bluuebunny/crossref_metadata_2025 huggingface dataset:
Stationary waves on cylindrical fluid jets
Authors: Awati K. M. , Howes T.
Published: March 2005

An obstacle in the path of a water jet emerging from a tap gives rise to a stationary wave pattern upstream of the obstacle. In this paper, the wavelengths and the damping coefficients of these waves are calculated for various jet radii and velocities. The calculations indicate that the wavelength decreases and the damping coefficient increases with increasing jet velocity, in qualitative agreement with observations.
Direct calculation of time dilation
Authors: Jefimenko Oleg D.
Published: March 2005

The possibility of explaining time dilation as a dynamic cause-and-effect phenomenon is explored by calculating the rates of three elementary electromagnetic clocks in a stationary and in a moving reference frame. The operation of the clocks is based on the interaction between a field-experiencing electric point charge and different field-producing electric charge configurations. The calculations show that, when the clocks move, they run as predicted by the special relativity theory. The slowing down of the three moving clocks is due to a different electromagnetic field produced by the moving field-producing charges (and hence due to a different force acting on the field-experiencing charges) as well as due to a change of the effective mass of the moving field-experiencing charges. Thus, for the clocks under consideration, time dilation can be considered a dynamic cause-and-effect phenomenon and not merely a kinematic effect, as time dilation is usually explained in conventional presentations of the special relativity theory.
A novel geometry for Rutherford scattering
Authors: Dodds S. A. , Mutchler G. S.
Published: March 2005

We describe a new geometry for a Rutherford scattering experiment which utilizes an annular detector and movable target. The apparatus provides both a good counting rate and simple data reduction. Both the angular dependence and the absolute value of the cross section can be obtained for a reasonable range of scattering angles.
Angular momentum conservation (a freshman experiment)
Authors: Akyüz R. Ö.
Published: March 2005

A simple turntable and a simple spring gun mounted on it demonstrate the angular momentum conservation principle by providing independent measurements of the angular momenta of the turntable, and of a metal ball, projected horizontally—and tangentially—from the spring gun.
The converse relativistic Doppler theorem
Authors: Bachman R. A.
Published: March 2005

It is shown that, for a relativistic Doppler effect to depend on one-dimensional source and observer motions only through their relative velocity, then the wave speed must equal the speed of light in vacuum or satisfy the dispersion relation for a collisionless electron gas. The three-dimensional case is briefly examined, showing that the same results apply. The appropriate Doppler formula is derived, showing the explicit dependence upon the relative velocity; the one-dimensional and vacuum optical cases are readily deduced as corollaries.
The pumping of a swing from the standing position
Authors: Case William B.
Published: March 2005

The pumping of a swing from a standing position is modeled as a rigid object forced to rotate back and forth at the lower ends of supporting ropes. This model after some approximations leads to a harmonic oscillator with driving and parametric terms. It is then argued that in the regime of the common playground swing the driving terms dominate and the pumping of a swing in the standing position is best characterized as a driven oscillator. Examination of the relative phase of the swinger and the swing also supports this conclusion. This model is compared with earlier work which claimed that the swing pumped by a standing swinger is characterized as a parametric oscillator. Simple demonstrations of both mechanisms are described. A comparison of pumping while standing and seated is also made.
Photon states made easy: A computational approach to quantum radiation theory
Authors: Johnston I. D.
Published: March 2005

Students first meet the wave-particle paradox through the photon and wave descriptions of light. Yet, in basic courses on quantum mechanics, they study matter particles only, because the mathematics of the quantized radiation field is usually considered too advanced. An oscillating electromagnetic field is formally similar to a harmonic oscillator, whose energy eigenstates can represent states of well-defined photon number. Using a computer program from the CUPS project, an approach will be described which demonstrates the action of the annihilation operator on these states, constructs coherent states which behave like classical electromagnetic fields, and shows how such states can be squeezed. All of these have practical relevance in modern optics. This is just one example of the computer making a hitherto unapproachable subject accessible to ordinary undergraduates. Computers have already changed how much of quantum mechanics is taught. As more such possibilities are realized, the teaching of the whole subject must surely change radically.
Toy calculations to estimate critical exponents for random walks
Authors: Saavedra Filho N. C. , da Cunha Bruno G. C. , Gomes M. A. F.
Published: March 2005

A simple method based on the enumeration of all random walk configurations for a very reduced number of steps is used to obtain the critical exponent ν for self-avoiding random walks in two and three dimensions.
On the bound states of a charged, nonrelativistic particle in the field of a stationary magnetic dipole: An introduction
Authors: Wolsky Alan M.
Published: March 2005

The motion of ions above the earth’s atmosphere is introduced by discussing the nonrelativistic motion of a charged particle in the field of a stationary magnetic dipole. Unlike the Kepler or Coulomb problem, no way is known to separate our problem into one-dimensional problems and a fortiori an exact analytic solution is not known. However, an effective potential can be identified whose study clarifies the qualitative and semiquantitative features of the bound states. We ask about the periodicity of bound states, taken for granted by one exposed only to the Kepler or Coulomb problem, and show how consideration of phase space can provide a partial answer, Poincaré recurrence. The treatment is accessible to students who have a first acquaintance with the canonical formalism and Liouville’s theorem, for example first-year graduate students.
Use of pressure transducers in laboratory experiments. I. Experimental verification of the fundamental equation of fluid statics. Application to density measurements
Authors: Victoria L. , Molina C. , Arenas A. , Ibáñez J. A.
Published: March 2005

The use of inexpensive pressure sensors, with minimum installation problems, has allowed several experiments to be designed for the physics class. An experimental device provided with a pressure sensor and a level sensor has now made it possible to verify the fundamental equation of fluid statics. The device has been applied to density measurements of several fluids (water, aqueous solution of NaCl and ethanol) at constant temperature.
Test of the Biot–Savart law to distances of 15 m
Authors: Ruppeiner George , Grossman Michael , Tafti Ali
Published: March 2005

We present direct tests of the Biot–Savart law to distances of 15 m. This undergraduate experiment involves an audio-frequency signal generator, magnetic coils, and a lock-in amplifier. The major experimental difficulty was geophysical magnetic fields resulting from induced eddy currents. The Biot–Savart law was confirmed to a precision of about 1%.
Electric field line diagrams don’t work
Authors: Wolf Alan , Van Hook Stephen J. , Weeks Eric R.
Published: March 2005

Electric fields produced by coplanar point charges have often been represented by field line diagrams that depict two-dimensional slices of the three-dimensional field. Serious problems with these ‘‘conventional’’ field line diagrams (CFLDs) have been overlooked. Two of these problems, ‘‘equatorial clumping’’ and ‘‘false monopole moment,’’ occur because a two-dimensional slice lacks information vital to the accurate representation of an inherently three-dimensional field. Equatorial clumping causes most CFLDs to exhibit unphysical behavior such as irregular spacing between field lines terminating on negative charges. CFLDs can also mistakenly indicate that a neutral charge distribution has a significant monopole moment. Such phenomena make the visual estimation of local field strengths impossible and render CFLDs of little utility for representing three-dimensional fields. While these ‘‘projection’’ problems can be avoided by using two-dimensional field line diagrams to represent two-dimensional (1/r) electric fields, or by using three-dimensional field line diagrams to represent three-dimensional fields, other forms of distortion generally remain.
Solving one-dimensional Schrödinger-like equations using a numerical matrix method
Authors: Van der Maelen Uría Juan F. , García-Granda Santiago , Menéndez-Velázquez Amador
Published: March 2005

A numerical method for the solution of one-dimensional Schrödinger-like equations with arbitrary numerical or analytical potentials is presented. The method takes advantage of matrix algebra for both obtaining several eigenvalues and eigenvectors at the same time and saving computer time. On the other hand, the method illustrates the close relationship between differential and algebraic eigenvalue problems, as well as the mathematical origin of quantization. Several examples are worked out in the text and the procedure for applying a user friendly routine to other problems is given.
An undergraduate experiment on x-ray spectra and Moseley’s law using a scanning electron microscope
Authors: Conover C. W. S. , Dudek John
Published: March 2005

We describe an undergraduate laboratory experiment developed for sophomore modern physics students, using the x-ray analysis feature of a scanning electron microscope. The experiment described is a fundamental physics measurement performed with a state-of-the-art apparatus not usually used in pedagogical physics experiments. The characteristic x-ray spectrum of elements shows a simple progression that can be quantitatively explained by the conceptually important Bohr–Rutherford shell model of atomic structure. Students measure the Kα and Kβ x-ray spectra from metals in the range of 12≤Z≤41. The measurements allow the verification of Moseley’s law scaling of x-ray energies with atomic number and a quantitative measure of the data’s fit to the shell model.
The three-volume Sears—50 years later
Authors: Templin Jacques D.
Published: March 2005

This year is the 50th anniversary of the publication of the final volume of Francis Sears’s three-volume Principles of Physics. This text, which was very successful, marked the beginning of a new type of introductory physics course. A comparison is carried out between Principles of Physics and an older text, Physics by Hausmann and Slack. It is argued that the two texts represent different views of physics. An attempt is made to draw lessons concerning the conditions required for a radical change in the introductory course.
The twin ‘‘paradox’’ and the conventionality of simultaneity
Authors: Debs Talal A. , Redhead Michael L. G.
Published: March 2005

A new approach to understanding the twin paradox, based on the conventionality of simultaneity, is presented and illustrated. The canonical version of the twin paradox is discussed with reference to its historical origins and the standard explanations given for the differential aging of the twins. It is shown that these are merely specific examples of an infinite class of possible accounts, none of which is privileged. The bounds of this class are given a novel geometrical interpretation. Nonstandard versions of the twin paradox are discussed, and the conventionality of the simultaneity approach is generalized. The role of accelerated reference frames in explaining the twins’ aging is also critically examined. The application of the conventionality of simultaneity to the twin paradox hopefully provides a way to settle the often discussed issue of the twins’ differential aging.
Elementary derivation of Kepler’s laws
Authors: Vogt Erich
Published: March 2005

A simple derivation of all three so-called Kepler laws is presented in which the orbits, bound and unbound, follow directly and immediately from conservation of energy and angular momentum. The intent is to make this crowning achievement of Newtonian mechanics easily accessible to students in introductory physics courses. The method is also extended to simplify the derivation of the Rutherford scattering law.
The rise of a liquid in a capillary tube revisited: A hydrodynamical approach
Authors: Duarte A. A. , Strier D. E. , Zanette D. H.
Published: March 2005

We use the time-dependent Navier–Stokes equation to study the dynamics of a liquid rising in a capillary tube. We show that the evolution consists of an initial stage of inertial motion, followed by a dynamical-balance stage in which gravity and viscosity compensate the capillarity force. This approach is compared with other formulations, based on the study of variable mass systems or on some simplified hydrodynamical formulas. Our attention is then focused on the crossover between the regimes of monotonic and oscillatory motion, and we find that numerical solutions to the relevant equations are in good agreement with an analytical linearized approach.
‘‘Top-down teaching’’ in noncalculus-based introductory physics classes
Authors: Dudley J. M. , Bold G. E. J.
Published: March 2005

Traditional methods used to teach physics to students who are physics or engineering majors are inappropriate for introductory, ‘‘science literacy’’ courses. We describe here an alternative ‘‘top-down’’ teaching method which has been used successfully to enhance such a course given at the University of Auckland in New Zealand. The approach reverses the traditional sequence of instruction and is based on beginning all lecture treatments with discussions of complex, yet familiar phenomena and working backward to discussions of the simple physical laws underlying them. We make extensive use of demonstrations and give examples of the particular application of this method to the teaching of electronics. The advantages and problems of this approach compared to traditional teaching methods in physics are also discussed.
On the natural optical activity in an isotropic medium: An exactly solvable model
Authors: Vekstein G. E.
Published: March 2005

A model of a chiral isotropic medium (a gas of randomly oriented handed molecules) is presented, which allows exact calculation of the optical rotation.
The Newton two-knife experiment: Intricacies of wedge diffraction
Authors: Silverman M. P. , Strange Wayne
Published: March 2005

About a century before Young’s celebrated two-slit experiment, Isaac Newton quantitatively investigated the diffraction of light from a wedge aperture, but failed to understand the implications of his findings. We have reexamined this unusual system theoretically within the framework of the Fresnel–Kirchhoff scalar diffraction theory, and experimentally using a laser light source with pinhole spatial filter and CCD camera. Both the far-field shadow region and near-field directly illuminated region reveal aesthetically striking images that are deducible from the mathematical analysis, but whose interpretation is subtle and best elucidated by an alternative and less widely known perspective of diffraction.
Fermat’s principle and multiple imaging by gravitational lenses
Authors: Nandor M. J. , Helliwell T. M.
Published: March 2005

Gravitational lensing is now regularly observed by astrophysicists, including the lensing of distant quasars by galaxies, and the lensing of stars in the galactic nucleus and in the Larger Magellanic Cloud by more nearby stars. The lensing is readily understood with the help of Fermat’s principle of stationary time to find the paths of light rays. Conventional discussions of Fermat’s principle in introductory physics and optics courses may easily be extended to include gravitational lensing, to show for example that even the simplest gravitational lens can produce multiple images of the same source.
Preliminary IUPP results: Student reactions to in-class demonstrations and to the presentation of coherent themes
Authors: Di Stefano R.
Published: March 2005

The methods of analysis that were applied to the information gathered during the 1991–1992 field tests of the Introductory University Physics Project are demonstrated through the study of two specific questions. The first question addresses the effectiveness of in-class demonstrations as an aid to learning. The relative importance of demonstrations, a feature relevant to most implementations of introductory science courses, emerged from comments contributed by students in both comparison and model courses. The second question is about the effectiveness of teaching and learning an area of physics (such as mechanics) through the use of an overarching context (such as ‘‘Interplanetary Travel’’). This question was inspired by the test of a specific model, Physics in Context.
The analogy between the calculation of a two-dimensional electrostatic field and that of a two-dimensional magnetostatic field
Authors: Zhou Ying-yan
Published: March 2005

The analogy between the calculation of a two-dimensional electrostatic field and that of a two-dimensional magnetostatic field is exposed and yields a new theorem.
Student measurement of radon gas concentrations
Authors: Riley James A.
Published: March 2005

A sodium iodide crystal connected to a multichannel pulse height analyzer card in a microcomputer is used to detect and analyze the progeny of radon gas present in the ambient air of several buildings. Relative levels are obtained in three buildings and an attempt is made at calculating absolute levels.
Mean occupation number for noninteracting paraparticles in degenerate energy levels
Authors: Kishore R.
Published: March 2005

The combinatorial solution of finding the number of ways of distributing n particles into g distinguishable groups such that no group contains fewer than q objects or more than q+a objects is used to obtain the mean occupation number of noninteracting paraparticles in degenerate energy levels. It is shown that the donor electrons in an impurity level of a semiconductor behave as paraparticles under constraints, called slave paraparticles.
Strong focusing and the radiofrequency quadrupole accelerator
Authors: Wangler Thomas P.
Published: March 2005

The ‘‘New Problems’’ department presents novel problems for use in undergraduate physics courses beyond the introductory level. In this article the problems and solutions use basic principles of electromagnetism to explain strong-focusing accelerator known as the radiofrequency quadrupole. Their solutions use Laplace’s equation and require the extraction of information from boundary conditions. They also introduce the quasistatic approximation and show how under appropriate conditions Laplace’s equation can be used to solve time-dependent problems. The problems are suitable for a course in electromagnetism and may be of interest for a cours in classical mechanics.
Features of a nonlinear normal-mode problem
Authors: Brehm J. J.
Published: March 2005

A model of nonlinear oscillations is developed. The model decouples at once and nonlinear normal modes result. The solutions describe nonisochronous motion on invariant tori in phase space. Among the orbits there is a dense set on which the normal frequencies are in resonance. This oscillating system serves to illustrate many of the ideas of nonlinear dynamics, particularly the concept of integrability. The integrable system also provides the point of departure for an exploration of Hamiltonian chaos.
The evolution and revival structure of localized quantum wave packets
Authors: Bluhm Robert , Kostelecký V. Alan , Porter James A.
Published: March 2005

Localized quantum wave packets can be produced in a variety of physical systems and are the subject of much current research in atomic, molecular, chemical, and condensed-matter physics. They are particularly well suited for studying the classical limit of a quantum-mechanical system. The motion of a localized quantum wave packet initially follows the corresponding classical motion. However, in most cases the quantum wave packet spreads and undergoes a series of collapses and revivals. We present a generic treatment of wave-packet evolution, and we provide conditions under which various types of revivals occur in ideal form. The discussion is at a level appropriate for an advanced undergraduate or first-year graduate course in quantum mechanics. Explicit examples of different types of revival structure are provided, and physical applications are discussed.
Specific heats and the equipartition law in introductory textbooks
Authors: Gearhart Clayton A.
Published: March 2005

A majority of introductory calculus-based physics textbooks, including many widely used ones, give misleading or incorrect explanations for the failure of the equipartition law to describe correctly the classically expected rotational degrees of freedom in monatomic and diatomic gases. This article outlines typical textbook treatments and reviews the quantum mechanical explanation.
Reaction forces on a ladder leaning on a rough wall
Authors: González Alejandro G. , Gratton Julio
Published: March 2005

The determination of the reactions on a ladder is discussed including friction against the wall. In a recent article, this problem was studied considering elastic compression and it was argued that an additional condition holds that allows one to find all the reactions. We show that this condition is incorrect for typical ladders, when flexion is important. We clarify the issues of static determinacy by means of an analysis that takes into account both compression and flexion. We find that when the climber arrives at the top, the result depends on which deformation prevails. We conclude that the reactions can never be determined using only statics, because there is no way to ascertain which kind of deformation dominates, and so which limiting condition will be attained, if any.
Paradoxical twins and their special relatives
Authors: Price Richard H. , Gruber Ronald P.
Published: March 2005

We present a variation and extension of the twin paradox recently put forth by Boughn. These additional considerations make a strong case that there is no meaning to the question of ‘‘where’’ the aging difference occurs in the twin paradox.
More on the quantum propagator of a particle in a linear potential
Authors: Arrighini Giovanni P. , Durante Nicola L. , Guidotti Carla
Published: March 2005

The construction of the exact quantum propagator of a particle subjected to a constant force offers a challenge to existing propagator methodology. Here, besides considering the traditional approach, which involves an expansion in the complete set of energy eigenstates, we illustrate (i) the merits of a rather more elegant procedure founded on the ‘‘disentanglement’’ of the time-evolution operator and (ii) the power of a general treatment based on a time-dependent variational approach.
Perturbation analysis of rolling friction on a turntable
Authors: Soodak Harry , Tiersten Martin S.
Published: March 2005

The effect of rolling friction on the motion of a ball rolling on a uniformly spinning horizontal turntable is evaluated by a first-order perturbation approach, in which the unperturbed trajectories are the circular gyrations of the rolling ball in the absence of rolling friction. The analysis provides qualitative and quantitative understanding of the effect of rolling friction by itself and in combination with other ‘‘perturbations,’’ such as a tilt of the turntable.
Geometry of the Schmidt decomposition and Hardy’s theorem
Authors: Aravind P. K.
Published: March 2005

The Schmidt decomposition theorem allows us to express an entangled wave function of two quantum systems in a particularly simple form. The purpose of this paper is to describe a geometrical method of performing the Schmidt decomposition that complements the usual algebraic method. This geometrical method is worked out in detail for a pair of spin-1/2 particles and its utility is illustrated by giving a simple discussion of several aspects of Hardy’s version of Bell’s theorem.
Conformally dual fields in relativistic classical and quantum mechanics
Authors: Mitchell Thomas P.
Published: March 2005

The conditions governing the existence of conformally dual scalar fields in both classical and quantum theories are derived. The transformation properties of the Hamilton–Jacobi and Klein–Gordon equations under conformal mappings are established and utilized as the basis for the analysis. The existence of self-dual fields is demonstrated and examples are presented. Previously known results applicable to the Schrödinger equation and to Newtonian mechanics are shown to follow in the nonrelativistic limit as special cases of the present study.
An experiment on the liquid–vapor equilibrium for water
Authors: Gesari Susana , Irigoyen Beatriz , Juan Alfredo
Published: March 2005

In the present paper we propose a simple and easy method to determine the latent heat of vaporization of pure water, using the Clausius–Clapeyron equation. The vapor pressure of water was calculated from measurements of temperature and volume, assuming an ideal gas behavior for the vapor. The calculated heat of phase change is in a good agreement with the latent heat of vaporization, obtained from the empirical Antoine equation and from the literature.
Direct use of variational principles as an approximation technique in classical mechanics
Authors: Gray C. G. , Karl G. , Novikov V. A.
Published: March 2005

The Hamilton least action principle, a reformulated Maupertuis least action principle, and their reciprocals, are shown to be useful as direct methods for approximate solutions of dynamics problems. We discuss applications to trajectories of all types, i.e., periodic, quasiperiodic, chaotic, scattering, and arbitrary segments of arbitrary trajectories. The analogy with the standard technique used in quantum mechanics is very striking, especially in one of the reformulations (extremization of the mean energy), and in the calculational procedure (Rayleigh–Ritz type).
Relativistic precession
Authors: Hamilton J. Dwayne
Published: March 2005

Inertial frames of reference and nonrotating frames of reference are discussed. Using geometric algebra as the principal mathematical tool, the Thomas precession of torque-free gyroscopes in special relativity is then derived in an exact fashion in two different ways. First, the equations of Fermi–Walker transport are employed to derive expressions for the precession; second, a torque-free reference frame is compared to one in which the coordinate axes are forced by torques to remain parallel to a fixed direction. The precession of a freely falling gyroscope in a gravitational field concludes the paper.
Measuring the speed of digital signals (speed of light)
Authors: Graham John R.
Published: March 2005

An odd number of digital not-gates connected in a closed loop circuit will produce a relatively stable free running oscillator. The frequency of oscillation is determined by the number and type of not-gates, the circuit supply voltage, and the total length of connection wire used between the not-gates. Measuring the frequency for various lengths of connection wire enables the speed of the digital signals in the wire to be calculated. The method is sensitive enough to reveal that signals traveling in 22 gauge insulated copper wire propagate about 5% slower than those in 22 gauge bare copper wire. The speed in insulated wire is (2.87±0.03)×108 m/s and the speed in bare wire is (3.03±0.02)×108 m/s. This experiment has been found to be a very popular undergraduate laboratory due to its low cost, straightforward theory, and relatively high (∼1%) precision. The absence of a light source eliminates complicated optics and impresses students with the fact that visible light is not the only thing that travels with the speed of light!
Resonant Faraday rotation as a probe of atomic dispersion
Authors: Van Baak D. A.
Published: March 2005

The Faraday effect (the rotation of the plane of polarization of light as it propagates through a sample parallel to a static magnetic field) is readily detected in room-temperature rubidium vapor by a diode-laser experiment near the D2 resonance line at 780 nm, and the theoretical treatment of this effect provides an unusually clear insight into the relation between absorption and dispersion in the interaction of light with matter.
Holographic real-time imaging of standing waves in gases
Authors: Peterson Richard W. , Pankratz Stephan J. , Perkins Trent A. , Dickson Adam , Hoyt Chad
Published: March 2005

Stroboscopic holographic interferometry has been developed at an advanced undergraduate level allowing real-time imaging of standing sound waves in gas filled, closed tube resonators. A heterodyne Mach–Zehnder interferometer was first built by students to show the feasibility of interferometric detection of sound waves in a small cell. In the subsequent holographic study, the laser irradiance is modulated by an acousto-optic cell at frequencies near that of the standing wave, and a video camera records the fringe motion due to sound pressure changes. Fractional fringe shifts are observed for an air filled cell, and multiple fringe shifts are imaged for the case of freon. Sound reflections from the cell ends are easily observed, with nonsinusoidal waveforms dominating at high intensities due to superposition of resonator harmonics.
The transient magnetic field outside an infinite solenoid
Authors: Protheroe Raymond J. , Koks Don
Published: March 2005

The electromotive force (emf) in a loop outside an infinite solenoid with changing current is usually calculated using the vector potential because the magnetic field outside an infinite solenoid is supposed to be zero. However, the magnetic field will only be zero for steady currents. A change in the applied voltage will give rise to a change in the current, which will propagate along the solenoid in the same way as a wave on a transmission line. This gives rise to a transient magnetic field outside the solenoid. It is quite possible to calculate this transient magnetic field and use it in Faraday’s law to calculate the emf directly without using the vector potential. In practice, it is usually simpler to use the vector potential. However, care should be taken to ensure that students are not given the impression that there is no magnetic field and that it is the vector potential that acts on charges in the loop. We give examples of the magnetic field configuration outside an infinite solenoid for a steplike change in driving voltage and for an ac driving voltage.
Why are the energy levels of the quantum harmonic oscillator equally spaced?
Authors: Royer Antoine
Published: March 2005

The quantum harmonic oscillator has the unique property that its energy levels are equally spaced. This property is connected, via the Wigner function, to the circular symmetry of the Hamiltonian in phase space, hence to the close relation between harmonic oscillations and rotations, very familiar at the classical level. We here have an example of a spectral regularity which is due to a symmetry in phase space, rather than in configuration space, as is more usual.
The optical–mechanical analogy in general relativity: New methods for the paths of light and of the planets
Authors: Evans James , Nandi Kamal K. , Islam Anwarul
Published: March 2005

The optical–mechanical analogy involves the expression of geometrical optics and particle mechanics in the same mathematical language. In this paper, an especially simple version of the optical–mechanical analogy is extended to general relativity. A variational principle for the trajectories of photons and particles is obtained which is applicable to a broad class of metrics. This permits us to cast the exact equations of motion for both massive and massless particles into the form of Newtonian mechanics. The new equations of motion are illustrated by applications to the Schwarzschild metric.
Updating Monte Carlo algorithms
Authors: Drugowich de Felício J. R. , Líbero Valter L.
Published: March 2005

Using the long-range Ising model, we present modern Monte Carlo techniques—single and multiple histogram and entropic sampling—which permit increasing the amount of information obtained from a simulation. Numerical results for the density of states, mean energy and specific heat are compared with exact calculations, easily handled in this case. As a consequence of the simplicity of the model, the ability of those methods to generate continuous plots of thermodynamical quantities can be appreciated even by students taking basic courses of statistical physics.
An exactly soluble Fresnel diffraction model of two-slit interference
Authors: Lock James A.
Published: March 2005

Using the formalism of Fresnel diffraction, we examine the diffraction and interference of two initially widely separated parallel Gaussian light beams. This two-beam configuration is a version of Young’s two-slit interference problem that is free of the mathematical complexity that occurs in most Fresnel diffraction calculations. As a result, it clearly and simply illustrates the transition from ray optics to wave interference.
More than misconceptions: Multiple perspectives on student knowledge and reasoning, and an appropriate role for education research
Authors: Hammer David
Published: March 2005

This article analyzes an excerpt of a discussion from a high school physics class from several different perspectives on students’ knowledge and reasoning, illustrating a range in what an instructor might perceive in students’ work and take as tasks for instruction. It suggests a view of current education research as providing perspectives to expand, refine, and support instructors’ perceptions and judgment, rather than as providing definitive principles or proven methods.
Ripples in the energy of a damped oscillator: The experimental point of view
Authors: Basano Lorenzo , Ottonello Pasquale , Palestini Valeria
Published: March 2005

An irreversible transformation of mechanical into thermal energy takes place during the motion of a damped harmonic oscillator, with the result that the level of the total mechanical energy of the system, as a first approximation, decays exponentially with time. A detailed description of this decrease, however, is not usually supplied in textbooks of classical mechanics or general physics. As Karlow has recently pointed out, the negative-exponential decay is modulated by a sequence of energy ripples, owing to the dissipation rate being not constant during the motion. Up to now, the analysis of this behavior has been based only on theoretical considerations; in this work we present the corresponding experimental evidence based on a couple of laboratory demonstrations that use an electrical RLC circuit and a hydrodynamically damped mechanical pendulum.
Experimental projects in graduate theoretical physics courses
Authors: Rosner Jonathan L.
Published: March 2005

Some beginning graduate courses in physics at the University of Chicago have been taught with final projects in addition to or in place of written final examinations. Although these courses and many of the projects are theoretical, experimental projects have been encouraged, with some success. A few examples are discussed.
When charge meets flux: Classical view of a quantum paradigm
Authors: Horner M. L. , Goldhaber Alfred S.
Published: March 2005

Quantum mechanics is known to forbid charged, spinless particles from entering an infinitely thin tube of magnetic flux, though particles which do possess spin may even be bound inside. For spin 1/2 the particles may be ‘‘quasibound,’’ so that some penetration from outside to inside is allowed. We use freshman physics and plane geometry to explore such charge-flux systems in classical electrodynamics, finding remarkable similarities to the quantum case, along with characteristic differences. Both aspects illuminate the relationship between classical and quantum physics.
High-altitude free fall
Authors: Mohazzabi Pirooz , Shea James H.
Published: March 2005

The problem of an object falling from high altitudes where the variation of atmospheric pressure cannot be neglected is investigated. The equation of motion for the variation of the velocity of the object as a function of altitude is solved exactly. The results show that, unlike an object falling in a uniform atmosphere whose speed monotonically increases and approaches the terminal speed, the speed of a high-altitude falling object first increases, goes through a maximum, and then decreases and approaches the terminal speed from above. The results also show that if the initial altitude of the object is greater than a critical value, the object always strikes the ground with a speed that is higher than its terminal speed by a finite value, in contrast to the case of a freely falling object in a uniform atmosphere.
The multivariate Langevin and Fokker–Planck equations
Authors: Gillespie Daniel T.
Published: March 2005

A novel derivation of the Langevin equation that was recently presented in this journal for a univariate continuous Markov process is generalized here to the more widely applicable multivariate case. The companion multivariate forward and backward Fokker–Planck equations are also derived. The derivations require just a few modest assumptions, and are driven by a self-consistency condition and some established theorems of random variable theory and ordinary calculus. The constructive nature of the derivations shows why a multivariate continuous Markov process must evolve according to equations of the canonical Langevin and Fokker–Planck forms, and also sheds new light on some uniqueness issues. The need for self-consistency in the time-evolution equations of both Markovian and non-Markovian stochastic processes is emphasized, and it is pointed out that for a great many non-Markovian processes self-consistency can be ensured most easily through the multivariate Markov theory.
Simple demonstrations for introducing spatial coherence
Authors: Basano Lorenzo , Pontiggia Carlo , Piano Emanuele
Published: March 2005

When two quasiparallel identical beams, originating from the same laser, are superposed, the crossing volume becomes the seat of a system of interference fringes. The spatial coherence of the radiation filling this region may be evaluated by observing the interference pattern generated on a far screen. When the beams originate from two identical but different lasers, the fringe system in the crossing region will be washed out by mutual phase fluctuations: the radiation field, however, retains its ability to produce an interference pattern when it goes through a double slit. This remark may be the starting point for a simpler and intuitive approach to the van Cittert–Zernike theorem. Simple laboratory experiments are described which illustrate these results.
The impact of video motion analysis on kinematics graph interpretation skills
Authors: Beichner Robert J.
Published: March 2005

Video motion analysis software was used by introductory physics students in a variety of instructional settings. 368 high school and college students took part in a study where the effect of graduated variations in the use of a video analysis tool was examined. Post-instruction assessment of student ability to interpret kinematics graphs indicates that groups using the tool generally performed better than students taught via traditional instruction. The data further establishes that the greater the integration of video analysis into the kinematics curriculum, the larger the educational impact. An additional comparison showed that graph interpretation skills were significantly better when a few traditional labs were simply replaced with video analysis experiments. Hands-on involvement appeared to play a critical role. Limiting student experience with the video analysis technique to a single teacher-led demonstration resulted in no improvement in performance relative to traditional instruction. Offering more extensive demonstrations and carrying them out over an extended period of time proved somewhat effective. The greatest impact came from a combination of demonstrations with hands-on labs. The curricular modifications employed in the different classrooms and the methods used to evaluate them are discussed.
Using qualitative problem-solving strategies to highlight the role of conceptual knowledge in solving problems
Authors: Leonard William J. , Dufresne Robert J. , Mestre Jose P.
Published: March 2005

We report on the use of qualitative problem-solving strategies in teaching an introductory, calculus-based physics course as a means of highlighting the role played by conceptual knowledge in solving problems. We found that presenting strategies during lectures and in homework solutions provides an excellent opportunity to model for students the type of concept-based, qualitative reasoning that is valued in our profession, and that student-generated strategies serve a diagnostic function by providing instructors with insights on students’ conceptual understanding and reasoning. Finally, we found strategies to be effective pedagogical tools for helping students both to identify principles that could be applied to solve specific problems, as well as to recall the major principles covered in the course months after it was over.
The uncertainty principle for energy and time
Authors: Hilgevoord Jan
Published: March 2005

It is generally thought desirable that quantum theory entail an uncertainty relation for time and energy similar to the one for position and momentum. Nevertheless, the existence of such a relation has still remained problematic. Here, it is shown that the problem is due to a confusion between the position coordinates of a point particle (a material system) and the coordinates of a point in space: The time coordinate should be put on a par with the space coordinates, not with the canonical position coordinates of a material system. Whereas quantum mechanics incorporates a Heisenberg uncertainty relation between the canonical position coordinates and their conjugate momenta, there is no reason why a Heisenberg relation should hold between the space coordinates and the canonical momenta, or between the time coordinate and the energy of the system. However, uncertainty relations of a different kind exist between the space coordinates and the total momentum of the system and between the time coordinate and the total energy. These relations are completely similar and may be taken together to form a relativistically covariant set of uncertainty relations. The relation between the time coordinate and the energy implies the well-known relation between the lifetime of a state and its energy spread.
A simple model for Faraday waves
Authors: Bechhoefer John , Johnson Brad
Published: March 2005

We show that the linear-stability analysis of the birth of Faraday waves on the surface of a fluid is simplified considerably when the fluid container is driven by a triangle wave form rather than by a sine wave. The calculation is simple enough to use in an undergraduate course on fluid dynamics or nonlinear dynamics. It is also an attractive starting point for a nonlinear analysis.
A geometric-algebra treatment of the Feynman–Vernon–Hellwarth space in the two-state problem
Authors: Kennedy Stephen , Gamache Robert
Published: March 2005

Pauli algebra is reviewed and then related to Dirac’s braket algebra and a generalization of the Wigner–Jordan operators in the two-state problem. A method similar to the Feynman–Vernon–Hellwarth (FVH) method is developed from the Pauli algebra density operator. This yields a true geometric algebra treatment of the FVH space. The equation of motion for the density operator is developed from the Schrödinger equation. A general solution in laboratory coordinates is given. Ensemble effects are discussed.
A simple model for nonequilibrium fluctuations in a fluid
Authors: Baras Florence , Malek Mansour M. , Garcia Alejandro L.
Published: March 2005

In equilibrium systems, thermal fluctuations are correlated in time (fluctuation–dissipation theorem) yet their instantaneous values are uncorrelated in space over macroscopic distances. Out of equilibrium, long range spatial correlations are predicted by theory and have been observed in both laboratory experiments and computer simulations. In this paper, we present a simple model, called the train model, that illustrates this phenomenon. The theoretical analysis of the model and its connection with fluctuating hydrodynamics are outlined.
Exposing ‘‘hidden momentum’’
Authors: Comay E.
Published: March 2005

It is shown that ‘‘hidden momentum’’ is a real physical entity found in a continuous matter under pressure when observed from an improper inertial frame. Precisely the same results are obtained from an analysis of the mechanical motion of microscopic particles that create pressure. Analogous properties hold in a pressure created by standing electromagnetic waves enclosed between two parallel mirrors. The significance of the energy-momentum tensor and its divergence is pointed out. It is also shown that in certain cases there exists an ensemble of particles where the sum of the energy–momentum 4-vectors of its constituents does not transform as a 4-vector. Using these results, it is shown that a stationary classical system made of a magnet and electric charges has null linear momentum.
An elementary construction of the color wave functions in the quark model
Authors: von Brentano Peter , Frank Winfried
Published: March 2005

The color wave functions of the quark model for colorless multiquark configurations (color singlets) are constructed by an elementary method without an explicit use of group theory. It is shown that no normalizable color singlet wave functions exists for free quarks, free diquarks and free diquark–antiquarks. The color wave functions of the mesons and the baryons are derived.
Resource Letter TNA-1: Trapping of neutral atoms
Authors: Newbury N. R. , Wieman Carl E.
Published: March 2005

This Resource Letter provides a guide to the literature on trapping of neutral atoms.
Rayleigh–Gans scattering from polydisperse colloidal suspensions
Authors: Hobbie Erik K. , Sung Lipiin
Published: March 2005

The scattering of polarized light from a collection of dielectric spheres with model disorder in the particle dimensions is derived in the first Born approximation. The paper is intended as a brief pedagogical review of some of the essential physics behind static light scattering from complex fluids, and attempts to elucidate the natural emergence of the statistical-structure and form factors while emphasizing the role of polydispersity in the particle size. The criterion for the convergence of the Born series is examined. The problem is cast in the language of Fourier transforms and correlation functions at a level that should be accessible to advanced undergraduates.
Understanding the stability of stars by means of thought experiments with a model star
Authors: Herrmann F. , Hauptmann H.
Published: March 2005

The stability of the nuclear fusion reaction in a star is due to the negative specific heat of the system. Examining the literature one gets the impression that this phenomenon results from a complicated interplay of the various pertinent field variables. We introduce a simple model system, which displays the same behavior as a star and which can be treated quantitatively without solving any differential equation.
One-dimensional lattice dynamics with periodic boundary conditions: An analog demonstration
Authors: Eggert Jon H.
Published: March 2005

A mechanical analog for a one-dimensional harmonic lattice with periodic boundary conditions is presented. The system is appropriate for use as a lecture demonstration to illustrate the lattice dynamical concepts of normal modes, wave numbers, dispersion relations, band gaps, and localized impurity modes. The normal modes are dramatic, clearly observable, and qualitatively and quantitatively accurate.