bluuebunny/crossref_metadata_2025 huggingface dataset:
Time-dependent correlation and the evaluation of the stretched exponential or Kohlrausch–Williams–Watts function
Authors: Chung S. H. , Stevens J. R.
Published: September 2005

An elementary discussion of time-dependent correlation functions is presented. These functions are discussed in the context of dielectric relaxation and nuclear magnetic resonance for two forms of decay: Simple exponential and stretched (Kohlrausch–Williams–Watts) exponential. A guide to the calculation of the stretched exponential fitting parameters using numerical methods is given. Computational notes include comments on the truncation of mathematical series used.
Some remarks on classical electromagnetism and the principle of relativity
Authors: Bartocci Umberto , Capria Marco Mamone
Published: September 2005

In connection with a note by Rindler on relativity and electromagnetism, it is shown that classically interpreted electromagnetism and special relativity already diverge in their predictions on the behavior of a very simple electrodynamical system, even for ‘‘low’’ velocities.
Boundary effects in quantum mechanics
Authors: Berman David H.
Published: September 2005

A simple formula is presented for the change in energy of a quantum system in a box when the box is infinitesimally deformed. The result is applied to rederive a formula given by Barton et al., [Am. J. Phys. 58, 751–755 (1990)] for the difference in energy of a bound state calculated with and without box boundary conditions. The formula can also be used to discuss pressure in a quantum system. A generalization of the result has been used for calculating scattering amplitudes for waves scattered by a rough extended surface. Here, a similar manifestly reciprocal result is derived for scattering by bounded objects.
A pedagogical approach to the radiation fields
Authors: Walstad Allan
Published: September 2005

A pedagogical approach to the emission of electromagnetic radiation is outlined in which Maxwell’s equations are solved directly for E and B without making use of the vector and scalar potentials.
Born approximation and differential cross sections in nuclear physics
Authors: Kozack Richard E.
Published: September 2005

The elastic scattering of strongly interacting particles from a heavy nucleus is considered. For a specific model potential, a closed-form representation of the differential cross section is constructed within the Born approximation. This expression is used to relate some prominent features of the cross section to the geometry of the target nucleus. Effects arising from the Coulomb interaction are also discussed.
Student scanning tunneling microscope
Authors: Lewis R. A. , Gower S. A. , Groombridge P. , Cox D. T. W. , Adorni-Braccesi L. G.
Published: September 2005

A scanning tunneling microscope (STM) has been constructed as an undergraduate project. Its mechanical and electronic design are described and results obtained using it are presented. At the same time, the requirements to be met in STM design are noted. Design developments which have paved the STM’s way into the teaching laboratory are identified.
A student experiment on optical bistability
Authors: Lau C. S. , Shy Jow-Tsong
Published: September 2005

A hybrid system that consists of an oscilloscope and a photodiode is used to demonstrate optical bistability. The details of the experimental setup and its graphical solution will be presented.
The precession of a Foucault pendulum viewed as a beat phenomenon of a conical pendulum subject to a Coriolis force
Authors: Opat Geoffrey I.
Published: September 2005

A conical pendulum has slightly different frequencies of vibration when it rotates clockwise or anticlockwise in a laboratory on a rotating Earth. This splitting of the frequency is due to the presence of the Lorentzlike Coriolis force which presses either radially inward or outward on the pendulum bob depending on the sense with which it traverses its circular orbit. The precession of the plane of a Foucault pendulum may be viewed as a beat phenomenon in the planar superposition of the clockwise and anticlockwise circular motions of the conical pendulum.
The statistical mechanics of image recovery and pattern recognition
Authors: Cole James B.
Published: September 2005

Many kinds of problems in physics and engineering can be cast as optimization problems in which a solution must be picked out of a very large and ‘‘complicated’’ solution candidate space. The simulated annealing algorithm, which derives from statistical mechanical theory, and Bayes’ theorem are introduced and it is shown how they can be combined to solve such problems. As an example, the problem of image recovery from noisy data is considered.
The Dalgarno–Lewis summation technique: Some comments and examples
Authors: Mavromatis Harry A.
Published: September 2005

The Dalgarno–Lewis technique [A. Dalgarno and J. T. Lewis, ‘‘The exact calculation of long-range forces between atoms by perturbation theory,’’ Proc. R. Soc. London Ser. A 233, 70–74 (1955)] provides an elegant method to obtain exact results for various orders in perturbation theory, while avoiding the infinite sums which arise in each order. In the present paper this technique, which perhaps has not been exploited as much as it could be, is first reviewed with attention to some of its not-so-straightforward details, and then six examples of the method are given using three different one-dimensional bases.
The maximum efficiency of the conversion of solar energy into wind energy
Authors: De Vos Alexis , Flater Guust
Published: September 2005

In the present paper, the Gordon and Zarmi model is applied for the conversion of solar energy into wind energy, in such a way that simple calculations lead to a universal result: The upper bound for the conversion efficiency of solar energy into wind energy equals 8.3%.
The route to chaos in a dripping water faucet
Authors: Dreyer K. , Hickey F. R.
Published: September 2005

The dripping water faucet is a simple system which is shown in this article to be rich in examples of chaotic behavior. Data were taken for a wide range of drip rates for two different faucet nozzles and plotted as discrete time maps. Different routes to chaos, bifurcation and intermittency, are demonstrated for the different nozzles. Examples of period-1, -2, -3, and -4 attractors, as well as strange attractors, are presented and correlated to the formation of drops leaving the faucet.
The axial radiation field of a spherical shell section
Authors: Sciamanda Robert J.
Published: September 2005

Using the Huygens integral an exact, closed-form solution is obtained for the axial radiation field of a spherical shell section source. The calculation is appropriate to an introductory, calculus-based physics course. Applications include ultrasonic inspection transducers and optical diffraction.
Two-level quantum systems: States, phases, and holonomy
Authors: Urbantke H.
Published: September 2005

For a two-level quantum mechanical system, pictorial descriptions of states, state vectors, phases, and their time evolution on the two- and three-sphere are discussed, including adiabatic changes and Berry’s phase.
Fluid uptake by a blotter
Authors: Bean Charles P. , Bubb Jeffrey I. , Fanelli Dominick F.
Published: September 2005

The uptake of fluid in porous material is observed in an experiment which is simple to perform and which yields results of precision better than 1%. In agreement with theory appropriate to a horizontal blotter, the square of the distance traveled by the liquid is proportional to the time. For glycerol solutions the slope of this curve is shown to be proportional to the inverse of the square root of their viscosities.
A computer model of laser action in the teaching of computational physics
Authors: Andrews D. G. H. , Tilley D. R.
Published: September 2005

An undergraduate computational project is described. A set of rate equations for a four-level laser is presented. The steady-state equations are solved exactly to find nonlasing and lasing solutions and the critical pump rate for the transition between them. The steady-state solutions are used as a guide to the introduction of suitable dimensionless variables for the rate equations. Illustrative numerical solutions of the rate equations in dimensionless form are presented. The detailed account given of this example is used to bring out a number of points about teaching computational physics.
Learning optics with optical design software
Authors: Atneosen Richard , Feinberg Richard
Published: September 2005

The use of commercially available optical design software is described as a tool to aid in learning geometrical optics. Common optical phenomena are easily modeled and displayed graphically. The interactive nature of this type of software allows the student to develop a deeper understanding of the laws of optics.
Experiments utilizing an ultrasonic range finder
Authors: Gatland Ian R. , Kahlscheuer Robert , Menkara Hicham
Published: September 2005

Novel experiments with an ultrasonic range finder interfaced to a computer include: moving an object to follow a displayed graph; parabolic and exponential curves compared to falling body data; real-time kinetic, potential, and total energy displays for a harmonic oscillator; and wavelength measurement for ultrasonic sound.
Teaching the optical memories
Authors: Peiponen K.-E. , Tsuboi Taiju
Published: September 2005

Some simple experimental ideas are introduced to demonstrate optical memory. The optical memory is based on the use of the linear dichroism of FA color centers in KCl:Li crystal.
A remark about mode coupling in guided wave optics
Authors: Florjanczyk M. , Tremblay R.
Published: September 2005

An alternate derivation of a well-known coupled-mode theory of dielectric waveguides is presented to discuss the roles of slowly varying amplitude approximation and phase matching condition. The approach is based on two vector wave equations for electric and magnetic fields and no approximations are needed. The resulting coupled-mode equations for ideal modes are shown to be the same as those coming directly from Maxwell’s equations.
Image of a moving spheroidal conductor
Authors: Redžić Dragan V.
Published: September 2005

It is shown that a conducting spheroid, which is moving uniformly along its axis of revolution, produces the same electromagnetic field as a moving line charge or a point charge or a charged disk, depending on the shape of the spheroid.
Clairaut’s hydrostatics: A study in contrast
Authors: Casey James
Published: September 2005

Clairaut’s inventive approach to hydrostatics is contrasted with the later treatment of the subject in which the pressure field came to play a dominant theoretical role.
The mathematical knowledge of physics graduates: Primary data and conclusions
Authors: Breitenberger Ernst
Published: September 2005

Systematic observations were made of the mathematical knowledge of physics students from the U.S. and other countries during their first years of graduate study at Ohio University. It was found that all were deficient in general and in ‘‘modern’’ mathematical concepts, and in problem-solving skills. Sizable fractions of them did not even possess adequate concepts of ‘‘derivative,’’ ‘‘integration,’’ and ‘‘truth.’’ Nearly all were limited to some familiarity with rather elementary calculus, and with equally elementary differential and linear equations, but they showed some ability and a pronounced willingness to perform manipulations. Roughly, they regarded mathematics as mechanical method, not as constructive thinking. In view of the significantly higher levels of mathematical fluency demanded by contemporary advances in physics and in computer usage, none of these students was adequately prepared for future-oriented study, or for research and employment in physics and related areas at the close of the 20th century. It is intended to discuss the likely causes of this state of affairs elsewhere with a view toward remedial actions.
Classical view of the Stark effect in hydrogen atoms
Authors: Hezel T. P. , Burkhardt C. E. , Ciocca M. , Leventhal J. J.
Published: September 2005

The unique properties of the hydrogen atom, especially those that result from the dynamic symmetry of the 1/r potential, are presented from both classical and quantal points of view. Using these properties as a starting point, the response of a classical hydrogen atom, an electron executing a Keplerian ellipse about a proton, to a weak electric field is described. Because the field is weak, the elliptical orbit may be treated as a dynamical element itself, variations in its shape and orientation depicting the classical Stark effect. The behavior of this orbit is then correlated with the quantum mechanical description of the first-order Stark effect in hydrogen, a subject that is included in most introductory courses in quantum mechanics.
Floating equilibrium of symmetrical objects and the breaking of symmetry. Part 1: Prisms
Authors: Erdös Paul , Schibler Gérard , Herndon Roy C.
Published: September 2005

The equilibrium configurations of solid prisms of square and equilateral triangular cross section floating in a liquid are examined. It is found that these bodies float in different symmetrical or asymmetrical positions with respect to the vertical plane depending on the solid–liquid specific mass ratio, or depending on the height at which the body’s axis is held above the liquid level.
Demonstrating the bent tuning curve
Authors: Khosropour Roset , Millet Peter
Published: September 2005

A simple intermediate-level mechanical nonlinear oscillator experiment is described which is used both as a lecture demonstration and as the basis for senior thesis research. Its special features are that the experimenter can easily control the degree of nonlinearity, that it readily exhibits the jump phenomenon, and that it can be modeled by the Duffing oscillator.
Time dependence in quantum mechanics—Study of a simple decaying system
Authors: Onley D. S. , Kumar A.
Published: September 2005

A simple quantum-mechanical model consisting of a two-level system coupled to a continuum, where the interaction can be varied from perturbative to strong, is examined for what can be learned about quantum mechanical decay using elementary methods. The decay spectrum and time dependence of the amplitudes can be calculated in this model, without resorting to perturbation theory. The spectrum is not precisely Lorentzian nor is the decay precisely exponential, features that appear to be shared by all quantum-mechanical models of decaying systems. The conditions for exponential decay and some of the reasons for deviation from this at both short and long times are discussed.
Time evolutions of quantum mechanical states in a symmetric double-well potential
Authors: Senn Peter
Published: September 2005

The time evolution of quantum mechanical states in a square well of infinite depth with a Dirac δ function at its center has been examined for cases where the initial state was localized in one of the wells. Let well A denote the well in which the initial state is localized, and let P(t) denote the integrated probability density Ψ*Ψ in well A. For opaque barriers the time-dependent system is adequately described by a two-state model in which only the pair of stationary states of even and odd parity are considered whose wave functions in well A, apart from an arbitrary phase factor, are largely identical with the wave function of the initial state. For P(t) a harmonic oscillation is observed whose frequency νt is well approximated by the well-known formula for the tunneling frequency νt≂ΔE/h, where ΔE represents the energy separation among the pair of states in the model. For the present model of a symmetric double well it has been shown that for highly transparent barriers a three-state model can describe the time evolution adequately. The three stationary states involved in this model are a state of odd parity whose wave function in well A is largely the same as the wave function of the initial state and a pair of stationary states of even parity which on the energy scale are immediately above and below the first state. In this three-state model the function P(t) is a superposition of two sinusoidal functions with nearly identical amplitudes and frequencies plus a constant. As a consequence, the amplitude of P(t) changes harmonically. In the present model a δ function has been used as a barrier in order to minimize the mathematical detail involved in the time-dependent treatment. It is to be expected that the beating in P(t) can be observed also in the time evolution of a state localized in one of the wells of a symmetric double-minimum potential with a more realistic ‘‘low’’ barrier if the density of energy levels near the energies of the levels to be considered in the corresponding three-state model varies slowly with energy.
Optical properties of a metal film and its application as an infrared absorber and as a beam splitter
Authors: Bauer Siegfried
Published: September 2005

The optical properties of a thin metal film are derived, with a thin film defined as having a thickness smaller than the wavelength of the radiation and the skin depth. The derivation is based on the continuity equation for the electric field and on the energy balance for the incident, reflected, transmitted, and absorbed energy current. The use of thin metal films as anti-interference coatings, as absorbers for the infrared, as semitransparent mirrors in interferometric devices and beam splitters, and as mirrors is discussed.
The International Physics Olympiad
Authors: Eisenkraft Arthur , Kirkpatrick Larry D.
Published: September 2005

The United States has participated in the International Physics Olympiad since 1986. In these years, the physics educational community has recognized that our very best high school students are certainly competitive with their counterparts throughout the world. The physics teachers and professors who have worked with these students have also realized that these students are capable of solving problems that are far beyond our traditional expectations. The successes of the U. S. Physics Team in the International Physics Olympiad will be described as well as the methods used in selecting and training the Team.
An example of surface charge distribution on conductors carrying steady currents
Authors: Aguirregabiria J. M. , Hernández A. , Rivas M.
Published: September 2005

In order to constrain electrons to move along ohmic conductors carrying steady currents, there must be a surface charge density that is usually very difficult to calculate. An approximate analytic expression for this surface charge density on a conducting square ring is presented here where the only source of emf is a changing external magnetic field. The corresponding electric field is determined and it is checked that the energy balance for this system holds.
The dynamical theory of the baseball bat
Authors: Van Zandt L. L.
Published: September 2005

A theory of the elastic behavior of an irregularly shaped, cylindrically symmetric object is developed and applied to the study of the familiar baseball bat. The normal mode, standing wave patterns of elastic vibrations are obtained and displayed graphically. The lowest 20 normal modes, extending in frequency up to about 3 kHz, are used to study and display the elastic response of the bat in the first few milliseconds after striking a ball. The contribution of the normal mode elastic vibrations to the hit ball speed is also developed, and the consequences for the batter (and fielders) are explored.
Does quantum mechanics obey the correspondence principle? Is it complete?
Authors: Ford Joseph , Mantica Giorgio
Published: September 2005

This elementary review paper presents the compelling evidence which supports the notion that quantum mechanics is much too simple a theory to adequately describe a complex world. Rigorous arguments based on algorithmic complexity theory are used to show that both the quantum Arnol’d cat and a broad category of finite, bounded, undriven, quantum systems do not obey the correspondence principle, implying that quantum mechanics is also not complete. An experiment, well within current laboratory capability, is proposed which can expose the inability of quantum mechanics to adequately describe macroscopic chaos. In its final section, this paper describes a theoretical framework that provides a proper setting for interpreting these surprising results.
Thermodynamic properties of an anharmonic fermionic oscillator
Authors: de Souza S. M. , de Oliveira S. Moss , Thomaz M. T.
Published: September 2005

An exactly soluble fermionic system (anharmonic oscillator) is presented. Exact expressions for average quantities such as the number of particles, energy, and magnetization of an ensemble of quantum systems in equilibrium with a reservoir of particles and heat are derived. Critical curves of the average magnetization as a function of temperature are obtained for a lattice of interacting anharmonic oscillators within the mean field approximation. To clarify the role played by the parameters of the present model, the Ising model is studied as a limiting case.
A note on energy minimization and the quantum-mechanical virial theorem for the class of potentials V(x)=A‖x‖n
Authors: Mavromatis Harry A.
Published: September 2005

It is pointed out that for the class of potentials V(x)=A‖x‖n, the quantum-mechanical virial theorem 〈φm‖T‖φm〉=(n/2)〈φm‖V‖φm〉 is in fact valid for any multiparameter trial wave function ψt=(1/√b)φt (x/b,a0̄,a1̄,...ar̄), where a0̄,a1̄,...ar̄, are dimensionless parameters, provided b is chosen to minimize 〈ψt‖T+V‖ψt〉, i.e., one requires (∂/∂b)[〈ψt‖T+V‖ψt〉]=0. A particular trial wave function of this type is used to illustrate this result.
Magnetic dipole interactions on an air track
Authors: Lukefahr H. G.
Published: September 2005

General Physics Laboratory exercises which use permanent magnets and an air track to illustrate dipole–dipole interactions and mechanical stability are reported. These experiments, which use an apparatus reported previously, can be set up using equipment which is available in most physics departments. The experiments are particularly suitable for the transition from the study of classical mechanics to electricity and magnetism.
Plücker’s relations and the electromagnetic field
Authors: Nguyen D. B.
Published: September 2005

Every two-dimensional parallelogram in three dimensions casts three parallelogram-shaped shadows onto the three coordinate planes; the signed areas of these shadows are real numbers. Conversely, every set of three real numbers can always be identified with the signed areas of parallelogram-shaped shadows of some one parallelogram. It is never necessary in three dimensions to invoke more than one parallelogram for this purpose. In higher dimensions, however, this converse is not true; to be the signed volumes of the p-dimensional shadows of some one p-dimensional parallelopiped in n dimensions, a set of numbers must satisfy several quadratic equations known collectively as Plücker’s relations. When the six electromagnetic field components (three electric, three magnetic) are viewed as signed areas of the shadows of a parallelogram in space time, all inertial observers must agree on the number of parallelogram. Plücker’s relations applied to these six numbers must, therefore, produce relativistic invariants.
Time evolution of minimum uncertainty states of a harmonic oscillator
Authors: Gersch H. A.
Published: September 2005

A single closed-form expression is obtained for the probability amplitude ψ(x,t) for a harmonic oscillator whose initial state ψ(x,0) has a minimum value for the uncertainty product of position x and momentum p, Δx Δp=ℏ/2. This form describes both coherent and squeezed states. Oscillations in time for uncertainties in position and momentum, characteristic of squeezed states, are shown to follow directly from the derived form of ψ(x,t) and from Heisenberg equations of motion for operators x̂ and p̂. Expressions for average photon number and its uncertainty are obtained from calculations of average oscillator energy and fluctuations about this energy.
Research as a guide for curriculum development: An example from introductory electricity. Part I: Investigation of student understanding
Authors: McDermott Lillian C. , Shaffer Peter S.
Published: September 2005

This is the first of two closely related articles that together describe how results from research can be used as a guide for curriculum development. This first article shows how the investigation of student understanding of electric circuits by the Physics Education Group has contributed to the building of a research base. The second article describes how the group has drawn on this resource both in developing a curriculum for laboratory-based instruction and in adapting this curriculum to fit the constraints of a traditional introductory course. Also discussed is how, in turn, development and implementation of the curriculum have enriched the research base.
Stability and Hopf bifurcations in an inverted pendulum
Authors: Blackburn James A. , Smith H. J. T. , Gro/nbech-Jensen N.
Published: September 2005

The inverted state of a simple pendulum is a configuration of unstable equilibrium. This instability may be removed if the pivot is harmonically displaced up and down with appropriate frequency and amplitude. Numerical simulations are employed to investigate the stable domains of the system. The associated basins of attraction, extracted by interpolated cell mapping, are seen to be fractal. Loss of stability at high excitation amplitudes is observed to follow a Hopf bifurcation.
Multiple time scale methods for adiabatic systems
Authors: Anderson James L.
Published: September 2005

The method of multiple time scales is applied to adiabatic systems. Adiabatic theorems for both classical and quantum systems are derived and expressions for Berry’s phase and its classical counterpart are obtained within the framework of a consistent approximation scheme.
Some practical aspects of finding the roots of equations using fixed-point iteration with a computer program
Authors: Blair J. Morris
Published: September 2005

The fixed-point iteration procedure for locating the roots of nonlinear equations, as usually described, is limited in its range of applicability. With some modifications it can be used for additional equations and, for many equations, the number of steps of iteration needed is reduced. The revised procedures are easily applied with a short computer program.
A laboratory experiment to determine the complex refractive index of layered dielectrics at 9 GHz
Authors: Robertson S. H. , Buckmaster H. A.
Published: September 2005

This paper describes the development of a senior undergraduate experiment designed to provide experience with the determination of the complex refractive index of layered dielectrics at microwave frequencies. The steps taken to minimize diffraction effects are described. Measurements of 1.75-mm glass sheets yielded n=2.58(1) and k=0.0196(5), 0.50-mm acrylic plates yielded n=1.67(1) and k=0.0028(7), and 3.15-mm softwood plywood yielded n=1.51(5) and k=0.092(3). Research quality measurements of dielectrics can be obtained with 25×25-cm sheets with a thickness of about a tenth of a free space wavelength.
Why i?
Authors: Baylis W. E. , Huschilt J. , Wei Jiansu
Published: September 2005

How is it that complex numbers, involving the imaginary i=√−1 play such an important role in physics, which always measures real quantities? An answer can be given in the framework of the vector algebra of three-dimensional space, in which an associative, invertible product of vectors is defined. In this mathematical structure, also known as the Pauli algebra, i arises naturally and carries geometrical significance. In particular, i enters as the unit volume element, and imaginary vectors are pseudovectors which represent planes, such as planes of rotation or reflection. The i from the vector algebra is related to common applications of imaginary numbers in physics, including rotations in a plane, electromagnetic waves, and phase factors and operator relations in quantum mechanics. Moreover, the same algebra of real three-dimensional vectors which yields complex numbers also forms the basis for a complex four-dimensional space with the Minkowski metric and provides a natural formalism for compact, covariant treatments of relativistic phenomena.
The harmonic lattice, recoilless transitions, and the coherent state
Authors: Bateman David S. , Bose Subir K. , Dutta-Roy Binayak , Bhattacharyya Manoranjan
Published: September 2005

The probability for recoilless transitions, relevant for the understanding of x-ray scattering from atoms bound in a crystal (applicable also to elastic scattering of neutrons from solids and to the Mössbauer effect), given by the Debye–Waller factor, is derived in a novel manner using the coherent state basis for the normal mode oscillators describing the harmonic lattice, a method which, while being simple and elegant, also reveals the relationship to a heuristic classical discussion of the problem.
The electron g factor and factorization of the Pauli equation
Authors: Alder Ronald J. , Martin Robert A.
Published: September 2005

The gyromagnetic ratio or g factor of the electron is correctly predicted by the Dirac equation to be 2. However, it is also possible to obtain this value from nonrelativistic quantum mechanics, as shown by Sakurai, who credits Feynman. It is noted here that the same trick used by Sakurai allows a factorization of the time independent Pauli equation. The result is an equivalent first-order equation which is referred to as the spin-momentum equation. In the absence of a scalar potential, the spin-momentum equation is the eigenvalue equation for the inner product of spin and kinetic momentum operators. The spin-momentum equation is solved directly for a constant magnetic field, and the solution is compared with the well-known Pauli equation solutions.
The reaction force on a Helmholtz resonator driven at high sound pressure amplitudes
Authors: Boullosa Ricardo R. , Orduña-Bustamante Felipe
Published: September 2005

A review of the simple oscillator model of the Helmholtz resonator is presented and the nonlinear behavior of the elastic force is analyzed in terms of the thermodynamic process occurring in the air enclosed in the resonator. This nonlinearity is shown to explain the appearance of an excess average pressure inside the resonator and a net reaction force acting on the resonator itself when the resonator is driven at high sound pressure amplitudes. A direct measurement of the net reaction force on a resonator confirms quantitatively the predictions from the model. Finally, a simple demonstration is presented in which four identical resonators are mounted in an anemometerlike rotor and set into motion solely by the action of a strong periodic sound field at the resonance frequency of the resonators.
Modeling games in the Newtonian World
Authors: Hestenes David
Published: September 2005

The basic principles of Newtonian mechanics can be interpreted as a system of rules defining a medley of modeling games. The common objective of these games is to develop validated models of physical phenomena. This is the starting point for a promising new approach to physics instruction in which students are taught from the beginning that in science ‘‘modeling is the name of the game.’’ The main idea is to teach a system of explicit modeling principles and techniques, to familiarize the students with a basic set of physical models, and to give them plenty of practice in model building, model validation by experiment, and model deployment to explain, to predict, and to describe physical phenomena. Unfortunately, a complete implementation to this approach will require a major overhaul of standard instructional materials which is yet to be accomplished. This article lays down physical, epistemological, historical, and pedagogical rationale for the approach.
Inverse-square orbits: Three little-known solutions and a novel integration technique
Authors: Weinstock Robert
Published: September 2005

Three methods, none of them widely known, are presented for determining the orbit of a particle subject solely to an inverse-square central force: One is by Laplace, another by Jacobi; the third may be here making its first appearance in print. All three differ markedly in major thrust; all of them culminate, of course, in conic-section orbits. Also included is use of a novel integration technique in the execution of a standard textbook solution of the same inverse-square orbit problem.
High-resolution solar spectroscopy in the undergraduate physics laboratory
Authors: Ratcliff Stephen J. , Noss Darcy K. , Dunham Jeffrey S. , Anthony Eric B. , Cooley John H. , Alvarez Alberto
Published: September 2005

The richness of the solar spectrum at visible wavelengths makes it ideally suited for many laboratory exercises in optical spectroscopy. A number of such experiments taking advantage of a high-resolution scanning spectrometer are described as they have been performed by seniors at Middlebury College. Physical principles emphasized include optical depth, the nature of molecular spectra, the Doppler effect, and the Zeeman effect. These experiments are suitable for advanced undergraduate physics and astronomy majors.
Solitary wave solutions of nonlinear wave equations
Authors: Malfliet W.
Published: September 2005

A method is proposed for obtaining traveling-wave solutions of nonlinear wave equations that are essentially of a localized nature. It is based on the fact that most solutions are functions of a hyperbolic tangent. This technique is straightforward to use and only minimal algebra is needed to find these solutions. The method is applied to selected cases.
Continuum computer solutions of the Schrödinger equation
Authors: Greenhow R. C. , Matthew J. A. D.
Published: September 2005

Computer integration of Schrödinger’s time-independent wave equation with graphical display of solutions provides a valuable teaching aid, and is much used in the study of bound states. Much less attention has been paid to continuum solutions although these provide a richer set of phenomena. Programs are described that integrate the one-dimensional equation for potential steps and barriers, and model impedance matching, barrier penetration, and field emission. The radial equation for spherically symmetric potentials is also integrated and graphical demonstrations of scattering phase shifts, a simple model of the Ramsauer effect, and resonance scattering are provided. The programs have been used by undergraduates to investigate resonance scattering from spherical step and Woods–Saxon potentials, and a new power law relating resonance cross-section breadths and energies has been established.
Equipartition for a relativistic gas
Authors: Landsberg P. T.
Published: September 2005

Equipartition theorem is postulated for a relativistic gas. (AIP)
A modern analysis of the Stern–Gerlach experiment
Authors: Platt Daniel E.
Published: September 2005

While the Stern–Gerlach experiment is an old and familiar problem, no analysis of this experiment is presented in the pedagogical literature using modern quantum mechanical techniques. Expositions of the Stern–Gerlach experiment are usually based on ‘‘old quantum theory,’’ i.e., semiclassical Bohr–Sommerfeld quantum mechanics. The experiment is also a popular one in discussions of the postulate of quantum measurement, which asserts that the process of measuring an observable forces the state vector of the system into an eigenvector of that observable, and the value measured will be the eigenvalue of that eigenvector. The most enduring of the philosophical arguments associated with quantum mechanics ultimately revolves around the mechanism of quantum measurement. Since the postulate of quantum measurement is expressed in terms well outside the realm of the old quantum mechanics, the traditional analysis of the Stern–Gerlach experiment cannot reveal any information about the relationship between dynamics and measurement. Therefore, a modern analysis of the Stern–Gerlach experiment must be made if this experiment is to reveal any information about the relationship between dynamics and the mechanism of quantum measurement. This paper presents such an analysis, and develops some of the implications for the theory of quantum measurement.
Hadronic numerics with quarks of f flavors
Authors: Holladay Wendell G.
Published: September 2005

According to the ‘‘standard model’’ of particles and fields, hadrons can be formed from a triplet of quarks (baryons), each of which may have any one of f flavors (d, u, s, c, b, etc.), or from a quark–antiquark pair (mesons) each one of which may have any flavor. Some numerics of flavor and electric charge content of baryons and mesons are presented. Multiplicity of symmetry types of baryons based on these simple numerical results is calculated without direct appeal to group theory in the hope that the dimensionality of hadron multiplets that contain the building blocks of normal matter will become more widely understood.
Erratum: ‘‘Analog demonstrations of Ampere’s law and magnetic flux’’ [Am. J. Phys. 6
0, 17–25 (1992)]
Authors: Heller Peter
Published: September 2005

We reproduce here Fig. 3 from that paper in its correct originally submitted form, which also appeared in the proof sent to the author. Subsequently, in their desire for a more uniform typographical style, the figure was altered by the American Institute of Physics staff at Woodbury, New York, without consultation with either the author or the editor. In so doing the letters indicating the figure sub-units were pasted back in the wrong order. The Woodbury staff has apologized to the author for this regrettable error. That apology is hereby transmitted to the readers of this Journal.
Finite-dimensional matrix representations as calculational tools in quantum optics
Authors: Mufti A. , Schmitt H. A. , Sargent M.
Published: September 2005

A powerful operator-algebra technique is used to calculate several useful relations encountered in quantum optics, such as the disentangling of the squeezing operator. The technique uses a faithful finite dimensional matrix representation of a Lie algebra to perform representation-independent calculations and often requires considerably less computation than other methods. While it has had little exposure within the quantum optics community, the method is quite popular with mathematical physicists in field theory.
Compression of wavelets
Authors: Bloch S. C.
Published: September 2005

Compression of spread-spectrum wavelets (deterministic, noisy, and pseudorandom) is discussed with emphasis on Crawford’s experiment involving spreading and subsequent compression of wavelets in a dispersive medium. Detailed instructions are provided for building spreadsheet worksheets which are useful for Crawford-type experiments and also for general applications in signal detection in laboratory experiments; suggestions are given for auxiliary hardware for use with a personal computer. An experiment is described in which pseudorandom wavelets can be constructed and identified so that numerous student experiments using acoustic or electromagnetic waves can simultaneously coexist without measurable interference, as in a micro-Global Positioning System.
A computer-simulated Stern–Gerlach laboratory
Authors: Schroeder Daniel V. , Moore Thomas A.
Published: September 2005

An interactive computer program is described that simulates Stern–Gerlach measurements on spin-1/2 and spin-1 particles. The user can design and run experiments involving successive spin measurements, illustrating incompatible observables, interference, and time evolution. The program can be used by students at a variety of levels, from nonscience majors in a general interest course to physics majors in an upper-level quantum mechanics course. Suggested homework exercises are given using the program at various levels.
Scale invariance and the Bohr–Wilson–Sommerfeld (BWS) quantization for power law one-dimensional potential wells
Authors: Cariñena J. F. , Farina C. , Sigaud Cássio
Published: September 2005

The classical periods of motion τ(E) are computed for a particle under the influence of a potential well of the form U(x)=α‖x‖ν, with both ν and α positive real constants. Assuming the reflection convention at the origin, these results can be extended to the cases where both ν and α are negative real constants. Also, the scale invariance exhibited by these potentials is analyzed using dimensional arguments directly on the classical equations of motion as well as the more powerful Lie method, appropriate for studying one-parameter symmetry groups of differential equations. The action variables J(E) are obtained from τ(E) and the Bohr–Wilson–Sommerfeld (BWS) quantization rule for the energy spectrum of all the above potentials is reobtained. An interpretation of the results is given in the light of semiclassical arguments.
An introduction to geometric algebra with an application in rigid body mechanics
Authors: Vold Terje G.
Published: September 2005

This paper presents a tutorial of geometric algebra, a very useful but generally unappreciated extension of vector algebra. The emphasis is on physical interpretation of the algebra and motives for developing this extension, and not on mathematical rigor. The description of rotations is developed and compared with descriptions using vector and matrix algebra. The use of geometric algebra in physics is illustrated by solving an elementary problem in classical mechanics, the motion of a freely spinning axially symmetric rigid body.
An introduction to geometric calculus and its application to electrodynamics
Authors: Vold Terje G.
Published: September 2005

A tutorial of geometric calculus is presented as a continuation of the development of geometric algebra in a previous paper. The geometric derivative is defined in a natural way that maintains the close correspondence between geometric algebra and the algebra of real numbers. The use of geometric calculus in physics is illustrated by expressing some basic results of electrodynamics.
Parametric solution of the phase diagram of a mean-field Ising model exhibiting a tricritical point
Authors: Velasco S. , White J. A. , Güémez J.
Published: September 2005

A mean-field approach to an Ising lattice with two-spin (pair) and four-spin (quartet) interactions is presented as an instructional example of a system exhibiting a tricritical point. In the absence of an external magnetic field, it is shown that the phase diagram of this system presents second- and first-order transition lines in accordance with the relative strength of the pair and quartet interaction constants. These lines meet at a tricritical point. A parametric solution of the metastability (spinodal) and coexistence curves is reported.
Talbot’s bands
Authors: Givens M. Parker
Published: September 2005

This classic experiment has been largely ignored by modern text book authors. It is worth reviewing for historical reasons and also because it provides a simple yet striking example of the role of group velocity in interferometry.
Seeing the Fraunhofer lines with only a diffraction grating and a slit
Authors: Luo William W. , Gerritsen Hendrik J.
Published: September 2005

The construction of a simple spectroscope is described, using a box with an adjustable slit, a holographic grating, and a wavelength calibrated strip. The grating spacing is calculated to have enough resolving power to allow the Fraunhofer lines in the solar spectrum to be observed by the naked eye. Furthermore, the calibration strip allows the user to determine the wavelengths of the spectral lines. While not having the accuracy and the resolving power of more elaborate instruments, the spectroscope’s inexpensiveness and simple operation will make it a useful instrument in a classroom environment.
Packing factors in diatomic crystals
Authors: Lewis John C. , Gillis Peter P.
Published: September 2005

It is sometimes overlooked that a function does not necessarily maximize where its derivative is zero. Oftentimes, a function will maximize at an end point of the range for which it is defined. Thus careful consideration must be given to the range over which functions are valid. In this paper a novel example of such a function is presented and a brief history and review of spherical particle packing in the context of crystallography are given.
Diagram of the second law of thermodynamics
Authors: Bucher Manfred
Published: September 2005

A generalization of a previous diagram for a Carnot cycle represents the entropy change ΔS for any reversible process of a PVT system geometrically by an angle σ. Applying the diagram to an irreversible process in an isolated composite system, the second law is illustrated by a clockwise arrow.
Longitudinal standing waves on a vertically suspended slinky
Authors: Young Richard A.
Published: September 2005

The vertically suspended slinky is a system where variable tension, and variable mass density, combine to produce a simple solution for the longitudinal normal modes. The time taken for a longitudinal wave to traverse a single turn of the slinky is found to be constant for a variety of slinky configurations. For the freely suspended slinky this constant traverse time yields standing wave frequencies that depend only on the length of the hanging slinky and not on the material, radius, or stiffness of the slinky. Data, obtained by students in a laboratory setting, are presented to illustrate the application of these results.
Parameter bias elimination for log-transformed data with arbitrary error characteristics
Authors: Gatland Ian R. , Thompson William J.
Published: September 2005

A method of eliminating parameter bias in linear fits to log data (typically from exponential decay experiments) is extended to cases with arbitrary error statistics. This includes the common case of errors proportional to the square root of the value. Also it is observed that the elimination of the bias can be important for data sets with as few as 50 points.
Classical mechanics and gauge theories
Authors: Debbasch Fabrice
Published: September 2005

It is shown that the free motion of a point mass in classical mechanics can be considered as a gauge theory. In such an approach, the gauge fields are the angular and translation velocity of the (possibly noninertial) frame in which the motion is studied. A brief comparison with other gauge theories is made.
Simulation of magnetic resonance experiments
Authors: Grivet Jean-Philippe
Published: September 2005

Several experiments in nuclear magnetic resonance have been simulated by numerical integration of the Bloch equations. The behavior of the magnetization vector has been studied in such cases as free precession, pulse excitation, Torrey oscillations, slow, adiabatic, and fast passages through resonance, excitation by Gaussian pulses. The numerical approach proved very convenient to demonstrate the role of the parameters that describe a spin system (T1 and T2) and the influence of the various operating parameters (sweep width and sweep rate, pulse length, frequency offset). Several types of graphic output are shown.
The chaotic oscilloscope
Authors: Levinsen Mogens T.
Published: September 2005

In spite of its apparent simplicity, a system consisting of a high-frequency oscilloscope operated in the x–y mode and a photodiode, which detects the light emitted from the trace while feeding the signal back to the oscilloscope, exhibits extraordinary complex behavior. Scenarios involved are limit cycles evolving into chaos through the Feigenbaum bifurcation route and low-frequency relaxation oscillations that can be phaselocked to external signals. Regions of complete phase lock are observable in this case. Furthermore, the Feigenbaum oscillations can be superimposed upon the relaxation oscillations. The different scenarios will be illustrated and the underlying mechanisms discussed.