bluuebunny/crossref_metadata_2025 huggingface dataset:
Theory of microwave surface impedance in superconductors and normal metals
Authors: Walsh P. J. , Tomaselli V. P.
Published: September 2005

The theory describing the surface impedance of a material is developed for normal conductors and high-critical-temperature superconductors. The discussion is extended to treat the nonlocal-field case, not usually considered in elementary approaches. A general solution to the field equation, appropriate when the charge carriers are specularly reflected from the conductor surface, is developed, and the result for the more complex case of diffuse scattering is given.
Electromechanical analog for Landau’s theory of second-order symmetry-breaking transitions
Authors: Marega E. , Zilio S. C. , Ioriatti L.
Published: September 2005

A simple electromechanical analog for Landau’s classical theory of second-order symmetry-breaking transitions is presented. The apparatus consists of a torsion pendulum, where a ceramic magnet suspended by two torsion springs is subjected to a uniform magnetic field. The pendulum angle is the analog of the order parameter in a phase transition, while the current passing through the Helmholtz coil, which produces the magnetic field, plays the role of temperature. With this setup, the critical exponents β, δ, γ, and γ′ can be determined with good accuracy.
An optical diffraction experiment for the advanced laboratory
Authors: Dodds S. A.
Published: September 2005

By treating scalar diffraction as a Fourier transform problem, it is possible to calculate the expected intensity patterns for arbitrary apertures using standard signal-processing software on a personal computer. This article presents a series of experiments on optical diffraction and spatial filtering phenomena, and quantitatively compares the results with calculations. Both the experimental and calculational methods are suitable for an advanced undergraduate laboratory.
The motion of an accelerating automobile
Authors: Calkin M. G.
Published: September 2005

A straight line is shown to provide an excellent fit to (speed)2-versus-time data for accelerating automobiles and the relevant kinematic relations are derived. Underlying dynamical reasons for this motion are discussed.
On a simple derivation of the Fresnel diffraction formula and a transfer function approach to wave propagation
Authors: Banerjee Partha P. , Poon Ting-Chung
Published: September 2005

The Fresnel diffraction formula is straightforwardly obtained by solving a partial differential equation (PDE) for envelope propagation using Fourier transform techniques. The PDE, in turn, can be derived from the dispersion relation of a linear medium by employing a simple operator formalism. The transfer function and impulse response of propagation follows as a spin-off and is used to solve illustrative problems. Huygens’ principle is visualized as a consequence of the convolution property of linear systems.
Resource Letter MNG-1: Measurements of Newtonian gravitation
Authors: Gillies G. T.
Published: September 2005

Presented in this Resource Letter is an annotated, selected bibliography of the literature on the various measurements of Newtonian gravitation that have been made over the past 2 centuries. The focus is on the unusual variety of effects for which Newtonian gravitation has been tested, as well as on the care that has gone into the determination of the absolute value of G. The letter E after an item indicates elementary level or material of general interest to persons becoming informed in the field. The letter I, for intermediate level, indicates material of somewhat more specialized nature; and the letter A indicates rather specialized or advanced material. An asterisk (*) indicates those articles to be included in an accompanying Reprint Book.
The force between two charged wires
Authors: Price Richard H. , Phillips Richard P.
Published: September 2005

For two circular cross-section ‘‘infinitely long’’ wires charged to opposite electric potential, it is a standard problem to calculate the potential field, the attractive force per unit wire length, etc. If, however, the potentials are not exactly opposite, the problem is not even well defined. As shown here, the problem becomes well defined when the physical environment of the wires is considered. An effective electrical ground is imposed on the problem either by the presence of nearby conductors or due to the finite length of the wires.
Phase-plane methods for central orbits
Authors: Anderson N. , Walsh G. R.
Published: September 2005

The elementary theory of central orbits is developed in terms of a convenient phase plane. The results of this analysis give considerable insight into the qualitative aspects of the problem; this is particularly true of the associated stability theory. The inverse-square law of force is considered in some detail, though other laws of force are also discussed. Phase-plane diagrams are given for some representative cases.
A rigorous lower bound for the ground-state energy of the hydrogen atom
Authors: Yue Zhang
Published: September 2005

Proving the existence of a lower bound on the energy of atoms is an important and noteworthy problem. Generally, people use the Heisenberg uncertainty relation to make their estimates. This article discusses the hydrogen atom and presents a new rigorous method for deriving the lower bound on the ground-state energy.
Successive reflections of a light beam on a pair of plane mirrors
Authors: Covarrubias M. Héctor
Published: September 2005

The pattern of points resulting from the successive reflections of a laser beam on two plane mirrors facing each other is contradictory to what students expect and, therefore, could motivate them to look for an explanation. A simple geometrical method is presented to solve this problem. The locus of the points is found to be a hyperbola and the locus of the light paths, a hyperboloid of revolution.
Eigensolution of the Coulomb Hamiltonian via supersymmetry
Authors: Valance A. , Morgan T. J. , Bergeron H.
Published: September 2005

The eigenvalues and eigenfunctions of the nonrelativistic hydrogen atom are obtained using supersymmetric quantum mechanics arguments and basic properties of the Schrödinger equation.
Efficiency reduction of heat engines due to power extraction
Authors: Ahlborn B. , Barnard A. J.
Published: September 2005

When power is extracted from a heat engine the working fluid must move. The generation of this motion consumes part of the engine power so that the efficiency is reduced. The energy loss per cycle is proportional to the maximum kinetic energy imparted to the working fluid and it is independent of the thermodynamic process. The power loss is proportional to the cube of the engine frequency.
Physics nomenclature in China
Authors: Zhao Kai-hua
Published: September 2005

Creating modern scientific terminology in their own languages has been the common problem of all developing countries. Direct borrowing of Graeco–Latin terms from western languages is the most straightforward way in countries using alphabetic writing systems; it is, however, quite inconvenient for Chinese. In this article the effort to work out a Chinese nomenclature for physics by the CPS is reviewed. The significance for physics education of assimilating terminology in the mother tongue is also examined at the end.
Harmonic or Fourier synthesis in the teaching laboratory
Authors: Whaite Geoffrey , Wolfe Joe
Published: September 2005

The design of an electronic device that synthesizes and adds the low-order harmonics of a fundamental sine wave is described. Frequency and phase are digitally controlled to ensure stability, and amplitude is analog controlled. The harmonics are synthesized digitally and so the harmonic distortion is low (−48 dB). The device is used in the teaching laboratory of a course on the physics of music, where it shows clearly the effects of amplitude and phase of the spectral components on waveform and timbre. Because of the phase stability and low distortion inherent in the digital design, the device gives an effective demonstration of Fourier synthesis, and it is used as a lecture demonstration for students in introductory physics courses.
Laser deflection through a spark
Authors: Enloe C. L. , Brake M. L. , Repetti T. E.
Published: September 2005

An experiment that uses laser deflection through a spark is described. The experiment uses an automobile battery and ignition system to generate a spark in atmospheric pressure air. A 5-mW He–Ne laser beam is deflected by the hot reduced density channel. The deflection is measured with a sensitive position detector, and the radial density profile is unfolded using an Abel inversion. Results indicate that the spark creates a weak shock wave, followed by a reduction in density on the order of half an atmosphere.
The phase relation between reflected and transmitted waves, and some consequences
Authors: Lekner John
Published: September 2005

The relative phase of waves reflected from and transmitted through a symmetric stratification is (under certain constraints) known to be an odd multiple of π/2. The phase difference is shown to change by π when the reflectivity passes through zero. Continuity arguments indicate that a surprisingly large proportion of symmetric stratifications share the property of zero reflectance at certain angles. The results apply to acoustic and particle waves, as well as to electromagnetic waves of both polarizations.
Research and computer-based instruction: Opportunity for interaction
Authors: McDermott Lillian C.
Published: September 2005

This article describes the fruitful interaction that can occur between research in physics education and the development of instructional software. The first part illustrates how results from research can guide the design of instructional software; the second part demonstrates how the computer itself can be used as an investigatory tool for conducting research on student understanding in physics. The discussion is in the context of specific examples based on work by the Physics Education Group at the University of Washington.
Application of the variational method to one-dimensional infinite wells with internal c
x
n potentials
Authors: Keeports David
Published: September 2005

The variational method is applied to the problem of a cxn potential within an infinite one-dimensional well. Approximate ground- and excited-state wavefunctions are constructed as linear combinations of two-term even and odd polynomials. Comparisons are made between calculated approximate wavefunctions and energies, and results predicted from perturbation theory and from the behavior of related systems.
Electron wavelike behavior: A historical and experimental introduction
Authors: Matteucci G.
Published: September 2005

Following the Fresnel theory of light and the consequent scientific debate that his formulation generated, two key experiments with electrons, diffraction by means of a circular hole and a circular obstruction, have been realized to show the existence of the Fresnel zones and of the so-called ‘‘Poisson spot.’’ The basic arguments concerning the quantum mechanical nature of electrons can be introduced by taking advantage of the vivid impression stimulated by the experimental images.
The random walk method for dc circuit analysis
Authors: Sorensen Raymond A.
Published: September 2005

A novel method for circuit analysis is presented, which can help in the development of intuition about the current distribution in a complicated circuit with an emf source and resistors, and can be used for analytic and numerical calculations.
Subjective measurement of resolution of a slit-limited eye
Authors: Miles Carol L.
Published: September 2005

By creating a visual target on a computer screen similar to a Sayce chart, it is possible for students to see that a slit aperture will limit their eye’s resolution according to the classical slit-diffraction equation. This gives an ‘‘eyes-on’’ (versus ‘‘hands-on’’) experience for the meaning of a diffraction-limited optical system.
Do darker objects really cool faster?
Authors: Bartels Richard A.
Published: September 2005

A common laboratory experiment in radiative heat transfer involves measuring the cooling rate of two water-filled metal cans, one can left unpainted and the other painted black. The shiny unpainted can cools more slowly, and the student can be led to the incorrect conclusion that bodies that are poor emitters (good reflectors) of light are also poor emitters of heat. A variation of this experiment was done with the shiny unpainted can replaced by one painted white. The experiment still compares a good and poor reflector of light, but in this case there is essentially no difference in cooling rates. These results are explained and are discussed in terms of other phenomena involving radiative heat transfer.
Spring–mass chains: Theoretical and experimental studies
Authors: Santos Mônica Silva , Rodrigues Eduardo Soares , de Oliveira Paulo Murilo Castro
Published: September 2005

The problem of a vibrating chain of springs and masses is solved by various methods, and its density of states is obtained. The ordered chain solution is exact, and disordered cases are treated by both exact and approximate methods. Green’s function methods, iterative renormalization group calculations, concepts of statistical fluctuation and localization, as well as computational tools currently used in statistical mechanics are introduced to undergraduate students. Furthermore, the present classical system is formally the same as the tight-binding one-orbital approximation for electronic systems, and also can be used to introduce this quantum problem. Finally, the results of an experiment performed on an air track are presented and compared with their theoretical counterparts.
Green’s functions and a hierarchy of sum rules for the eigenvalues of confining potentials
Authors: Sukumar C. V.
Published: September 2005

It is shown that for confining potentials in one dimension, it is possible to establish a hierarchy of sum rules for the inverses of the eigenvalues in terms of integrals involving a Green’s function. It is also shown that for symmetric confining potentials, sum rules involving the eigenvalues of the odd states may be formulated in terms of integrals that involve only the ground-state wavefunction.
How much does the rigid body rotate? A Berry’s phase from the 18th century
Authors: Montgomery Richard
Published: September 2005

A formula, apparently new, is derived for the spatial rotation of a free rigid body during one period T of its body angular momentum vector. This formula has the structure of recent phase formulas of Berry [Proc. R. Soc. London Ser. A 392, 45–57 (1984); Sci. Am. 259 (6), 46–55 (1988)] and Hannay [J. Phys. A 18, 221–230 (1985)]; namely, it consists of a geometric and a dynamic part. It is derived by applying Stokes’ theorem to a certain closed curve in phase space.
The Graduate Record Examination as an indicator of learning of the curriculum taught to physics majors in US institutions
Authors: Halley J. W. , Adjoudani Azin , Heller Patricia , Terwilliger James S.
Published: September 2005

A study is described to evaluate the Graduate Record Examination (GRE) as an indicator of learning by undergraduate physics majors. Measures were obtained of the overlap of the Graduate Record Examination in physics with the curriculum as it is taught to physics majors in US colleges and universities. The output of the project, for a given subfield f and set j of institutions, was two numbers Rj, f1 and Rj, f2. These two numbers estimated the extent to which (1) for Rj, f1, the curriculum prepares students at institutions j to take that part of the GRE which covers subfield f and (2) for Rj, f2, the GRE covers the materials in subfield f taught in the curriculum of institutions j. The subfields f  were mechanics, electricity and magnetism, statistical mechanics and thermodynamics, modern physics, and ‘‘other’’ (including experimental, mathematical, and solid-state physics). The institutions j were grouped into four categories: ‘‘top graduate’’ (those with the 20 best-ranked graduate programs); ‘‘top undergraduate’’ (those participating in the Oberlin Conference on College Science); ‘‘random graduate’’ (other institutions with graduate programs); and ‘‘random undergraduate’’ (other institutions without graduate programs). Generally the results show that the GRE does not cover the entire curriculum (low values of R2) for any institutional type. With regard to the coverage of the GRE by the curriculum (R1 values), there are significant differences between institutions of different types. Institutions with graduate programs have curricula that cover the modern physics and statistical mechanics aspects of the GRE significantly better than institutions without graduate programs.
Magnetic charges in special relativity
Authors: Adawi I.
Published: September 2005

Magnetic charges are used to discuss electromagnetic phenomena in which the symmetry between the electric and magnetic fields is fully displayed. A simple derivation of the transformation equations of the fields (E, B) is given. It is shown that the Lorentz force as an axiom can be replaced by the simpler definition that the force on a particle of electric charge q and magnetic charge g in its rest frame is qE+gB (where E and B are the rest frame fields).
Variational approach to the stationary states of the double-oscillator potential
Authors: Mirhashem Behzad , Ferrell Richard A.
Published: September 2005

A variational approach to the calculation of the two lowest eigenvalues of Schrödinger’s equation for the double-oscillator potential is presented. A family of two-parameter double-Gaussian trial functions provides an alternative to the exact series expansions for the energy eigenfunctions and yields energy estimates of high accuracy.
Gauge invariance and threshold photon scattering on a composite target
Authors: Williams H. T.
Published: September 2005

The threshold amplitude for Compton scattering is known to be proportional to the square of the total charge of the target. A naive application of the impulse approximation would give a result that would depend upon the sum of squares of the charges of the individual particles comprising the target. Resolution of these incompatible results depends upon careful treatment of the center-of-mass coordinate of the target. This treatment is presented in the context of nonrelativistic perturbation theory.
A numerical study of quantum barrier penetration in one dimension
Authors: Leming Charles W. , Van Smith Andrew
Published: September 2005

Elementary numerical methods are used to evaluate solutions to Schrödinger’s equation for a variety of one-dimensional potential barriers and to determine the transmission coefficients of free particles. These techniques are used to study the oscillatory variations in transmission coefficients for both continuous and discontinuous potentials. The amplitude of the variations is found to be strongly increased by discontinuities in the potential function but small variations exist even for a smooth, continuous potential function. The techniques described are suitable for intermediate-level undergraduate physics students.
Time-of-flight measurement of the speed of light using an acousto–optic modulator
Authors: Deblaquiere J. A. , Harvey K. C. , Hemann A. K.
Published: September 2005

An experiment is described in which the speed of light is measured by time of flight. The equipment in this experiment includes a laser and an acousto–optic modulator. A laser beam was rapidly switched on and off by an acousto–optic modulator and the time that was taken for a light pulse to go a known distance was measured. The group velocity of light was found to an accuracy of about 1.5% using a calibrated oscilloscope as the time reference. Further, by making a least-squares fit to a set of measurements for different travel times, an uncertainty of 0.5% was obtained. This experiment illustrates acousto–optic modulators, optics, time-of-flight instrumentation, and data analysis.
Computer simulation of space charge
Authors: Yu K. W. , Chung W. K. , Mak S. S.
Published: September 2005

Using the particle–mesh (PM) method, a one-dimensional simulation of the well-known Langmuir–Child’s law is performed on an INTEL 80386-based personal computer system. The program is coded in turbo basic (trademark of Borland International, Inc.). The numerical results obtained were in excellent agreement with theoretical predictions and the computational time required is quite modest. This simulation exercise demonstrates that some simple computer simulation using particles may be implemented successfully on PC’s that are available today, and hopefully this will provide the necessary incentives for newcomers to the field who wish to acquire a flavor of the elementary aspects of the practice.
The role of boundary conditions in separation of variables: Quantum oscillator in a box
Authors: Tanner A. C.
Published: September 2005

The Schrödinger equation for two (or more) particles can sometimes be separated into two (or more) one-particle equations. However, the boundary conditions can recouple the variables even though the Schrödinger equation itself is separable.
An inexpensive gas effusion apparatus for the introductory laboratory
Authors: Amato Joseph C. , Williams Roger E.
Published: September 2005

An inexpensive, easy to build gas effusion apparatus for measuring molecular velocities is described. The instrument features a liquid nitrogen cooled adsorption pump to replace more costly diffusion and rotary vacuum pumps. Low cost, low maintenance, and simplicity of operation render the experiment suitable for introductory physics students. A straightforward measurement consistently yields average velocities within 10% of the calculated values.
Teaching astronomy for the blind: Providing a lecture and laboratory experience
Authors: Spagna George F.
Published: September 2005

A general education course in astronomy was successfully adapted to provide a meaningful laboratory science experience for a visually-impaired student. Minor alterations to the style of lecture, coupled with an edition of the text on audio cassette tapes, allowed the student to keep pace with the theory component of the course. Laboratory equipment was modified to provide tactile measuring apparatus, which allowed the student to perform all the same processes of data acquisition and analysis required of sighted students.
Noether’s theorem and local gauge invariance
Authors: Al-Kuwari Hemyan A. , Taha M. O.
Published: September 2005

The conditions of local gauge invariance under a general non-Abelian group are discussed. They imply the field equations for the gauge vector fields and the existence of conserved Noether’s currents of global gauge invariance. There are no extra conserved currents associated with local gauge invariance.
Chaoticlike motion of a l
i
n
e
a
r dynamical system
Authors: Mendelson Kenneth S. , Karioris Frank G.
Published: September 2005

The free oscillations of a chain of identical masses connected by identical springs can be very complicated, resembling the chaotic oscillations of nonlinear systems. These oscillations, however, differ in significant ways from chaotic oscillations. They are actually oscillations of a type called almost periodic that are also observed in nonlinear systems. This article solves the equations of motion for longitudinal oscillations in a finite linear chain. The resulting oscillations are discussed and compared with chaotic oscillations. The linear chain can easily be set up as a demonstration.
Equivalent magnetization approach for calculating magnetic fields of localized steady-state current distributions
Authors: Carrascal Basilio , Estévez Gentil A. , Lorenzo Vicente
Published: September 2005

In the evaluation of the magnetic fields produced by magnetized bodies in a vacuum the bodies can be replaced by fictitious ‘‘magnetization’’ currents. Therefore, it should be possible to calculate magnetic fields of real currents by replacing them with fictitious magnetized bodies. This possibility is explored in the present article. In one of the examples considered the net magnetic field due to a uniformly charged sphere spinning on its axis is calculated. Other applications are suggested.
Springs and masses as a stationary wave problem
Authors: Bonnet Jean-Pierre
Published: September 2005

The two-degree-of-freedom oscillator consisting of two masses and three springs whose masses are not negligible is studied in terms of stationary waves. The corrected eigenfrequencies are calculated. It is shown that a recently published treatment of the same problem is valid only if the masses of the springs are very much smaller than the masses of the oscillating bodies.
Perturbative treatment of a general driven time-dependent oscillator in a time-dependent basis
Authors: Lo C. F.
Published: September 2005

This paper examines the possibility of applying the time-dependent perturbation theory to the systems with a time-dependent unperturbed part. Analyses indicate that time-dependent perturbation theory is valid even if the unperturbed Hamiltonian H0 depends on time, provided that the pseudostationary states of H0 are known. It is also shown that this new perturbative treatment provides a useful tool for tackling the problem of a general driven time-dependent oscillator.
Concept of relativistic temperature via the Crawford technique
Authors: Menon V. J. , Agrawal D. C.
Published: September 2005

Using the Crawford technique of calculating the energy loss of gas atoms colliding with a wall, it is demonstrated that relativistic temperature measures the average value of the product of the atomic velocity with momentum, i.e., 〈vp〉 per translational degree of freedom. This confirms a passing observation made by ter Haar and Wergeland 20 years ago. The mean number of collisions needed to attain equilibrium can also be estimated theoretically.
A magnetic model for the demonstration of phase transitions and excitations in molecular crystals
Authors: Nöldeke C. , Press W. , Hüller A.
Published: September 2005

A magnetic model for the demonstration of structural properties and the lattice dynamics of molecular crystals is presented. It is used to visualize an orientational order–disorder phase transition. The orientational order of the low-temperature phase observed on the model is also obtained from a mean field calculation. A simple theory for harmonic excitations of the model is presented, which gives the dispersion relation for an infinite crystal. The frequencies of the observed resonances of the finite model are compared with the results of a numerical eigensystem analysis and with the dispersion relation. Within the limitations given by the construction of the model the results are in rather good agreement.
Putting: How a golf ball and hole interact
Authors: Holmes Brian W.
Published: September 2005

The equations of motion for a golf ball interacting with a hole on a putting surface are found. A computer is used to predict the outcome of the ball’s encounter with the hole as a function of the impact parameter and the initial velocity of the ball at the rim. If the ball does not skid or bounce when it collides with the opposite rim, it is predicted that a uniform ball must travel at 1.626 m/s or less to be captured; that the British ball is easier to sink than the slightly larger American ball; that a ball with a larger moment of inertia is more difficult to sink; and that bouncing and skidding (factors that vary from green to green) result in capture at greater speeds. Experimental studies support these predictions.
Theory of a nonharmonic oscillator
Authors: Gatland Ian R.
Published: September 2005

When introducing oscillations, beginning physics courses typically only discuss the harmonic oscillator. This is natural, but this exclusive focus may disguise its special features (e.g., frequency-amplitude independence). Using an air track, our students investigate oscillations experimentally and match experimental data with theoretical curves. An additional theoretical choice, along with the damped harmonic oscillator, is the solution for the nonharmonic force law F=−F0 sgn(x)−γv. When there is no damping (γ=0) there is a difference of less than 0.06 between the nonharmonic and the harmonic oscillator curves if both have unit amplitude and the same frequency and phase. Still, the accuracy of the data allows discrimination between these models. However, the difference shows up most clearly when damping is present since then the period of the nonharmonic oscillator changes with the amplitude and curves that start in phase become out of phase. A simple approximate solution for this damped nonharmonic oscillator has been obtained.
Making zone plates with a laser printer
Authors: Clark Charles W. , Demkov Yurii N.
Published: September 2005

A simple program is presented for producing zone plates on laser printers, and some of its results and possible applications are discussed.
Lienard–Wiechert treatment of charges traversing a periodic potential
Authors: Glass Solomon J. , Jones John Bentley , Mendlowitz H.
Published: September 2005

The Lienard–Wiechert formalism is applied to the problem of a charged particle traversing a one-dimensional periodic potential. An expansion is made in terms of the ratio of the amplitude of the periodic potential to the incident energy. It is found that a discrete radiation spectrum is obtained to lowest order of the expansion.
Defining physics: The Nobel Prize selection process, 1901–1937
Authors: MacLachlan James
Published: September 2005

The great prestige of the Nobel Prizes has come virtually to define physics in the public mind. An examination of the nominations and the selections in the first 37 years of Nobel awards shows that those in charge of the selections went through a process of development as they refined their conceptions of the kind of work appropriate to be rewarded. Analyses are presented of the 1800 nominations made by 448 nominators for 213 scientists, of whom 44 received physics prizes between 1901 and 1937, 10 more who were awarded Nobel Prizes in physics after 1937, and 12 in chemistry, although nominated also in physics.
Cube corner retroreflectors for sound waves
Authors: Crawford Frank S.
Published: September 2005

Thr reflection of sound waves from buildings on the University of California, Berkley campus is studied. (AIP)
Berry’s geometric phase and motional fields
Authors: Commins Eugene D.
Published: September 2005

An experiment is described that provides an example of how Berry’s geometric phase arises from motion of a particle with a magnetic moment in an electric field and an inhomogeneous magnetic field.
The linear chain with initial conditions
Authors: Munley Frank
Published: September 2005

The Laplace transform is used to introduce initial conditions into the equations of motion of a linear chain of N equal masses connected by equivalent springs. A concrete solution requires inversion of an N×N matrix and inversion of the Laplace transform. A recursive relationship is derived which allows the inverse matrix for N masses to be easily obtained from the matrix for N−1 masses, and the inverse Laplace transform is obtained by the method of partial fractions. A general expression for certain partial fraction coefficients is derived, which makes it possible to determine the motion of the end mass of a semi-infinite chain when this mass receives an impulse.
Approximating the finite square well with an infinite well: Energies and eigenfunctions
Authors: Barker Barry I. , Rayborn Grayson H. , Ioup Juliette W. , Ioup George E.
Published: September 2005

Polynomial expansions are used to approximate the equations of the eigenvalues of the Schrödinger equation for a finite square potential well. The technique results in discrete, approximate eigenvalues which, it is shown, are identical to the corresponding eigenvalues of a wider, infinite well. The width of this infinite well is easy to calculate; indeed, the increase in width over that of the finite well is simply the original width divided by the well strength. The eigenfunctions of this wider, infinite well, which to first order has the same width for the ground state and all excited states, are also good approximations to the exact eigenfunctions of the finite well. These approximate eigenfunctions and eigenvalues are compared to accurate numeric calculations and to other approximations from the literature.
The principle of identicality and the foundations of quantum theory. I. The Gibbs paradox
Authors: Pešić Peter D.
Published: September 2005

The development of the concept of indistinguishability in the writings of Gibbs is traced, leading from the ‘‘Gibbs paradox’’ to his definition of generic phase.
Linearization of the simple pendulum
Authors: Cadwell L. H. , Boyko E. R.
Published: September 2005

A new method is described to obtain the leading correction to the simple harmonic approximation of a simple pendulum for large-angle motion using an analytical and geometric approach.
Langevin’s derivation of the relativistic expressions for energy
Authors: Simon Y. , Husson N.
Published: September 2005

Langevin showed that the relativistic expression for the kinetic energy, as well as the inertia of energy, could be derived entirely from the principle of conservation of energy, in addition to the two usual postulates of special relativity. Unfortunately, this beautiful derivation, given in a lecture and not published by the author, passed almost unnoticed. The object of this paper is to popularize it in a modernized presentation. Langevin’s approach is compared with the well-known one starting from the relativistic law of linear momentum conservation, following an idea of Lewis and Tolman.
Chaos in the motion of an inverted pendulum: An undergraduate laboratory experiment
Authors: Duchesne B. , Fischer C. W. , Gray C. G. , Jeffrey K. R.
Published: September 2005

A suitable experiment for undergraduates is described which illustrates chaotic motion, i.e., a driven inverted pendulum. By varying the driving frequency, one finds a transition from regular (periodic) motion to chaotic motion. A sonar coupled to a microcomputer is used to measure the position of the pendulum as a function of time, and fast Fourier transforms are used to give the power spectrum for the motion. The chaos is detected by following the evolution of the power spectrum, as the driving frequency is varied, from a line spectrum to a continuous one; the former corresponds to regular motion and the latter to chaotic motion. A second characteristic nonlinear phenomenon, subharmonic response, is also illustrated with the apparatus.
An inexpensive, easy to build Fabry–Pérot interferometer and its use in the introductory laboratory
Authors: Amato Joseph C. , Williams Roger E. , Helm Hugh
Published: September 2005

A simple scanning Fabry–Pérot interferometer for use by students in the introductory physics laboratory is described. The apparatus is easy to construct, using inexpensive commercially made optical components and a few easily fabricated parts. The instrument is used to measure the isotope shift in the hydrogen–deuterium Balmer spectrum and then to calculate Mp/me. Typical results achieve better than 1% accuracy.
Quantum tunneling and imaginary-time paths
Authors: Burgess C. P.
Published: September 2005

It is widely believed that the WKB approximation to quantum barrier penetration is described in the path-integral formalism by a saddle-point approximation based on an expansion about an imaginary-time semiclassical path. This article examines the relationship between tunneling amplitudes and imaginary-time paths. It is shown, using a simple example, that for some tunneling amplitudes the dominant semiclassical path cannot be chosen to have purely imaginary time if all other variables are chosen to be real.
Inexpensive and accurate position tracking with an ultrasonic ranging module and a personal computer
Authors: Duchesne B. , Fischer C. W. , Gray C. G.
Published: September 2005

An inexpensive and simple interface and software for an IBM PC or clone is used to record the position of an object using the ultrasonic ranger module (a commercial sonar). The ultrasonic ranger module is controlled, through the parallel printer port, by a microcomputer (IBM PC compatible) which is also responsible for recording the distances in memory. Positional accuracy of 0.1% is demonstrated, and shown to be sufficient for velocity measurements, as well as position. Some applications to a damped pendulum and a chaotic pendulum are also described.
Learning to think like a physicist: A review of research-based instructional strategies
Authors: Van Heuvelen Alan
Published: September 2005

Many studies in physics education indicate that our conventional instruction fails to achieve objectives we desire for our students. Students leave introductory courses unable to reason qualitatively about physical processes. They use primitive formula-centered problem-solving techniques. Their minds contain a small number of facts and equations that are accessible only by random searches. In recent years, research by scientists interested in cognition and pedagogy has shown that we can do much better. This paper reviews this research and the instructional strategies that are suggested by it. The following paper reports the preliminary results of using these strategies in introductory physics courses that emphasize problem solving.
Overview, Case Study Physics
Authors: Van Heuvelen Alan
Published: September 2005

Overview, Case Study (OCS) Physics is an effort to integrate recent results from physics education research into instruction for introductory university physics courses that emphasize problem solving. Students actively construct a knowledge hierarchy on a foundation of qualitative understanding. They analyze physical processes and problems using methods similar to those used by experienced scientists. Students receive repeated exposure to concepts in a variety of contexts over an extended time interval. Preliminary trials of OCS Physics have produced promising gains in student qualitative understanding, in their ability to solve problems, and in their ability to form and access a knowledge hierarchy.
Dynamical symmetry breaking and chaos in Duffing’s equation
Authors: Olson Collin L. , Olsson M. G.
Published: September 2005

In certain frequency ranges a nonlinear damped and driven oscillator will respond asymmetri-cally even though the potential energy is a single symmetric well. This dynamical symmetry breaking heralds the onset of a period doubling transition to chaos.
Classroom exercises with the Terrell effect
Authors: Burke John Robert , Strode Frank J.
Published: September 2005

Because of the finite speed of light, the photographic appearance of a relativistic body would not simply show a Lorentz contraction. In its simplest version, this effect provides exercises, accessible to undergraduates, that illustrate concepts of simultaneity and use of the Lorentz transformation. Transformation of light intensity also provides useful exercises and interesting results.
A didactical approach to nontrivial dispersion relations
Authors: Delellis R. , Minotti F.
Published: September 2005

A first approach to nontrivial dispersion relations is presented. Some properties of these relations corresponding to dispersive and/or dissipative phenomena are analyzed by studying the surface waves in a viscous liquid of infinite depth.
The quantum bouncer by the path integral method
Authors: Goodings D. A. , Szeredi T.
Published: September 2005

The path integral formulation of quantum mechanics in the semiclassical or WKB approximation provides a physically intuitive way of relating a classical system to its quantum analog. A fruitful way of studying quantum chaos is based upon applying the Gutzwiller periodic orbit sum rule, a result derived by the path integral method in the WKB approximation. This provides some motivation for learning about path integral techniques. In this paper a pedagogical example of the path integral formalism is presented in the hope of conveying the basic physical and mathematical concepts. The ‘‘quantum bouncer’’ is studied—the quantum version of a particle moving in one dimension above a perfectly reflecting surface while subject to a constant force directed toward the surface. The classical counterpart of this system is a ball bouncing on a floor in a constant gravitational field, collisions with the floor being assumed to be elastic. Path integration is used to derive the energy eigenvalues and eigenfunctions of the quantum bouncer in the WKB or semiclassical approximation. The results are shown to be the same as those obtained by solving the Schrödinger equation in the same approximation.
On the use of direct variational methods to study confined quantum systems
Authors: Marin J. L. , Cruz S. A.
Published: September 2005

The direct variational method is used to study two simple confined systems, namely, the hydrogen atom and the harmonic oscillator within impenetrable spherical boxes. The trial wave functions have been assumed as the product of the ‘‘free’’ solutions of the corresponding Schrödinger equation and a simple function that satisfies the respective boundary conditions. The energy levels obtained in this way are extremely close to the exact ones, thus proving the utility of the proposed method. This might constitute a complementary exercise for undergraduate students since usual quantum mechanics textbooks do not explore the use of the variational method to study confined systems.
A simple example to introduce continuum discretization
Authors: Riera A.
Published: September 2005

Expansions in terms of L2 integrable functions, such as Slater or Gaussian orbitals, or Hermite functions, are usually employed to describe bound states of atomic and molecular systems. A less familiar property of these expansions is that they can accurately reproduce continuum wave functions in selected regions of configuration space, yielding a procedure that is widely used in the calculation of probabilities of predissociation and ionization, as well as of unimolecular and bimolecular reactions. In the present work it is argued that the essentials of this procedure can be introduced with a modicum of theory through an extremely simple example, which lends itself to further numerical experimentation.
Friction experiments with a capstan
Authors: Levin Eugene
Published: September 2005

The force of static friction on a cord wrapped through an angle θ around a rough-surfaced cylinder increases exponentially with θ. A small tension T1 at one end of the cord, maintaining contact between cord and cylinder, provides the condition for a substantially larger tension, of maximum value T2=T1 exp(μsθ), at the other end. The validity of this relationship is studied for the kinetic friction case. The suitability of this system for an undergraduate experiment is discussed, together with practical applications—the donkey engine and the capstan—with a digression on sea chanties.
An error in Isaac Newton’s determination of planetary properties
Authors: Garisto Robert
Published: September 2005

Isaac Newton introduced his theory of gravitation in Book III of the Principia. To demonstrate the power of his new theory, Newton for the first time calculated the mass, surface gravity, and density of Jupiter, Saturn, and the Earth (relative to the Sun). In the final printing of the Principia, an error appears in Newton’s calculation of the mass of the Earth and its origin is traced. In the course of reconstructing the source of the error, several other minor inconsistencies are resolved.
Schrödinger equation in two dimensions for a zero-range potential and a uniform magnetic field: An exactly solvable model
Authors: Perez J. Fernando , Coutinho F. A. B.
Published: September 2005

The spectrum and eigenfunctions of a particle moving in two dimensions under the influence of an external uniform magnetic field and in the presence of a ‘‘point interaction’’ is determined. This is done after an elementary discussion of how to construct a ‘‘point interaction’’ in two dimensions circumventing the well-known difficulties with the Dirac δ2(r) interaction.
Electron conversion for selected nuclides
Authors: Desmarais D. , Duggan J. L.
Published: September 2005

An analysis is made of the spectra resulting from the process of internal conversion to measure the inner-shell binding energy of certain nuclides. Use is made of the K/L ratio of the internal conversion coefficients to predict spin and parity changes in the electromagnetic transitions involved. Such an analysis can quite easily be introduced into an undergraduate nuclear laboratory program.
Resource Letter HEPP-1: History of elementary-particle physics
Authors: Hovis R. Corby , Kragh Helge
Published: September 2005

This Resource Letter provides a guide to literature on the history of modern elementary-particle physics. Histories that treat developments from the 1930s through the 1980s are focused on and a sampling is included of the historiography covering the period c. 1890–1930, the prehistory of elementary-particle physics as a discipline. Also included are collections of scientific papers, which might be especially valuable to individuals who wish to undertake historical research on particular scientists or subfields of elementary-particle physics. The introduction presents some statistical data and associated references for elementary-particle physics and surveys historiographical approaches and issues that are represented in historical accounts in the bibliography. All references are assigned a rating of E (Elementary), I (Intermediate), or A (Advanced) based on their technical or conceptual difficulty or their appropriateness for a person attempting a graduated study of the history of modern particle physics. That is, items labeled E are suitable for the layman or would be fundamental to a beginning exploration of the history of particle physics, whereas items labeled A are technically demanding (mathematically, historiographically, or philosophically) or would be most appropriate for specialized or advanced examinations of various topics.
Thomas precession and its associated grouplike structure
Authors: Ungar Abraham A.
Published: September 2005

M a t h e m a t i c s phenomena and discovers the secret analogies which unite them. Joseph Fourier. Where there is physical significance, there is pattern and mathematical regularity. The aim of this article is to expose a hitherto unsuspected grouplike structure underlying the set of all relativistically admissible velocities, which shares remarkable analogies with the ordinary group structure. The physical phenomenon that stores the mathematical regularity in the set of all relativistically admissible three-velocities turns out to be the Thomas precession of special relativity theory. The set of all three-velocities forms a group under velocity addition. In contrast, the set of all relativistically admissible three-velocities does not form a group under relativistic velocity addition. Since groups measure symmetry and exhibit mathematical regularity it seems that the progress from velocities to relativistically admissible ones involves a loss of symmetry and mathematical regularity. This article reveals that the lost symmetry and mathematical regularity is concealed in the Thomas precession. Following a presentation of the group axioms, analogous axioms underlying the grouplike structure of velocities in the relativistic regime are presented. These turn out to include the usual group axioms in which the associative–commutative laws are relaxed by means of the Thomas precession. In order to expose the physics student to the power and elegance of abstract mathematics, our results are placed in the context of an abstract real inner product space. However, not much is lost if the student always assumes that the abstract real inner product space is the familiar Euclidean three-space.
Essentials of the Casimir effect and its computation
Authors: Elizalde E. , Romeo A.
Published: September 2005

A historical introduction to the issues raised by the Casimir effect is provided, putting special emphasis on the experiments which attempt to test this and related phenomena. The classical and modern quantum interpretations are explained, and an account of the existing calculation methods is given. The discussion is illustrated with an example of the zeta-function regularization procedure.