bluuebunny/crossref_metadata_2025 huggingface dataset:
Alternate derivation of the Liénard–Wiechert fields of a point charge
Authors: Heras José A.
Published: March 2005

The Liénard–Wiechert fields for a point charge are derived from a suitable integral representation for the electric and magnetic fields. In this derivation one does not calculate derivatives of retarded functions. Retardation is introduced into the fields at the end of the calculations. The free-space retarded Green function turns out to be an essential ingredient in this derivation. A heuristic argument is given for introducing this Green function. The derivation presented here might be used in undergraduate courses on electromagnetic theory.
Complex speeds and special relativity
Authors: Asaro Catherine
Published: March 2005

The quest to find faster-than-light particles has intrigued physicists for decades, though it has yet to turn up any real candidates. Even if a superluminal universe does exist, we have no way to reach it given that we must go through the speed of light, which to the best of our knowledge is impossible. In this paper, I show that by making speed complex, we can go around the speed of light in a manner analogous to the way a car faced with an infinitely tall road block might leave the road to go around that barrier. The treatment is a mathematical device; no known physical interpretation exists for the imaginary part of a complex speed. However, it can provide an entertaining problem in special relativity, one that may encourage students to think about the connections between equations and the physical universe.
Using model systems to demonstrate instances of mathematical inequalities
Authors: Tykodi R. J.
Published: March 2005

By considering certain properties of model systems, one can sometimes demonstrate instances of appropriate mathematical inequalities. For example, by considering the temperature-equalization process in a set of contiguous metal blocks, one can demonstrate instances of the mathematical inequality that states that the arithmetic average of a set of non-negative real numbers is never less than the geometric average of those same numbers. For each of six different mathematical inequalities, an appropriate model system is used to demonstrate instances of the inequality.
Time-dependent, generalized Coulomb and Biot–Savart laws: A derivation based on Fourier transforms
Authors: Bellotti U. , Bornatici M.
Published: March 2005

On the basis of the solution of the Fourier transformed inhomogeneous wave equation expressed in terms of both the charge and current density source, two basic field equations are derived, from which the time-dependent generalized Coulomb and Biot–Savart laws are readily obtained. For the specific case of an arbitrarily moving point charge, the use of the Fourier-transform approach makes the derivation of two intermediate field equations, required to get the fields in both the Heaviside–Feynman and Liénard–Wiechert form, straightforward.
An experiment to observe the intensity and phase structure of Laguerre–Gaussian laser modes
Authors: Padgett M. , Arlt J. , Simpson N. , Allen L.
Published: March 2005

We outline an easily reproduced experiment that allows the student to investigate the intensity and phase structure of transverse laser modes. In addition to discussing the usual Hermite–Gaussian laser modes we detail how Laguerre–Gaussian laser modes can be obtained by the direct conversion of the Hermite–Gaussian output. A Mach–Zehnder interferometer allows the phase structure of the Laguerre–Gaussian modes to be compared with the phase structure of a plane wave with the same frequency. The resulting interference patterns clearly illustrate the azimuthal phase dependence of the Laguerre–Gaussian modes, which is the origin of the orbital angular momentum associated with each of them.
The IUPP evaluation: What we were trying to learn and how we were trying to learn it
Authors: Di Stefano R.
Published: March 2005

During two academic years (1991–1992, 1992–1993), four new model curricula for the college-level, calculus-based introductory physics course were tested. A total of nine colleges and universities around the country participated in this test. This paper provides an overview of the evaluation process. The evaluation was independent—that is, it was not linked to the model developers or to the sites, nor was it directly implemented by the group that sponsored the project, the Introductory University Physics Project. At each site, we set out to study both ‘‘model’’ and ‘‘comparison’’ sections of the introductory physics course. There was a pre- and post-test, and some limited use of in-class questionnaires. Faculty members and roughly 10% of the students were asked to keep journals. Each test site was visited by an evaluator at least twice during each academic year. This paper provides some of the background necessary to assess the results of the IUPP evaluation. Some evaluation results from the 1991–1992 field tests are included in the following paper [R. Di Stefano, Am. J. Phys. 64 (1), 58–68 (1996)]. The main body of our results, including those focusing on the 1992–1993 trials, will be presented in later papers.
Applications of a simple quantum mechanical formula
Authors: Goldenberg Lior , Vaidman Lev
Published: March 2005

New applications of the formula A|ψ〉=〈A〉|ψ〉+ΔA|ψ⊥〉 are discussed. Simple derivations of the Heisenberg uncertainty principle and of related inequalities are presented. It is also shown that a state corresponding to a maximal uncertainty of any given observable cannot be unique.
Resource Letter BELFEF-1: Biological effects of low-frequency electromagnetic fields
Authors: Hafemeister David
Published: March 2005

This Resource Letter provides a guide to the literature on the interaction of extremely low-frequency electromagnetic field (ELF/EMF) interactions with biological matter, and on the possibility that such interactions could have a harmful effect on human health. Journal articles and books are cited for the following topics: ELF/EMF theoretical interactions with biological cells, organs and organisms, magnetic dipole interactions, sensing by animals, biomedical–biophysical experiments, epidemiology, and litigation–mitigation risk issues.
Shielding of an oscillating electric field by a hollow conductor
Authors: Aguirregabiria J. M. , Hernández A. , Rivas M.
Published: March 2005

The electric and magnetic fields for a hollow conducting sphere located in a slowly varying uniform electric field background are computed to first-order in a power series expansion in the field frequency. These results are used to define an equivalent RC circuit and to test the circuit approach which is often used in electromagnetic compatibility (EMC). The case of an infinite cylindrical conducting tube under the influence of the same external field is also analyzed.
The Runge–Lenz vector and perturbed Rutherford scattering
Authors: Aguiar C. E. , Barroso M. F.
Published: March 2005

The scattering of a particle in a perturbed Coulomb field is studied by means of the Runge–Lenz vector. We show that this leads to a simple method for calculating the classical deflection function, valid for quite general perturbing forces. With the same techniques we obtain the relativistic correction of order c−2 to Rutherford’s scattering formula.
Teaching physics with 670-nm diode lasers—experiments with Fabry–Perot cavities
Authors: Boyd R. A. , Bliss J. L. , Libbrecht K. G.
Published: March 2005

In a previous paper we described details of the construction of stabilized 670-nm diode lasers for use in undergraduate physics laboratories. We report here a series of experiments that can be performed using the 670-nm diode laser, a homemade scanning Fabry–Perot cavity, a helium–neon laser, a simple photodiode, and a few pieces of electronics hardware. The experiments include: (1) an introduction to the scanning confocal Fabry–Perot cavity, and to its use as an optical spectrum analyzer; (2) laser frequency modulation and observation of FM sidebands using the optical spectrum analyzer; and (3) the Pound–Drever method for servo-locking a Fabry–Perot cavity to a laser. These experiments are relatively easy to set up and perform, yet they demonstrate a number of useful optical principles and experimental techniques.
Laser spectroscopy of the cesium dimer as a physics laboratory experiment
Authors: Terrell Mark , Masters Mark F.
Published: March 2005

Laser spectroscopy of the cesium dimer is presented for use in an undergraduate laboratory. The experimental apparatus consists of near 780-nm diode lasers, a glass cesium cell, a simple oven, and a monochromator. The experiment can be assembled quickly and at low cost. In the course of this experiment students can observe vibrational structure in molecular emission and learn about potential energy curves and Franck–Condon factors. The first vibrational constant of the X1Σg+ ground state is measured to be 42.7±1.6 cm−1.
The profile of a dew drop
Authors: Behroozi Feredoon , Macomber Hilliard K. , Dostal Jack A. , Behroozi Cyrus H. , Lambert Brian K.
Published: March 2005

A stationary dew drop assumes a shape that minimizes the sum of its gravitational and surface energies. This shape, however, cannot be described by a mathematical function in closed form because the governing differential equations of the drop do not admit of an analytical solution but must be integrated numerically to yield the drop profile. Hence, this problem provides a good case for using the calculus of variations to obtain the governing differential equations and presents advanced students with an opportunity to gain insight and experience in numerical computations involving a real and interesting physical problem. In this paper we obtain the differential equations governing the shape of the drop in two ways: (i) by considering the balance of forces on the drop in static equilibrium; (ii) by seeking the profile which minimizes the total energy of the drop through the use of the calculus of variations. The resulting differential equations are then integrated numerically to obtain the theoretical profile. Two computational strategies, one for each of the two classes of wetting and nonwetting drops, are discussed. Further, it is shown how one may obtain the values of the surface tension and the contact angle for a liquid drop by matching the computed profile to the experimentally observed shape.
The conical resistor conundrum: A potential solution
Authors: Romano Joseph D. , Price Richard H.
Published: March 2005

A truncated cone, made of material of uniform resistivity, is given in many introductory physics texts as a nontrivial problem in the computation of resistance. The intended method and answer are incorrect and the problem cannot be solved by elementary means. In this paper, we (i) discuss the physics of current flow in a nonconstant cross-section conductor, (ii) examine the flaws in the ‘‘standard’’ solution for the truncated cone, (iii) present a computed resistance found from a numerically generated solution for the electrical potential in the truncated cone, and (iv) consider whether any problem exists to which the standard solution applies.
Fermion–boson transmutation and comparison of statistical ensembles in one dimension
Authors: Schönhammer K. , Meden V.
Published: March 2005

The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low-energy excitations can be described in terms of bosonic degrees of freedom. This fermion–boson transmutation (FBT) which lies at the heart of the Luttinger liquid concept is presented in a way which does not require a knowledge of quantum field theoretical methods. As the basic facts can already be introduced for noninteracting fermions they are mainly discussed. As an application we use the FBT to present exact results for the low-temperature thermodynamics and the occupation numbers in the microcanonical and the canonical ensemble. They are compared with the standard grand canonical results.
Rest frames for a point particle in special relativity
Authors: Rowe E. G. Peter
Published: March 2005

The idea of a rest frame for a point particle is most useful when it is defined as a proper-time-dependent basis of the Minkowski vector space with time axis along the tangent vector to the particle’s worldline. There are many such rest frames; the different possibilities rotate with respect to each other. Methods are developed to make simple and workable the concepts and techniques to deal with the relative rotations. The Thomas precession becomes clear and easy to calculate. Applications are made to spin equations.
Modern physics concepts taught via a neutron activation analysis laboratory
Authors: McGuire Stephen C. , Clark David D. , Holcomb Donald F.
Published: March 2005

We describe a group laboratory exercise in which neutron activation analysis (NAA) is used to illustrate the concepts of nuclear reactions, nuclear energy levels, characteristics of gamma rays, radioactive decay and half-life, and Compton scattering. Small groups of 10–12 students participate in the 50-min laboratory period that includes a 15-min discussion of the basic principles that underlie NAA, followed by the irradiation and gamma-ray counting of a sample containing ‘‘unknown’’ elements. Students carry away copies of data printouts for out-of-class analysis. The exercise has been implemented in an introductory, calculus-based general physics course with approximately 200 students.
An elementary derivation of the midplane magnetic field inside a pair of Helmholtz coils
Authors: Calhoun Richard C.
Published: March 2005

A pair of Helmholtz coils is a standard piece of physics apparatus which is used to produce a region of uniform magnetic field. Such a field is used in the experiment to determine e/m for electrons. The question arises then exactly how uniform is the field along the path of these electrons. We provide an elementary derivation of this midplane field and compare the results with measured values.
Ehrenfest’s theorem and the particle-in-a-box
Authors: Rokhsar D. S.
Published: March 2005

Ehrenfest’s theorem states that as a quantum state evolves in time, the rate of change of the expectation value of momentum is equal to the expectation value of the force. In the familiar ‘‘particle-in-a-box,’’ however, the probability of finding the particle at a wall—the only place where forces act—is zero, so at first glance it appears that the expectation value of the force should vanish for any state, which would violate Ehrenfest‘s theorem. This argument is flawed, however, since the forces at the walls of the box are infinite. We consider the box as a limit of a very deep square well and confirm that Ehrenfest’s theorem emerges safe and sound.
Unified derivation of classical radiation forces
Authors: Bochove Erik J.
Published: March 2005

The ponderomotive and radiation forces acting on a free charge or an atom in an electromagnetic wave are derived in a unified way from the classical Lorentz force equation with radiation damping.
Measurement of the efficiency of a BF3 counter
Authors: Ahmed M. U. , Jones E. D.
Published: March 2005

A final year undergraduate nuclear experiment is described in which the efficiency of a boron trifluoride (BF3) counter is determined. This involves attaching neutron sensitive activation foils to the surface of the counter, exposing the foils to the neutron flux from an Am—Be neutron source for a given time, and measuring the total number of neutrons entering the sensitive volume of the counter. Several basic principles of nuclear physics are incorporated into one single experiment which has proved instructive and challenging to final year undergraduate students. The student is expected to understand and apply topics such as radioactive half-life, absorption of nuclear radiation, nuclear detection, neutron activation and nuclear decay schemes in a single experiment. The experiment can also be converted into an open ended project where, in addition, the student can study several other aspects of the subject including the kinetics of (α,n) reactions.
Effective Lagrangians and nonlinear electromagnetism
Authors: Muñoz Gerardo
Published: March 2005

Lorentz invariance together with gauge invariance provide strong constraints on possible generalizations of classical electrodynamics. We show here how to construct the lowest-order corrections to the Maxwell Lagrangian, and examine the implications in a few interesting cases. While the above invariance principles are not sufficient to completely determine the model, specific predictions may be obtained if we allow the remaining arbitrary parameters to take on the values obtained within a given fundamental theory—QED in the context of the present paper. This straightforward approach provides the student with a new perspective on classical electromagnetism, and on the role played by the vacuum.
Mandated energy dissipation—e pluribus unum
Authors: Sciamanda Robert J.
Published: March 2005

A single mathematical model describes disparate phenomena involving colliding masses, interacting capacitors, or ‘‘dueling’’ springs. In each case the dissipation of a definite fraction of system energy is mandated when a conservation principle and a final state constraint are imposed. The mathematical ‘‘oneness’’ points not only to the physical similarity but also to a notable physical difference among the various phenomena. An important by-product is an enrichment of the usual treatment of two particle collisions.
Criticism of Feynman’s analysis of the ratchet as an engine
Authors: Parrondo Juan M. R. , Español Pep
Published: March 2005

The well-known discussion on an engine consisting of a ratchet and a pawl in [R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1963), Vol. 1, pp. 46.1–46.9] is shown to contain some misguided aspects: Since the engine is simultaneously in contact with reservoirs at different temperatures, it can never work in a reversible way. As a consequence, the engine can never achieve the efficiency of a Carnot cycle, not even in the limit of zero power (infinitely slow motion), in contradiction with the conclusion reached in the Lectures.
Thoughts on the magnetic vector potential
Authors: Semon Mark D. , Taylor John R.
Published: March 2005

We collect together several ideas that we have found helpful in teaching the magnetic vector potential A. We argue that students can be taught to visualize A for simple current distributions and to see A as something with physical significance beyond its bare definition as the ‘‘thing whose curl is B.’’
Cosmological Schwarzschild radii and Newtonian gravitational theory
Authors: Gautreau Ronald
Published: March 2005

We describe Friedmann–Robertson–Walker zero-pressure dust-filled universes using a Schwarzschild-like curvature spatial coordinate R along with the usual cosmological time coordinate t. In terms of coordinates (R,t), the geodesic equations of general relativity for the motion of the galaxies comprising the universe satisfy exactly a Newtonian inverse-square relationship. This allows us to formulate relativistic cosmology by starting first with Newtonian cosmology. After the mathematics of Newtonian cosmology is worked out, the general-relativistic metric for the universe is constructed from a well-defined prescription, and the behavior of light signals is then determined from the metric. It is found that certain radial light signals born at the Big Bang eventually reach a maximum distance in their journey through the universe, where they turn around and return to some arbitrarily chosen origin. The turning around takes place at an apparent horizon located at a Schwarzschild radius in the universe.
Realization of an interaction-free measurement of the presence of an object in a light beam
Authors: du Marchie van Voorthuysen E. H.
Published: March 2005

The gedanken experiment of Elitzur and Vaidman showing wave-particle duality was realized as a demonstration at a scientific exposition. Presence or absence of a mirror in one arm of an interferometer was measured while detecting one photon at a time. A reasonable fraction of events was ‘‘interaction-free,’’ which means that the conclusion that there was a mirror in the beam could be drawn from the signal of a photon that had not interacted with the mirror. The demonstration was found to be thought-provoking.
Tabletop time-reversal violation
Authors: Rosner Jonathan L.
Published: March 2005

Many electrical and mechanical systems with two normal modes are appropriate for illustrating the quantum mechanics of neutral kaons. The illustration of CP- or time-reversal violation in the neutral kaon system by mechanical or electrical analogues is more subtle. Some possibilities which could be realized in a tabletop demonstration are suggested.
A different approach to introducing statistical mechanics
Authors: Moore Thomas A. , Schroeder Daniel V.
Published: March 2005

The basic notions of statistical mechanics (microstates, multiplicities) are quite simple, but understanding how the second law arises from these ideas requires working with cumbersomely large numbers. To avoid getting bogged down in mathematics, one can compute multiplicities numerically for a simple model system such as an Einstein solid—a collection of identical quantum harmonic oscillators. A computer spreadsheet program or comparable software can compute the required combinatoric functions for systems containing a few hundred oscillators and units of energy. When two such systems can exchange energy, one immediately sees that some configurations are overwhelmingly more probable than others. Graphs of entropy vs. energy for the two systems can be used to motivate the theoretical definition of temperature, T=(∂S/∂U)−1, thus bridging the gap between the classical and statistical approaches to entropy. Further spreadsheet exercises can be used to compute the heat capacity of an Einstein solid, study the Boltzmann distribution, and explore the properties of a two-state paramagnetic system.
Answer to Question #45 [“What (if anything) does the photoelectric effect teach us?,’’ R. Q. Stanley, Am. J. Phys. 64 (7), 839 (1996)]
Authors: Milonni P. W.
Published: March 2005

The history of the photoelectric effect is described. An analysis that field quantization is not required for an explaination of the photoelectric effiect is also given. (AIP)
High friction limit of the Kramers equation: The multiple time-scale approach
Authors: Bocquet Lydéric
Published: March 2005

The purpose of the paper is to give a pedagogical introduction to the multiple time-scale technique, on the example of the high-friction limit of the Kramers equation. We begin with a discussion of the standard perturbation technique as presented in van Kampen’s reference book, which will be shown to fail in the long-time limit. Application of the multiple time-scale technique avoids these difficulties and leads to a uniform expansion in powers of the inverse of the friction. Analogy with the Chapman–Enskog expansion is discussed.
Floating shells: The breaking and restoration of symmetry
Authors: Johnson R. C.
Published: March 2005

Floating shells illustrate symmetry breaking in a manner readily accessible to experiment. Shells containing some water show the unusual feature of symmetry restoration. The case of an ideal cylindrical shell (a “can”) is analyzed.
Compton scattering on blackbody photons
Authors: Brown Lowell S. , Steinke Ronald S.
Published: March 2005

We examine Compton scattering of electrons on blackbody photons in the case where the electrons are highly relativistic, but the center of mass energy is small in comparison with the electron mass. We derive the partial lifetime of electrons in the large electron positron (LEP) accelerator due to this form of scattering in the vacuum beam pipe and compare it with previous results.
Transverse standing waves in a string with free ends
Authors: Kashy E. , Johnson D. A. , McIntyre J. , Wolfe S. L.
Published: March 2005

A method to excite and visualize transverse standing waves on a vibrating string with one or both ends free is described. A stretched coil extension spring serves as the flexible vibrating string. A free end is achieved by attaching one end to a long thin steel wire that stretches the spring and thus provides tension with a nearly inertia-free suspension. The apparatus can be used as a qualitative lecture demonstration or as a quantitative experiment where it can serve as an instructive example of the application of boundary conditions.
Experimental study of a nonlinear system in the presence of noise: The stochastic resonance
Authors: Lanzara Elisa , Mantegna Rosario N. , Spagnolo Bernardo , Zangara Rosalia
Published: March 2005

Noise in a dynamical system is usually regarded as a nuisance. However, in certain nonlinear systems the addition of noise in the system can give counterintuitive dynamics. An illustrative phenomenon is stochastic resonance (SR). In this paper we present, an experiment demonstrating stochastic resonance in a bistable electronic device: the tunnel diode. This experiment is suitable both as a lecture demonstration and for student investigations. We introduce the statistical properties of the noise and the physical picture of the SR phenomenon. We describe the experimental setup and present typical results.
A mechanical analog of first- and second-order phase transitions
Authors: Fletcher G.
Published: March 2005

A mechanical model that exhibits first- and second-order phase transitions is analyzed. The possible configurations are found first by using Newtonian mechanics and second by determining the minimum of the effective potential energy taken from the Lagrangian. A comparison is made between the effective potential energy method and the Landau theory of phase transitions. Phase diagrams are obtained for the mechanical system and are compared with those of a ferromagnet.
Continuum states and fields in quantum optics
Authors: Santos David J. , Loudon Rodney , Fraile-Peláez Francisco J.
Published: March 2005

The relation between the continuous-mode quantization scheme used in quantum optics and the quantum system formed by a continuum of standard harmonic oscillators is established. The number and coherent states of this system are shown to be the ones introduced without explicit reference to the continuum by other authors.
Wave patterns on a water column
Authors: Sklavenites D.
Published: March 2005

An elementary analysis is given for some familiar wave patterns observed along a vertical water jet. The results follow from the fact that the group velocity of the short axially symmetric capillary waves is greater than the phase velocity, while the converse is true for the long waves having an azimuthal dependence. It is found that there is a close analogy between these stationary patterns and the two-dimensional wave pattern in the fishing-line problem.
Diffusion equation for one-dimensional unbiased hopping
Authors: Collins R. , Carson S. R. , Matthew J. A. D.
Published: March 2005

A computer simulation is presented of a one-dimensional particle migration by local hopping of Chandrasekhar type with no local bias but with hopping rates which vary with position in the system. Of the two possible diffusion equations to represent the process, one is clearly shown to be wrong while the other gives an accurate representation of the evolution of the system. The cases of both reflecting and absorbing boundaries are considered, and in the latter case a sum-rule previously derived for this type of random migration is verified. The concept of local particle traffic is introduced. Arguments are presented to show that the spatial traffic distribution gives a better insight into some aspects of particle activity than the probability distribution.
An underrated entanglement: Riccati and Schrödinger equations
Authors: Haley Stephen B.
Published: March 2005

The solution of the time-independent Schrödinger equation is fractionated by solving a corresponding Riccati equation. Simple particular solutions of the Riccati equation are used to construct exact ground state energy eigenvalues and eigenfunctions of otherwise complex problems without solving for the complete energy spectrum. In some instances, a partial series of the complete spectrum is also obtained with little extra effort. A procedure for obtaining the complete energy spectrum from the Riccati equation is also presented, and the entire method is illustrated by detailed analysis of several examples.
Dynamics of two interacting particles in a magnetic field in two dimensions
Authors: Curilef Sergio , Claro Francisco
Published: March 2005

The classical dynamics of two interacting particles of equal mass and equal or opposite charge, moving in a plane and a perpendicular magnetic field, is discussed. The simplest trajectories are similar to those of a single particle in the presence of crossed electric and magnetic fields (Hall configuration). Such motion occurs over a ribbon that may be straight (for opposite charges), or bent into a circle (for identical particles).
Continued fractions and the harmonic oscillator using Feynman’s path integrals
Authors: English L. Q. , Winters R. R.
Published: March 2005

The simple harmonic oscillator plays a prominent role in most undergraduate quantum mechanics courses. The study of this system using path integrals can serve to introduce a formulation of quantum mechanics which is usually considered beyond the scope of most undergraduate courses. However, given the current interest in the interpretation and foundations of quantum mechanics, nonstandard approaches such as Feynman’s path integral formalism can be helpful in developing insights into the structure of quantum mechanics. In this paper we evaluate the path integration appearing in Feynman’s treatment in a natural and direct manner utilizing a symbolic computational program. This approach makes the use of the path integral formulation of quantum mechanics accessible to most undergraduate physics majors. As a by-product of our approach, we find a representation of the reciprocal of the sinc function, sinc (x)≡sin(x)/(x), in terms of an infinite product of partial approximates of a continued fraction. We have not found this representation in the literature.
Nonlinear dynamics of a sinusoidally driven pendulum in a repulsive magnetic field
Authors: Siahmakoun Azad , French Valentina A. , Patterson Jeffrey
Published: March 2005

The dynamics of a sinusoidally driven pendulum in a repulsive magnetic field is investigated theoretically and experimentally. The experimental data are acquired using a shaft encoder interfaced to a PC which measures the angular displacement of the pendulum as a function of time. Both the theoretical simulations and the experimental measurements exhibit regions of periodic and chaotic behavior, depending on the system parameters. Amplitude jumps, hysteresis, and bistable states are also observed. The simplicity of the apparatus makes this experiment suitable for an advanced undergraduate laboratory.
Repulsive Casimir force as a result of vacuum radiation pressure
Authors: Hushwater V.
Published: March 2005

We study the Casimir force between a perfectly conducting and an infinitely permeable plate with the radiation pressure approach, used by earlier authors for the case of two perfectly conducting plates. This method illustrates in a very simple context how a repulsive force arises as a consequence of the redistribution of the vacuum-field modes corresponding to specific boundary conditions. We show that the result is independent of the cutoff function used for regularization.
Noncentral potentials and spherical harmonics using supersymmetry and shape invariance
Authors: Dutt Ranabir , Gangopadhyaya Asim , Sukhatme Uday P.
Published: March 2005

It is shown that the operator methods of supersymmetric quantum mechanics and the concept of shape invariance can profitably be used to derive properties of spherical harmonics in a simple way. The same operator techniques can also be applied to several problems with noncentral vector and scalar potentials. As examples, we analyze the bound state spectra of an electron in a Coulomb plus an Aharonov–Bohm field and/or in the magnetic field of a Dirac monopole.
Concepts first—A small group approach to physics learning
Authors: Gautreau Ronald , Novemsky Lisa
Published: March 2005

Since 1991, we have been using Alan Van Heuvelen’s Overview, Case Study: Physics (OCS physics) methodology in introductory physics courses at New Jersey Institute of Technology (NJIT) with remarkable success. With the OCS method, physics concepts are presented first, with no mathematics. Only after the concepts are understood is math brought into the picture at the appropriate level. In addition, much of the learning is accomplished with students working together in small groups of three or four. In these collaborative settings, students actively engage each other in the learning process, working on specially designed small group problems, while the instructor acts as a facilitator of the on-going learning. We present various comparisons showing the effectiveness of OCS instruction over traditional teaching. In particular, since the introduction of OCS physics into NJIT’s summer Educational Opportunity Program (EOP), which involves mostly minority students, EOP students have significantly outperformed non-EOP students in their fall physics courses. Interviews with students and observations of videotapes suggest that “second teaching” takes place in small groups following “first teaching” by the instructor. Second teaching is interpreted on the basis of ideas developed by Vygotsky.
Temperature dependence of Doppler-broadening in rubidium: An undergraduate experiment
Authors: Leahy Chris , Hastings J. Todd , Wilt P. M.
Published: March 2005

This paper describes experiments performed by undergraduate physics majors to measure the temperature dependence of Doppler-broadening in Rb absorption lines over the interval 290–500 K. We report measurements made with a laser-diode spectrometer on the resolved hyperfine transitions of Rb87 (5 2S1/2 F=1 to 5 2P1/2, F=1 and 2) near 795 nm, and on the unresolved envelope of the transitions of Rb85 (5 2S1/2 F=2 to 5 2P3/2, F=1, 2 and 3) near 780 nm. Agreement between measured and predicted linewidths is very good.
On the barometric formula
Authors: Berberan-Santos Mário N. , Bodunov Evgeny N. , Pogliani Lionello
Published: March 2005

The barometric formula, relating the pressure p(z) of an isothermal, ideal gas of molecular mass m at some height z to its pressure p(0) at height z=0, is discussed. After a brief historical review, several derivations are given. Generalizations of the barometric formula for a nonuniform gravitational field and for a vertical temperature gradient are also presented.
Lorentz transformations of the electromagnetic field for beginners
Authors: Ferraro Rafael
Published: March 2005

The relativistic transformations for the electric and magnetic fields are obtained without mention of test charges or transformation properties of the sources, in a way which is suitable for a beginner’s course. The transformation laws follow from the fact that an electromagnetic plane wave is plane in every inertial reference system.
Resource Letter GPP-1: Geometric Phases in Physics
Authors: Anandan Jeeva , Christian Joy , Wanelik Kazimir
Published: March 2005

This Resource Letter provides a guide to the literature on the geometric angles and phases in classical and quantum physics. Journal articles and books are cited for the following topics: anticipations of the geometric phase, foundational derivations and formulations, books and review articles on the subject, and theoretical and experimental elaborations and applications.
Scanning, spherical-mirror Fabry–Perot interferometer: An upper-division optics laboratory experiment
Authors: Nachman Paul , Bernstein Aaron C.
Published: March 2005

Students in our upper-division/graduate physical optics laboratory course assemble a high-finesse Fabry–Perot interferometer (FPI) from components, mode-match it to a helium–neon (HeNe) laser, and examine some of the FPI system’s properties and uses. Here, we specify the necessary equipment and describe experimental procedures. For example, the experiments use the FPI’s high spectral resolution to monitor the laser’s behavior as it warms up; in another experimental step, they confront the issue of the photodetection system’s electronic bandwidth. We also provide a review of Gaussian beam formulas and detail their use in mode-matching calculations.
An introduction to space–time diagrams
Authors: Mermin N. David
Published: March 2005

A purely geometrical approach to Minkowski space–time diagrams is described that exploits only the symmetries of appropriate rhombi and rectangles. No explicit use is made of rectangular or oblique coordinate axes. Although designed for presenting the subject to nonscientists, the approach might also be illuminating to some scientists.
A note on rotating coordinates in relativity
Authors: Weber T. A.
Published: March 2005

In this paper, the rotating disk as an example of a non-Euclidean space is carefully examined; the basic arguments of Einstein are emphasized. A new approach is also presented which resolves the Ehrenfest paradox.
If light waves are stretched by gravitational waves, how can we use light as a ruler to detect gravitational waves?
Authors: Saulson Peter R.
Published: March 2005

I give an answer to the frequently asked question of the article’s title, based on an analogy between the description of gravitational waves in the transverse-traceless gauge and the description of an expanding universe in comoving coordinates. Both use freely falling masses to define the coordinate system. Taking advantage of the insight that has been achieved in cosmology, I show how to understand the operation of an interferometric gravitational wave detector in a way that resolves the apparent paradox.
Some time evolution properties of an electromagnetic wave
Authors: Brownstein K. R.
Published: March 2005

We investigate several time evolution properties of a free, spatially bounded, electromagnetic wave in empty space. In particular, we obtain expressions for the second time derivative of the second (energy) moment of the position vector r:∫[(r−R)(r−R)u]dτ/W [u is the energy density, W is the stored energy, R is the centroid of energy]. This is shown to evolve qualitatively differently than, say, for a Schrödinger wave packet. Another quantity considered is ∫(G⋅G/u)dτ [G is the momentum density]. This is shown to approach a constant for  t→±∞ and to vanish for at most one instant of time. The implication of this for so-called E parallel to B waves (E∥B) is discussed.
On the asymptotic decay law for wave packets in free space
Authors: Unnikrishnan K.
Published: March 2005

The Cauchy wave packet is introduced, whose probability density in free space depends on time asymptotically as [ln(t)]6/t3, thus displaying a remarkable departure from the commonly expected t−3 behavior.
Motion of articulated bodies: An application of gauge invariance in classical Lagrangian mechanics
Authors: Lopez L. F. , Coutinho F. A. B.
Published: March 2005

In this paper we develop, in a very elementary way, the formulation of the Lagrangian mechanics of a system viewed from an arbitrary reference frame. In the parlance of differential geometry, this means that we formulate Lagrangian mechanics as a gauge theory. The formalism is shown to be very useful for describing the dynamics of deformable bodies in general. In particular, as we show through examples, it simplifies greatly the computation of the motion of systems of articulated rigid bodies that may be used to model diverse systems, such as trampolinists performing somersaults and twists, or direction mechanisms in satellites.
Some simple chaotic jerk functions
Authors: Sprott J. C.
Published: March 2005

A numerical examination of third-order, one-dimensional, autonomous, ordinary differential equations with quadratic and cubic nonlinearities has uncovered a number of algebraically simple equations involving time-dependent accelerations (jerks) that have chaotic solutions. Properties of some of these systems are described, and suggestions are given for further study.
Measuring orbitals and bonding in atoms, molecules, and solids
Authors: Vos Maarten , McCarthy Ian
Published: March 2005

The cloud of negative charge that determines the relative positions of the nuclei in a molecule or solid can be understood in terms of the motion of the electrons that form the cloud. Usually one pictures the charge cloud as a distribution in coordinate space. One can equally well picture it as a distribution of velocities, i.e., in momentum space. The probability that an electron has a certain energy–momentum combination is called the energy–momentum density. It is directly measured by electron-momentum spectroscopy. The results of this technique provide the most direct experimental documentation of simple ideas of orbitals and bonding, thus opening a fresh and comprehensive perspective on electronic structure. We show how measurement of the motion of electrons in solids can help us understand the bonding of atoms in molecules and solids. We give examples of a free-electron metal and an ionic insulator.
The origin of the molecular field in ferromagnets
Authors: Coles B. R.
Published: March 2005

Since students find it difficult to follow the discussions of ferromagnetism based on the exchange integral (J) that appears in the Heitler–London treatment of the hydrogen molecule, partly because there it clearly favors antiparallel spins and partly because the curves showing its possible variation with the d-shell radius are clearly completely speculative, it is suggested that an approach based on the molecular orbital treatment, which explains the magnetic moment of the oxygen molecule, gives a more transparent basis for discussions of the origin of the molecular field in 3d metals.
Atomic polarizabilities: Quantal and classical perspectives
Authors: Baugh J. F. , Edmonds D. A. , Nellesen P. T. , Burkhardt C. E. , Leventhal J. J.
Published: March 2005

The mechanism by which an external electric field induces in an atom an electric dipole moment is discussed from classical and quantal points of view. It is shown that the expressions for the atomic polarizability α derived from each of these viewpoints are, to the same level of approximation, identical. The classical perspective is, however, more intuitive and provides a more insightful picture. The presentation is at the undergraduate level.
Measuring the speed of light with a fiber optic kit: An undergraduate experiment
Authors: Gülmez E.
Published: March 2005

The speed of light in an optical fiber is measured using a simple, commercially available educational kit. The procedure consists of determining the time-delay for a modulated light pulse traveling through fibers of different lengths. The time-delay caused by the electronic circuits is then accounted for in a systematic way.
Photorefractive nonlinear optics in the undergraduate physics laboratory
Authors: Matlin Mark D. , McGee David J.
Published: March 2005

The field of nonlinear optics has grown significantly within the last two decades. Photorefractive materials in particular have been utilized in a wide variety of applications. Recently, the photorefractive inorganic crystals used to demonstrate nonlinear optical phenomena and applications have begun to decrease significantly in cost, bringing them within the budgetary limits of smaller physics departments. In addition, within the last five years photorefractive organic polymers have been developed which could serve as the focus of interesting interdisciplinary activities between undergraduate physics and chemistry programs. This article provides a starting point for educators in such programs who have an interest in developing undergraduate laboratory projects based on photorefractive materials. We present some background on the physics of photorefractive phenomena and materials, brief descriptions of some of the demonstrations and applications that employ these materials, and original references on these applications.
Charged particle in a constant electromagnetic field: Covariant solution
Authors: Muñoz Gerardo
Published: March 2005

We present a fully covariant solution to the problem of a charged particle in a time-independent, spatially uniform electromagnetic field Fαβ. No restrictions are imposed on the strengths or orientations of the electric and magnetic fields E, B. Our general result is then applied to a few special cases, and the answers are shown to reduce to expressions available in the literature once a specific inertial frame is chosen.
Nuclear rotations
Authors: Bertsch G. F. , Janssens R. V. F.
Published: March 2005

An analysis of the gamma-ray spectra produced using the quantum mechanical rotational energy formula is presented for nuclei with large angular momentum. This analysis is suitable for quantum mechanics, modern physics, or nuclear physics courses. (AIP)
A superconducting persistent current experiment for an undergraduate laboratory
Authors: Tiernan W. M.
Published: March 2005

Observing a persistent current in a superconducting ring is a classic superconductivity experiment that can explore the magnetic behavior of type II superconductors. Using an exchange gas cryostat immersed in liquid nitrogen, a 12-mT variable magnet, a low cost Hall sensor, and basic electronic instrumentation, we have performed persistent current experiments on polycrystalline YBa2Cu3O7−δ (YBCO) rings at various magnetic fields. The relatively small critical fields of polycrystalline YBCO make it possible to explore a range of type II magnetic behavior for B<12 mT. Experiments described here measure the critical current density and lower critical field of a YBCO ring and investigate qualitative differences between the Meissner and vortex state. Time-dependent measurements observe logarithmic time decay of persistent currents. This paper describes the practical implementation of this experiment, including descriptions of sample fabrication as well as experimental apparatus and techniques. It also provides an elementary description of the theory related to critical currents and magnetic effects in type II superconductors.
Proton or prouton?: Rutherford and the depths of the atom
Authors: Romer Alfred
Published: March 2005

Rutherford envisioned the proton in 1914 when experiments on alpha-particle scattering led him to suggest that the hydrogen nucleus was the carrier of both positive charge and mass in the structure of all heavier atoms. This was supported by his discovery in 1919 that bombardment by alpha particles expelled hydrogen from nitrogen. In 1920, he proposed the name proton for the hydrogen nucleus in this role but refrained from using it, perhaps from what he considered a lack of direct experimental evidence. That constraint continued as he and Chadwick found hydrogen expelled from most other light nuclei. He abandoned it at last when Blackett’s cloud chamber showed the capture of the alpha particle by a nitrogen nucleus at the time the proton was emitted.
A ball rolling on a freely spinning turntable
Authors: Weckesser Warren
Published: March 2005

We consider a ball rolling on a freely spinning turntable. We show that the path of the ball (in an inertial frame) is a conic section. This generalizes the well-known problem of a ball rolling on a turntable that is spinning with constant angular velocity, for which the path is a circle.