allow measurements of the energy gap of semiconductor samples in introductory laboratory courses. Both transmission spectra and ‘‘photoconductive effect’’ spectra may be obtained. Results for Ge, Si, GaAs, and InP are reported.
Products of rotations: A geometrical point of view
Authors: Sivardière Jean
Published: March 2005

Products of rotations can be studied by a very simple and concise geometrical method based on the decomposition of a rotation into two mirror operations: use of dyadics, quaternions, or even matrices is not necessary. The Rodrigues formulas are derived. Products of finite order rotations and Euler rotations are considered.
Dispersive and nonlinear propagation of dual-frequency pulses in optical fiber
Authors: Carney Sean N. , Thompson John R.
Published: March 2005

Analytic solutions for limiting forms of the nonlinear Schrödinger equation are presented for dual-frequency input pulses propagating through single-mode, polarization-maintaining fiber. Linear dispersion and nonlinearity are considered separately. The article concludes with mathematica code appropriate for use by undergraduate students to explore dispersive and nonlinear propagation of light in an optical fiber.
Nondispersive accelerating wave packets
Authors: Besieris Ioannis M. , Shaarawi Amr M. , Ziolkowski Richard W.
Published: March 2005

Motivated by the work of Berry and Balazs and Greenberger on the 1-D Schrödinger equation, we have investigated a class of nonspreading solutions to the 3-D Schrödinger equation involving accelerating Airy envelopes. These solutions are characterized by an asymmetric structure, in contrast to recently derived spherically symmetric packets moving with constant velocities. The field of a characteristic Airy packet extends in an oscillatory fashion behind its peak amplitude, while it quickly disappears in front of the packet’s center. A particle modeled by such a packet seems to leave a wake of its field behind as it accelerates in a certain direction. On the other hand, a wave packet moving with a constant velocity has a field which is symmetrically distributed in all directions. Our work on Airy-type solutions to the 3-D Schrödinger equation has led us also to analogous solutions for the 3-D scalar wave equation.
Jefimenko’s formulas with magnetic monopoles and the Liénard–Wiechert fields of a dual-charged particle
Authors: Heras José A.
Published: March 2005

Jefimenko’s formulas for the time-dependent electric and magnetic fields are generalized to include magnetic monopoles. To illustrate this generalization of Jefimenko’s formulas, the electric and magnetic fields of an arbitrarily moving dual-charged particle, i.e., one containing both electric and magnetic charge, are obtained in the Heaviside–Feynman form as well as in the Liénard–Wiechert form. These fields are shown to be perpendicular to one another in the radiation zone but not in the near-field zone.
Relativistic (an)harmonic oscillator
Authors: Moreau William , Easther Richard , Neutze Richard
Published: March 2005

The relativistic extension of one-dimensional simple harmonic motion is developed in the Lagrangian formalism. The relativistic equations of motion are derived and solved analytically. The motion with respect to proper time is analyzed in terms of an effective potential energy. While the motion remains bounded and periodic, the effect of time dilation along the world line is to cause it to become anharmonic with the period increasing with amplitude and the curvature concentrated at the turning points.
Hidden invariance of the free classical particle
Authors: García Santiago
Published: March 2005

A formalism describing the dynamics of classical and quantum systems from a group theoretical point of view is presented. We apply it to the simple example of the classical free particle. The Galileo group G is the symmetry group of the free equations of motion. Consideration of the free particle Lagrangian semi-invariance under G leads to a larger symmetry group, which is a central extension of the Galileo group by the real numbers. We study the dynamics associated with this group, and characterize quantities like Noether invariants and evolution equations in terms of group geometric objects. An extension of the Galileo group by U(1) leads to quantum mechanics.
Genetic algorithms: A general search procedure
Authors: Sutton Patrick , Boyden Sheri
Published: March 2005

The genetic algorithm is presented as a straightforward computerized search method capable of solving problems from a wide variety of problem domains. A brief overview of the mechanics of the algorithm is presented, and the results of its application to function optimization, and the determination of ground state energies of the spin glass and related models are shown.
A new approach to the symmetric rectangular quantum well: Analytic determination of well width from energy levels
Authors: Fouillant C. , Alibert C.
Published: March 2005

Many articles on the determination of the energy levels of a symmetric rectangular quantum well (SRQW) have been published in this Journal over the past 20 years. Standard textbooks of quantum mechanics as well as research papers offer graphical solutions. Exercises on quantum well (QW) remain rather difficult for students, because transcendental equations must be solved with boundaries at which the solution will be discontinuous. Numerical solutions generally determine the energy (En), assuming that the thickness is known, for each level number n. In this note, we show that the width L of an SRQW can be expressed directly as a function of the energy En for n=0,1,2,3,... .
Relation between equations in the international, electrostatic, electromagnetic, Gaussian, and Heaviside–Lorentz systems
Authors: Desloge Edward A.
Published: March 2005

A brief description of the method of suppression and restoration of constants is given. The method is then applied to the constants in the basic equations of electromagnetism in the international system and shown to permit passage back and forth between it and the electrostatic and electromagnetic systems, but not between it and the Gaussian and Heaviside–Lorentz systems. Introduction of an added dimension of magnetic charge is then shown to lead to a new system, designated the universal system, containing an additional constant. The method of suppression and restoration of constants is then applied to the constants in the universal system and shown to permit passage back and forth between it and the international, electrostatic, electromagnetic, Gaussian, and Heaviside–Lorentz systems. Simple rules for effecting conversions between the above six systems are provided in appendices. The above methodology is shown not only to facilitate conversions but also to explain the fundamental relationships between the different systems.
Scaling properties in the diffraction of focused waves and an application to scanning beams
Authors: Forbes G. W.
Published: March 2005

From the Fresnel approximation to the Rayleigh–Sommerfeld solution for scalar wave propagation it follows that the field generated by a focused wave passing through an arbitrary aperture is simply related to the field generated by a collimated beam that is diffracted by any aperture of the same shape—the transverse intensity patterns are simply scaled and shifted. In fact, this result provides a simple, diffraction-based model for the action of a lens. A closed-form expression is found for the width of the beam generated by a focused uniform field that is diffracted by a circular aperture and, as an illustrative application, the beam of smallest maximum width over a fixed scanning depth is investigated.
On the physics of Landau damping
Authors: Sagan David
Published: March 2005

Landau damping—the damping of coherent oscillations in a system of oscillators with feedback—has been observed in many diverse systems from plasmas to quarks to the flashing of fireflies. There are two general approaches that have been used to understand Landau damping: One approach analyzes Landau damping in terms of the dephasing of oscillators. Another approach explains Landau damping as the result of an energy drain to those oscillators that are resonant with a coherent oscillation. Both approaches are studied in this paper and it is shown that while the two approaches may seem different, they are both valid descriptions of Landau damping.
Velocity fields inside a conducting sphere near a slowly moving charge
Authors: Aguirregabiria J. M. , Hernández A. , Rivas M.
Published: March 2005

Explicit expressions for first-order electric and magnetic fields created inside a conducting sphere by a nearby slowly moving charge are given. They are found to be independent of the sphere radius. On the contrary, outer first-order fields, which are also computed, depend on it. The energy dissipation by Joule effect is calculated and shown to agree with the external first-order work done on the charge to maintain its uniform motion.
Graphical representations of Fraunhofer interference and diffraction
Authors: Mechtly Bruce , Bartlett Albert A.
Published: March 2005

Traditional textbook presentations of Fraunhofer interference and diffraction are usually limited to a few discrete examples of one, two, and sometimes more sources, in which the analysis yields graphs of intensity versus distance y on a screen that is at a large distance D in the x direction from the sources. This paper presents two separate sets of graphical representations that can assist students and teachers in improving their understanding of the Fraunhofer phenomena. The polar intensity plots stress the angular nature of the interference phenomena, and stress the fact that the phenomena need not be limited to a narrow angular range around the forward direction. The three-dimensional plots illustrate the unity of diffraction and interference by examining the patterns when one makes a continuous variation of the geometrical parameters that characterize the sources.
Statistical mechanical distributions for small numbers of systems
Authors: Simons S.
Published: March 2005

We consider the problem of deriving the appropriate modification of the standard Maxwell–Boltzmann, Fermi–Dirac, and Bose–Einstein distributions for the situation where the number of systems is not necessarily very large and thus the usual derivations break down. We obtain for each case a modified formula which yields only integer values for the relevant occupation number and which reduces to the standard result in the limit of large numbers.
Modeling the tearing of paper
Authors: O’Keefe Robert
Published: March 2005

A model is presented which predicts the path along which ordinary machine-made paper will tear. Based on the idea of minimum work being done as the paper tears, this model leads to curve-generating equations which are solved numerically via a simple basic program. A key feature making this a pedagogically attractive activity is that immediate experimental feedback is possible by printing out the theoretical curves and comparing them to the actual tearing curves produced when the printouts are torn. Typical results obtained when this is done are included.
Relationship between thermal diffusivity and mean free path
Authors: Yang G. , Migone A. D. , Johnson K. W.
Published: March 2005

The thermal diffusivity is a parameter that determines the speed and attenuation of a thermal wave propagating through a material. In this paper we show, using the kinetic model for thermal transport, that the thermal diffusivity is also proportional to the mean free path of the heat carriers. Thus, the thermal diffusivity has the added feature of being directly related to an important transport property of the excitations that carry the heat. Thermal diffusivity and mean free path data are presented for an amorphous insulating solid, Pyrex 7740 glass, in the temperature range from 25 to 300 K.
Suppose Newton had invented wave mechanics
Authors: Lamb Willis E.
Published: March 2005

It is difficult to understand quantum mechanics. A major reason for this is that people do not realize that classical mechanics can be very well described by quantum mechanics. It would all have been much easier if Newton had not developed classical mechanics from the equation relating force, mass, and acceleration of a particle, but had started from a simple form of the Schrödinger wave equation. The equation F=ma could just as well have waited for its derivation from quantum mechanics by Paul Ehrenfest in 1927.
Singing corrugated pipes revisited
Authors: Cadwell Louis H.
Published: March 2005

A long corrugated tube open at both ends sings notes which depend on the flow velocity of air flowing through the tube. The notes it sings are natural harmonics of the tube. In 1974, Crawford suggested an explanation for this: A given note will sing when the flow velocity is such that the ‘‘bump frequency’’ equals the frequency of the note, provided also that the flow velocity is sufficiently high to induce turbulent flow. He suggested two theories to explain the singing in terms of turbulence. One assumed that the onset of turbulence agrees with the classic Reynolds number for smooth tubes (Rsmooth≊2000) in which the characteristic length of the object that has air flowing in is equal to the diameter. The second assumed the characteristic length of the object was equal to the distance between the corrugations. Crawford reported having good agreement between the classic diameter-induced turbulence theory and experiment for some pipes. However, for other tubes he observed singing at Reynolds numbers that were much smaller than the classical result of 2000. For these, he could not establish if he was observing corrugation-induced turbulence. (He stated he did not have sufficient pipes.) After looking at a variety of tube diameters and corrugation lengths, we also observed (as Crawford reported) that some of the data agreed with the classic diameter-induced turbulence, and some did not. Ironically, the hypothesis Crawford introduced (and rejected) as an alternative possibility seems to fit ALL of our data quite well. A new Reynolds number associated with the onset of turbulence for corrugated pipes is presented: Rcorr≊500.
Time-delay oscillator and instability: A demonstration
Authors: Case William B.
Published: March 2005

A harmonic oscillator where the force is dictated not by the current position but the position at a slightly earlier time is considered and shown to be unstable. This and closely related systems are called time-delay oscillators and the instability, when it is present, is called a time-delay instability. A simple, easy to construct demonstration is presented and analyzed. A discussion of the robust nature of the instability is also given.
Teardrop and heart orbits of a swinging Atwood’s machine
Authors: Tufillaro Nicholas B.
Published: March 2005

An exact solution is presented for a swinging Atwood’s machine. This teardrop–heart orbit is constructed using Hamilton–Jacobi theory. The example nicely illustrates the utility of the Hamilton–Jacobi method for finding solutions to nonlinear mechanical systems when more elementary techniques fail.
Brewster’s angle and optical anisotropy
Authors: De Smet D. J.
Published: March 2005

Brewster’s angle has been determined for a transparent oriented anisotropic material. For simple orientations of the material a polarizing angle can be found, but the propagation vectors for the reflected and refracted light are not perpendicular at this angle of incidence. In addition, Brewster’s law, n′=tan θ, does not apply in this case. For an arbitrary orientation of the material there is usually no angle of incidence that produces linearly polarized reflected light. These results can be understood by considering the direction of oscillation of induced dipoles within the material.
Dispersion-free linear chains
Authors: Reinsch Matthias
Published: March 2005

General formulas are given for the masses and spring constants of one-dimensional finite chains with linear dispersion relations, examples of which were given by Herrmann and Schmälzle in 1981 in their discussion of a well-known collision apparatus. The mathematical similarity to the problem of a Boson in a constant magnetic field is shown. The explicit formulas make a study of the continuum limit possible. This is shown to be related to the system of uniform rods studied by Bayman in 1976. Examples are given of chains with quadratic dispersion relations. Resonances that give singularities in the interaction time are discovered in certain chains of elastic spheres.
Frequency-domain description of a lock-in amplifier
Authors: Scofield John H.
Published: March 2005

The basic principles behind the operation of a lock-in amplifier are described. Particular emphasis is placed on looking at the frequency components of the signal present at the various stages of the lock-in during a typical measurement. The description presented here has been used successfully to explain lock-in operation to upper-level laboratory students at Oberlin College.
Charge-coupled device detection of two-beam interference with partially coherent light
Authors: King B. Tom , Tobin W.
Published: March 2005

In a demonstration of the advantages of charge-coupled device detectors in the undergraduate laboratory the Thompson and Wolf experiment on the effect of partial coherence on fringe visibility was repeated. Confirmation of the van Cittert–Zernike theorem to a few percent accuracy was attained.
Soliton like solutions of the Schrödinger equation for simple harmonic oscillator
Authors: Yan C. C.
Published: March 2005

By solving exactly with a simple method the time dependent Schrödinger equation for simple harmonic oscillator, we demonstrate that the probability density associated with any displaced eigenstate has the following properties: (a) Its centroid oscillates according to the classical law. (b) Its wave packet form remains rigid. The same method is also applied to solve exactly the problem of simple harmonic oscillator with the force constant depending on time. In this case, probability densities with the same wave packet structures as that of the usual simple harmonic oscillator can be found to move in such a way that their centroids follow the classical law but their wave packets deform in time. Depending on how the force constant varies with time, the wave packets can spread, contract or pulsate.
Behavior of a ball on the surface of a rotating disk
Authors: Sokirko Artjom V. , Belopolskii Alexandr A. , Matytsyn Andrei V. , Kossakowski Dmitri A.
Published: March 2005

Energy dissipation motion of a ball on a rotating disk (a turntable) has been considered. It is shown that the motion consists of two consequent stages—the motion towards the disk center along a cardioidic curve and the motion from the center along an unreeling helix. The limits of applicability of the results obtained are analyzed and qualitative comparison with experimental data is carried out.
The variational method—Why stop halfway?
Authors: ten Hoor Marten J.
Published: March 2005

An optimization procedure, such as the variational method, is usually carried out halfway, i.e., the values of the parameters of a trial function are found for which a property of the system under consideration, such as the energy, reaches its optimum value. However, the procedure can only be considered to be completed, when these parameters have been expressed as functions of physical constants, such as the atomic number. How this can be done is illustrated in the case of a two-parameter variational function, which describes the ground state of an atomic two-electron system.
21 cm line of atomic hydrogen
Authors: Storey J. W. V. , Ashley M. C. B. , Naray M. , Lloyd J. P.
Published: March 2005

Discovered in 1951, the 21 cm hyperfine line of atomic hydrogen has become one of the best-studied spectral features in radioastronomy. Used to trace the distribution and velocity of atomic gas in our own and in other galaxies, the line has made an enormous contribution to our understanding of galactic structure. Now, 40 years after the line’s discovery, a low-cost receiving system can be assembled from items of consumer electronics to enable study of the line in an undergraduate laboratory.
A simple, conservative understanding of many time-driven systems
Authors: Kaplan Harvey
Published: March 2005

Examination of two alternative models of a bead sliding on a rotating circular wire reveals the meaning of a conserved Hamiltonian where it is not the total energy. Analogies to other such dual treatments are discussed.
Kamerlingh Onnes and the discovery of superconductivity
Authors: Meijer Paul H. E.
Published: March 2005

Many papers begin with the statement that Kamerlingh Onnes discovered superconductivity in 1911; one wonders what urged him to do the experiment that led to this discovery. Superconductivity was definitely not foreseen at that moment, and for many years the theory could not even predict it. Hence what drove Kamerlingh Onnes to measure the electrical resistivity at a temperature range where one could not expect to find anything radically new? What were the prevailing theories at that time? This is discussed after a general description of the man, his laboratory, and the state of physics in the preceding years. Conclusion: Although the driving factor in the low temperature resistance work was most likely the need for a reliable and reproducible thermometer, the speculations about what would happen in these regions were based on Kelvin’s theory, at least in the initial phase of the work. This theory predicted exactly the opposite of what was found eventually.
Amount of night sky at any place at any time of year
Authors: Aravind P. K.
Published: March 2005

The composition of the night sky, as well as its quantity, change slowly throughout the course of the year. While the change in the appearance of the night sky from season to season is familiar to most amateur astronomers, the amount of sky that can be seen during any night is hardly ever remarked upon (apart from the general statement that there is more sky to be seen in winter because the nights are longer). In this paper I use elementary vector methods to calculate the total solid angle of sky (in steradians) seen in the course of the night at any place (latitude) on any day of the year. The results are compared with the duration of night at that location throughout the year. The effect of twilight on these estimates is also considered.
The square wheel revisited
Authors: Takacs L.
Published: March 2005

The dynamics of the square wheel is re-evaluated. It is shown that the minimum coefficient of static friction required for pure rolling decreases from 1 for very slow motion to only 0.105 at the optimum kinetic energy, then increases again for faster motion. The kinetic energy and the equations of motion are derived considering translation of the center of mass and rotation about it in an inertial coordinate system attached to the roadbed and also for rotation about the point of contact. The fact that the instantaneous axis of rotation is accelerating is emphasized and its consequences are discussed.
Dynamic interpretation of Maxwell’s equations
Authors: Soodak Harry , Tiersten Martin S.
Published: March 2005

Conventional discussions of Maxwell’s equations in free space have for many years taken a historical approach starting with electrostatics and magnetostatics, and have taught us that the sources of E are electric charge and Ḃ, and the sources of B are electric current and Ė. However, a direct dynamic reading of Maxwell’s differential equations leads unquestionably to the surprisingly different conclusions that the sources of E are electric current and curl B, and the single source of B is curl E. In this dynamic reading of Maxwell’s equations, electric field is generated locally by electric current, and fields propagate away from the current source by the dual mechanisms of curl E generating B locally and curl B generating E locally.
General covariance, Lorentz covariance, the Lorentz force, and the Maxwell equations
Authors: Crater Horace W.
Published: March 2005

We examine the problem of defining the electric and magnetic fields in the presence of a gravitational field and/or an accelerating coordinate system. The standard definitions given in an inertial coordinate system do not apply in a noninertial frame and further are not unique. We relate this result to the apparent freedom of choice of which components of the electromagnetic second-rank F tensor, (contravariant, covariant, mixed), one uses to express in terms of the electric and magnetic three-vector fields. This same ambiguity carries over in determining the three-vector form of the Maxwell equations in a noninertial frame. We discuss the various definitions given in standard textbooks and research literature and relate this ambiguity to the fact that the space-time coordinate xμ is not a four vector in general relativity. Using the example of the one-piece Faraday generator we show that through lowest order in 1/c the contravariant and covariant conventions yield the same integral forms of the Faraday flux law.
On the resistance between two points on a grid
Authors: Venezian Giulio
Published: March 2005

The resistance between two adjacent nodes on an infinite square grid of equal resistors can easily be found by superposition. This paper addresses the corresponding problem for two arbitrary nodes. A solution is found by exploiting the symmetry of the grid and using the method of superposition. The mathematical problem involves the solution of an infinite set of linear, inhomogeneous difference equations which are solved by the method of separation of variables.
Southern California Area Modern Physics Institute (SCAMPI): A model enhancement program in modern physics for high school teachers
Authors: Nanes Roger , Jewett John W.
Published: March 2005

This article describes a National Science Foundation funded program aimed at assisting high school physics teachers in Southern California to incorporate modern physics concepts into the high school curriculum. Summer and academic year activities in the program are described. Extensive assessment and evaluation of the project indicated success both in promoting modern physics instruction in the high schools as well as an increase in teachers’ professional attitudes toward themselves and their careers. Statistical analysis of the results of these assessments is briefly discussed.
Experiment on the physics of the PN junction
Authors: Sconza A. , Torzo G. , Viola G.
Published: March 2005

Simple apparatus, suitable for an undergraduate laboratory, allows precise measurements of the forward characteristics of Si and Ge ‘‘transdiodes’’ at different temperatures in the range 150–300 K. The experimental results are used to obtain a fairly accurate value of the universal constant e/k (elementary charge to Boltzmann constant ratio) and of the energy gap of Si and Ge.
Quantum mysteries refined
Authors: Mermin N. David
Published: March 2005

A gedanken experiment discovered by Lucien Hardy is translated into a very direct black-box gedanken demonstration of quantum nonlocality with red and green lights, using only two far apart detectors each of which operates in only two modes. The quantum mechanical underpinnings of the gedanken demonstration are quite simple. (This paper provides a text for the Klopsteg Memorial Lecture to the American Association of Physics Teachers at Notre Dame University, August 11, 1994.)
What is truth? A course in science and religion
Authors: Brancazio Peter J.
Published: March 2005

Are science and religion independent or conflicting systems of thought? This question was the focus of a course on science and religion given at Brooklyn College. The class explored the underlying metaphysical assumptions, sources of knowledge, and methodologies of science and religion from philosophical and historical perspectives. The conclusion is that science and religion are basically independent modes of inquiry, but they have come into conflict over questions about the origin, history, and nature of the physical world. These are areas in which science has been far more successful in providing fruitful explanations and predictions. Nevertheless, the limitations of science and the scientific method must be understood and respected.
Einstein and stimulated emission: A completely corpuscular treatment of momentum balance
Authors: Friedberg R.
Published: March 2005

The famous ‘‘1917 paper’’ of Einstein on the Quantum Theory of Radiation is revisited. Emphasis is placed on the little-known bulk of the paper dealing with momentum balance. The most difficult part of the calculation is here simplified by regarding the ‘‘drag force’’ on a body moving within a blackbody cavity as due to the same quantized impulses that give rise to random recoil.
Research as a guide for teaching introductory mechanics: An illustration in the context of the Atwood’s machine
Authors: McDermott Lillian C. , Shaffer Peter S. , Somers Mark D.
Published: March 2005

A problem on the Atwood’s machine is often introduced early in the teaching of dynamics to demonstrate the application of Newton’s laws to the motion of a compound system. In a series of preliminary studies, student understanding of the Atwood’s machine was examined after this topic had been covered in a typical calculus-based course. Analysis of the data revealed that many students had serious difficulties with the acceleration, the internal and external forces, and the role of the string. The present study was undertaken to obtain more detailed information about the nature and prevalence of these difficulties and thus provide a sound basis for the design of more effective instruction. The context for the investigation is a group of related problems involving less complicated compound systems. Specific examples illustrate how this research, which was conducted primarily in a classroom setting, has served as a guide in the development of tutorial materials to supplement the lectures and textbook in a standard introductory course.
Chaos at the amusement park: Dynamics of the Tilt-A-Whirl
Authors: Kautz R. L. , Huggard Bret M.
Published: March 2005

Analysis of the dynamics of an amusement-park ride reveals that the passengers experience chaotic motion.
The mass of a gas of massless photons
Authors: Kolbenstvedt H.
Published: March 2005

Using minimal formalism, we demonstrate that the massless photons, constituting the radiation in a cavity, contribute to the mass of the cavity in agreement with Einstein’s mass–energy formula. We assume that a photon has energy and momentum related to frequency by E=hν, p=hν/c. Restricting velocities to nonrelativistic values, we impart a uniform acceleration to the cavity. Reflection from a moving mirror produces a Doppler shift, and thus the momentum delivered to the front and rear walls can easily be calculated in the laboratory frame. A simple application of F=ma leads to the usual conclusion that the mass of a gas of photons of total energy U is U/c2. An alternative argument based on calculations in the co-accelerating frame is also given.
Dispersive Airy packets
Authors: Nassar Antônio B. , Bassalo J. M. F. , Alencar Paulo de Tarso S.
Published: March 2005

We present the solution of Schrödinger’s equation for time-dependent quadratic potentials in terms of an Airy packet. We demonstrate new features of the Airy packet in light of its apparent unfamiliar properties discovered by Berry and Balazs (who found a nonspreading and accelerating Airy packet to be a unique solution to the free-particle Schrödinger equation). Our solution, found using space-time scale transformations, not only overcomes the packet’s tendency to accelerate, but also make it possible to spread or contract in time.
Invariant Hamiltonians for relativistic particles
Authors: Hall Michael J. W. , Anderson Malcolm R.
Published: March 2005

The invariant Hamiltonian of a relativistic free particle can be derived via a strong consistency constraint. Invariant mass appears as a constant of the motion, and minimal coupling to electromagnetic and scalar fields arises naturally from the constraint form. The Hamiltonian formulation yields a simple derivation of the general relativistic equations of motion. The corresponding Lagrangian formulation is briefly discussed.
Hysteresis in magnetic systems
Authors: Chatterjee B. K.
Published: March 2005

A simple mean-field approach to the problem of hysteresis in magnetic systems is presented here. This model is instructive and has also been applied to understand ac susceptibility and Curie–Weiss law, and has been checked against the Steinmetz rule.
The atomic nuclide with the highest mean binding energy
Authors: Fewell M. P.
Published: March 2005

It seems to be widely believed that 56Fe is the most tightly bound atomic nuclide. Data are compiled showing that this is not so: Both 58Fe and 62Ni are more strongly bound than 56Fe, with 62Ni having the highest mean binding energy. Reasons for the erroneous favoring of 56Fe are canvassed. The history of atomic-mass measurements does not provide an explanation, nor does the liquid-drop model; an analysis using this model shows that, if we could switch off shell effects and allow both the atomic number and the mass number to be fractional, but retain the underlying liquid-drop characteristics of real nuclei, then the most tightly bound nuclide would have A≊58.3, Z≊26.6. It seems that belief in 56Fe as the most tightly bound atomic nuclide may originate from studies of stellar nucleosynthesis.
Maxwell’s equations in a rotating medium: Is there a problem?
Authors: Pellegrini Gerald N. , Swift Arthur R.
Published: March 2005

In 1908 Einstein and Laub used special relativity to predict that a moving magnetic dipole develops an electric dipole moment. The classic 1913 experiment of Wilson and Wilson on a polarizable, permeable medium rotating in an external magnetic field has long been cited as verifying this prediction. We argue that since the experiment involved rotation rather than uniform translation, it did not test special relativity. The analysis should properly be done in a rotating coordinate system. The field equations for a rotating object are well known and the analysis is straightforward, but the result disagrees with the Wilson experiment. After carefully examining all steps in the derivation, we conclude that either the experiment is wrong or the theoretical analysis must be modified. One possible resolution of the conflict is the hypothesis that the dielectric constant ε and permeability μ are well defined only in a frame in which the medium is at rest and time and space are orthogonal coordinates.
Quantum mechanics in momentum space: The Coulomb system
Authors: Holstein Barry R.
Published: March 2005

We examine the Coulomb system in momentum space. Both by directly summing the multiple scattering series as well as by use of symmetry techniques we demonstrate how the familiar results for scattering amplitude and bound state wave functions/energy levels can be derived.
The physical description of elementary surface phenomena: Thermodynamics versus mechanics
Authors: Pellicer Julio , Manzanares José A. , Mafé Salvador
Published: March 2005

A unified treatment of elementary surface phenomena based on the formalism of thermodynamics is presented and compared to more familiar treatments based on the formalism of Newtonian mechanics. Emphasis is put on the surface free energy concept rather than on surface tension, not only because the former is more fundamental, but also because the latter may mislead if pushed too far. The examples discussed (Young–Laplace and Young–Dupré equations, and capillary rise) can be easily described with the help of the Helmholtz function, and clearly show some of the advantages of the thermodynamic approach. In particular, several misleading results appearing in elementary treatments can be avoided by using this approach. It is concluded that: (i) thermodynamics and physical chemistry courses should favor the formalism of thermodynamics rather than mechanics when dealing with surface phenomena; and (ii) when the mechanical approach is still preferred, some weak points in the standard derivations (e.g., the existence of an adhesion force in the explanation of the Young–Dupré equation and the nature and balance of forces in capillary rise) should be properly dealt with.
Shot-noise measurements of the electron charge: An undergraduate experiment
Authors: Spiegel D. R. , Helmer R. J.
Published: March 2005

We report the design and performance of a simple apparatus for measurement of shot-noise fluctuations in the current from a vacuum photodiode illuminated with a pilot-lamp light bulb. After calibrating the frequency-dependent gain of the measurement electronics, the charge e of the electron can be obtained by measuring the mean-square shot noise as a function of the dc photodiode current. We employ op-amp circuits and a rms-to-dc integrated circuit to amplify, filter, and detect the shot noise, so that commercial bandpass filters and rms voltmeters are unnecessary. The apparatus is therefore not expensive and can be built using readily available components. Repeated measurements employing different pilot lamps yield a value of e=(1.581±0.015±0.032)×10−19 C, where the uncertainties represent random (2σmean) and systematic error, respectively. The experiment thus permits reasonably precise measurements of a fundamental constant while allowing the undergraduate student to gain a hands-on understanding of fluctuation phenomena.
Coherent backscattering of light
Authors: Corey R. , Kissner M. , Saulnier P.
Published: March 2005

Coherent backscattering of light (CBS) is a phenomenon in which partial waves traversing time-reversed (momentum-reversed) scattering paths interfere constructively in the backscattering direction leading to the appearance of an intensity cone. This increase in reflectivity reduces the amount of light transported through the colloidal media. As an advanced undergraduate laboratory CBS introduces the student to low-level light detection, precision angular resolved measurements, and sophisticated data analysis techniques. Additionally, the concept of photon self-interference, usually discussed in Modern Physics class in the context of Young’s double slit experiment, is beautifully illustrated by CBS.
Comment on ‘‘Classical orbits in power-law potentials’’
Authors: Wu Hua , Sprung D. W. L.
Published: March 2005

The duality relationship (α+2)(ᾱ+2)=4 between the power law potentials with powers α and ᾱ is studied for the limiting cases α→±∞, which correspond to a hard spherical well and to a hard sphere scattering problem respectively. The related power law potential approaches the inverse square potential.
Autocorrelation of electrical noise: An undergraduate experiment
Authors: Passmore J. Loren , Collings Brandon C. , Collings Peter J.
Published: March 2005

An undergraduate experiment is described in which the output of a noise generator is sampled by a computer equipped with a data acquisition board, after which the autocorrelation function is calculated. If the output of the noise generator passes through a low-pass filter before it is sampled by the computer, then the autocorrelation function is a decreasing exponential function with a decay constant equal to the time constant of the low-pass filter. The theory necessary to understand this phenomenon involves basic concepts in electrical noise, the analysis of linear systems, and Fourier transforms. In this paper the theoretical background for the experiment is discussed, typical data are presented, and a full analysis of these data is described.
Why isn’t every physicist a Bayesian?
Authors: Cousins Robert D.
Published: March 2005

Physicists embarking on seemingly routine error analyses are finding themselves grappling with major conceptual issues which have divided the statistics community for years. While the philosophical aspects of the debate may be endless, a practicing experimenter must choose a way to report results. The results can depend on which of the two major frameworks, classical or Bayesian, one adopts. This article reviews reasons why most data analysis in particle physics has traditionally been carried out within the classical framework, and why this will probably continue to be the case. However, Bayesian reasoning has recently made significant inroads in some published work in this field, and many other particle physicists may frequently think in a Bayesian manner without realizing it. I illustrate the issues involved with a few simple, commonly encountered examples which reveal how each framework can sometimes lead to unsatisfying results.
Transmission line exercises for the introductory physics laboratory
Authors: Watson George H.
Published: March 2005

Several exercises are reviewed for introducing the essential elements of transmission lines to students of introductory electricity and magnetism. A simple circuit is presented for generating ∼100 ns pulses suitable for demonstrating reflection and superposition of pulses on long coax cable using an inexpensive oscilloscope.
Poincaré’s proof of the quantum discontinuity of nature
Authors: Prentis Jeffrey J.
Published: March 2005

In his last memoir on mathematical physics, Henri Poincaré presented one of the most profound and compelling proofs of the hypothesis of quanta. This highly original proof, which is actually three separate proofs, is based on first principles and is full of physical insight, mathematical rigor, and elegant simplicity. The memoir is refreshingly uncluttered by some of the conventional, and more abstract concepts, such as temperature and entropy, that Planck and others relied on in their work. Poincaré’s analysis is based on an ingenious physical model consisting of long-period resonators interacting with short-period resonators. A unique formulation of statistical mechanics, based on the calculus of probabilities, Fourier’s integral, and complex analysis, logically unfolds throughout the memoir. Poincaré invents an ‘‘inverse statistical mechanics’’ that allows him to prove a crucial result that no one had proved before: The hypothesis of quanta is both a sufficient and a necessary condition to account for Planck’s law of radiation. In a separate, more universal proof, Poincaré proves that the existence of a discontinuity in the motion of a resonator is necessary to explain any observed law of radiation. Given the significant impact of Poincaré’s memoir on quantum theory and statistical physics, it is surprising that most physicists are not aware of its valuable mathematical and physical ideas. Poincaré’s tour de force proofs are presented here in a form suitable for use in a standard course in quantum mechanics, statistical mechanics, or mathematical physics.
Ball on a rotating turntable: Comparison of theory and experiment
Authors: Ehrlich Robert , Tuszynski Jaroslaw
Published: March 2005

We have extended the work of others in developing a model for the motion of a ball on a rotating turntable. The numerical model does not impose the constraint of rolling without slipping, and includes both rolling and sliding friction. Computer output from the model is compared with experimental trajectories obtained from time exposures, and found to be in excellent agreement.
Information-theoretical analysis of a classical relativistic gas under a steady heat flow
Authors: Ferrer Maria , Jou David
Published: March 2005

The aim of this paper is to provide a simple illustration of how the thermodynamic analysis of equilibrium states may be generalized to nonequilibrium steady states characterized by a nonvanishing heat flow. To achieve this aim, we use maximum-entropy arguments to describe a relativistic ideal gas under the constraints on the mean values of the internal energy and the heat flow. The partition function, the entropy, and the pressure tensor are obtained in terms of the internal energy, volume, number of particles, and heat flow. In the limit of vanishing heat flow, we recover the usual equilibrium thermodynamics. Thus our analysis exhibits in an explicit way some of the most relevant modifications of the thermodynamic quantities in presence of the heat flow.
On the optical–mechanical analogy in general relativity
Authors: Nandi Kamal K. , Islam Anwarul
Published: March 2005

We demonstrate that the Evans–Rosenquist formulation of the optical–mechanical analogy, so successful in the application to classical problems, also describes the motion of massless particles in the Schwarzschild field of general relativity. It is possible to obtain the well-known equations for light orbit and radar echo delay which account for two exclusive tests of Einstein’s field equations. Some remarks including suggestions for future work are also added.
Statistico-thermodynamic properties of a binary alloy
Authors: Porta Marcel , Castán Teresa
Published: March 2005

We use the antiferromagnetic Ising model to obtain the equilibrium properties of a bcc binary alloy AxB1−x which undergoes an order–disorder transition. We use Monte Carlo simulations to obtain the μ–T phase diagram, for different values of x, and discuss how to interpret the results in relation to experiments.
Retardation and relativity: Derivation of Lorentz–Einstein transformations from retarded integrals for electric and magnetic fields
Authors: Jefimenko Oleg D.
Published: March 2005

Lorentz–Einstein space–time transformations as well as transformations for electric and magnetic fields and charge density are derived from retarded integrals for electric and magnetic fields. The derivation shows that the theory of retarded electromagnetic fields and relativistic electrodynamics, although very different in their mathematical formulations, are very closely related in their basic physical content. On the basis of this derivation a novel method for introducing relativistic electrodynamics in courses on electricity and magnetism is suggested.
An ancient time machine: The Dial of Ahaz
Authors: Sadler Philip M.
Published: March 2005

The principles of optics are used in examining the claims of an unusual bowl sundial whose inscription taunts us with an ability to recreate a miracle of the Old Testament, that of reversing time. Ray tracing is first employed as a tool to allow restoration of the instrument to its original condition so that the sun’s shadow moves backwards. A mathematical model is developed to test this phenomena on different dates and at a variety of locations. Directions are given to easily demonstrate this phenomena in the classroom.
Atoms in orthogonal electric and magnetic fields: A comparison of quantum and classical models
Authors: Hilborn Robert C.
Published: March 2005

The well-known Zeeman and Stark effects can lead to unusual atomic state dynamics when both magnetic and electric fields are present. In this paper we analyze quantum mechanical and classical models of the time evolution of the angular momentum of an atom in the presence of weak, orthogonal electric and magnetic fields. The anisotropic electric polarizability of the atom plays a crucial role in the dynamics. The classical model leads to nonlinear evolution equations, and we investigate how quantum mechanics ‘‘avoids’’ the nonlinearity. Finally, we note that the classical equations of motion are identical to those used to describe the time evolution of Stokes vectors for polarized light propagating in an optically nonlinear medium. The treatment is appropriate for an undergraduate course in quantum mechanics.