bluuebunny/crossref_metadata_2025 huggingface dataset:
Klopsteg Memorial Lecture (August, 1992): What science knows about violins—and what it does not know
Authors: Weinreich Gabriel
Published: September 2005

This is the edited text of the Klopsteg Lecture delivered to the Summer Meeting of the AAPT on August 13, 1992. It sketches the current state of knowledge about the violin—at least as seen by the author—in two parts, Physics of the Bowed String and The Violin as a Radiator of Sound, punctuated by a number of ‘‘meditations’’ about the nature of scientific knowledge.
Fluctuation and dissipation in Brownian motion
Authors: Gillespie Daniel T.
Published: September 2005

An analysis of Brownian motion based upon a ‘‘Langevin equation’’ form of Newton’s second law provides a physically motivated introduction to the theory of continuous Markov processes, which in turn illuminates the subtle mathematical underpinnings of the Langevin equation. But the Langevin approach to Brownian motion requires one to assume that the collisional forces of the bath molecules on the Brownian particle artfully resolve themselves into a ‘‘dissipative drag’’ component and a ‘‘zero-mean fluctuating’’ component. A physically more plausible approach is provided by a simple discrete-state jump Markov process that models in a highly idealized way the immediate effects of individual molecular collisions on the velocity of the Brownian particle. The predictions of this jump Markov process model in the continuum limit are found to precisely duplicate the predictions of the Langevin equation, thereby validating the critical two-force assumption of the Langevin approach.
The electrostatics and magnetostatics of a conducting disk
Authors: Friedberg R.
Published: September 2005

A method due to Copson for treating the electrostatics of a disk is modified so that each step can be understood physically. Using this method we easily find the capacitance 2a/π and the electric polarizability 4a3/3π of a conducting disk. We also find in closed form the Green’s function along the axis and the self-force (the force due to induced charges) on a point charge on the axis. We similarly treat magnetic problems, finding the normal polarizability of a superconducting disk and the ‘‘levitating’’ force on a point monopole or vertical point dipole on the axis. All results are in closed form.
Effective mass of a classical linear chain
Authors: Martínez E. N.
Published: September 2005

After a short introduction to response functions, the force-acceleration response function is calculated for a forced classical semi-infinite linear chain. This response function, which can be called a frequency-dependent inverse effective mass, allows a thorough and graphical discussion of motions and energy transport in the chain. The nature of extended motions for forcing frequencies within the band and of localized surface modes for high frequencies is clearly shown by this treatment.
Photoemission energy distribution measurements in a simple metal: A modern physics undergraduate laboratory
Authors: Zangara Rosalia , Lanzara Elisa
Published: September 2005

Measurement of energy distribution curves (EDCs) is one of the more powerful techniques for investigating the electronic band structure of solids. It would be profitable for undergraduate students to perform an experiment introducing them to this aspect of modern spectroscopy. In this paper we describe an arrangement we use in our course of modern physics for engineering students utilizing a commercial photocell. After a theoretical background on the photoemission process in metal, we present measurements on the EDCs obtained by graphical differentiation of the I–V characteristics of the photocell and by using an ac method where the differentiation is performed electronically.
Carnot-like processes in finite time. II. Applications to model cycles
Authors: Pathria Raj K. , Nulton James D. , Salamon Peter
Published: September 2005

Physical implications of the thermodynamic inequality derived in the preceding paper are examined in the context of Carnot-like cyclic processes. In terms of the power P and the degradation D associated with such a process, a geometrical picture is developed which vividly describes a number of important results. Our picture also leads to the concept of time efficiency as a natural complement to the concept of power efficiency. Extensions to Carnot-like refrigerators and heat pumps are carried out. Finally, the influence of a heat leak between the two reservoirs is analyzed.
Correlation in the Langevin theory of Brownian motion
Authors: Li X. L. , Ford G. W. , O’Connell R. F.
Published: September 2005

In a paper with the same title as the above, Manoliu and Kittel calculated the high temperature ensemble average of the nonequal time product of the displacement and random force in the classical Brownian motion problem. Here, using a generalized quantum Langevin equation (GLE), we generalize these considerations to the quantum case and to the case of an arbitrary heat bath (such as, e.g., the blackbody radiation heat bath). Also, we consider an arbitrary temperature and we generalize beyond Brownian motion to the case of a harmonically bound particle in a heat bath. In addition, we point out that correlations of the type considered are widely used in many applications in a variety of different areas of physics and we review some recent applications of the GLE.
Adiabatic invariance derived from the Rund–Trautman identity and Noether’s theorem
Authors: Neuenschwander Dwight E. , Starkey Shawna R.
Published: September 2005

The generators of the infinitesimal transformations that lead to adiabatic invariance are derived from the Rund–Trautman identity by solving the Killing equations for a fairly generic class of models. Noether’s theorem then yields the conserved quantity, which for periodic motion with period T is 〈H〉T, where 〈H〉 is the time average of the Hamiltonian over one cycle. Further it is shown that if 〈H〉T is adiabatically invariant then so is the action ∮pdq, as the two differ by an invariant constant. Our approach (1) requires essentially no new concepts beyond those of a junior-level mechanics course, (2) shows how adiabatic invariance fits into the larger picture of the general connection between invariances and conservation laws, and (3) not only confirms and generalizes the results of Boltzmann, Clausius, and Ehrenfest for what is adiabatically invariant, but also predicts the rescaling transformations that lead to this type of invariance.
Laser Doppler velocimetry using a bulk optic Michelson interferometer: A student laboratory experiment
Authors: Belansky Richard H. , Wanser Keith H.
Published: September 2005

The Doppler frequency of reflected light from a moving mirror is measured using a Michelson interferometer and a low cost spectrum analyzer. The experimental data for the Doppler frequency are in agreement with the calculated theoretical values with a standard percent error of 0.54%. The concept of optical mixing of a phase-modulated signal with the Doppler signal is presented, with a derivation of the resulting detected signal power, using the small phase modulation amplitude approximation. An experiment is described using laser Doppler velocimetry to heterodyne the Doppler signal with an acoustic wave. The experiment provides a good illustration of the Doppler effect, spectral analysis, and principles of optical mixing and interferometry in an advanced undergraduate laboratory.
The natural structure of physics
Authors: Kriss Victor
Published: September 2005

There has been a current feeling of dissatisfaction in the physics community concerning the content and direction of introductory physics courses. The presented position is that this unease does not originate from the lack of exotic, new physics in introductory courses, but rather from the outdated philosophical picture that these courses paint. Research in the area of fundamental interactions has revealed a natural structure that seems to cover all of physics. This structure is centered on a dynamics nested in the space-time of relativity. The four fundamental interactions originate from internal symmetries embedded in these dynamics. This is the paradigm that should be the template of present physics courses.
The noncalculus expansion of gases experiment: U=?
NkT
Authors: Millet L. Edward
Published: September 2005

A noncalculus laboratory experiment using kinetic theory measures the expected difference in the internal energy behavior of gases of various atomic structures. The cost of equipment per lab station is less than $100.
On determining the phase difference introduced by a phase plate producing elliptically polarized light
Authors: Trester Seymour
Published: September 2005

An experiment is presented in which elliptically polarized light, produced by a mica phase plate, is analyzed to determine the phase angle difference δ introduced by the plate, as a function of λ, the wavelength of the light. This functional dependence of δ on λ is then compared to the one calculated using the indices of refraction for a mica phase plate.
The hydraulic jump (‘‘shocks’’ and viscous flow in the kitchen sink)
Authors: Godwin Robert P.
Published: September 2005

The radial location and flow discontinuity of the hydraulic jump in a sink are discussed. The importance of viscosity in determining the location of the jump is emphasized. A model, which highlights the importance of viscous flow near the sink surface, allows us to predict the jump radius and the flow depth on the upstream and downstream sides of the jump as functions of viscosity, gravity, and flow velocity. In our approximate treatment, the jump location is independent of gravity and inversely proportional to the cube root of the viscosity.
Critical current density of YBa2Cu3O7−x
Authors: Oldenburg K. E. , Morrison W. A. , Brown G. C.
Published: September 2005

An experiment to determine the critical current density of superconducting YBa2Cu3O7−x is described. The experiment has been used in a solid state physics course and would also be suitable for modern physics or advanced laboratory courses as well as for courses in physical or inorganic chemistry.
The envelopes of some families of fixed-energy trajectories
Authors: French A. P.
Published: September 2005

A standard technique is used to calculate analytic forms for the envelopes of trajectories for the following motions, given that all the trajectories of a particular family have the same energy and satisfy certain other conditions (e.g., all starting from the same point): parabolic motion under gravity; elliptic orbits in a harmonic-oscillator potential; elliptic orbits under an inverse-square force; and hyperbolic trajectories under an inverse-square force.
Photon spin and the paraxial wave equation
Authors: Haus H. A. , Pan J. L.
Published: September 2005

The spin of a circularly polarized wave in vacuo is clarified if one acknowledges the finite transverse extent of the wave. This is done self-consistently in the paraxial wave approximation.
The Schwarzschild black hole as a gravitational mirror
Authors: Stuckey W. M.
Published: September 2005

The gravitational field outside of a nonrotating black hole is described using the Schwarzschild metric. The geodesic equations of the Schwarzschild metric are derived and those describing null and circular timelike orbits are discussed. Some numerical solutions of the null geodesic equations are shown. These depict photon trajectories which circle the black hole one or two times and then terminate at their emission points. Thus a sequence of ring-shaped mirror images is produced. An equation which gives the angle between the photon’s trajectory and the radial direction at the emitter is derived and applied to the numerical solutions. These results serve to illustrate how an observer ‘‘passes through’’ his or her mirror image at r=3 MG/c2, as he or she moves toward a Schwarzschild black hole.
Relativistic equipartition via a massive damped sliding partition
Authors: Crawford Frank S.
Published: September 2005

A cylinder partitioned by a massive sliding slab undergoing nonrelativistic damped one-dimensional (1D) motion under bombardment from the left (i=1) and right (i=2) by particles having rest mass mi, speed vi, relativistic momentum (magnitude) pi, and (let c≡1) total energy Ei=(pi2+mi2)1/2 is considered herein. The damped slab of mass M transforms the system from its initial pi distributions (i=1,2) to a state, first, of pressure (P) equilibrium with P1=P2, but temperature T1≠T2, then, to P-T equilibrium with P1=P2 and T1=T2, given by the (1D) ‘‘first moment’’ equipartition relation (κ is Boltzmann’s constant), <q1≳=<q2≳≡κT [Eq. (A1)], where qi≡pi vi=Eivi2=pi2/Ei. In achieving first-moment equilibrium at a given κT the slab M can be taken sufficiently large, hence slab oscillation period τ sufficiently long (τ≫tmax where tmax=2Li/vmin is the round trip period of the slowest particle) to give ‘‘mechanical adiabatic invariance’’ (MAI), hence conservation of mechanical ‘‘action’’ piLi of each particle. This first-moment equilibrium is not yet ‘‘thermal’’ equilibrium, since the MAI process leaves the higher moments <qi2≳, <qi3≳, etc., with their original values, relative to <qi≳.

To achieve thermal equilibrium the slab damping is turned off and slab mass M is reduced, hence τ decreases, until τ≪tmax, whereupon MAI becomes ‘‘broken’’ and we achieve complete thermal equilibrium, given by Eq. (A1) plus the appropriate higher moments. Using straightforward extension of the relativistic technique used by Menon and Agrawal to find the first-moment relation (A1) we find that all of the moments of q1 satisfy the recursion relation <qin≳= nκT<qin−1≳ +(n−1)mi2κT<qin−1/Ei2≳, i=1 or 2, n=1, 2, 3, 4,... [Eq. (A2)].
A one-dimensional statistical mechanics model with exact transfer integral solution
Authors: Wysin G. M.
Published: September 2005

A simple one-dimensional model with scalar variables −1≤sn≤+1, coupled according to a Hamiltonian, H=−J∑n‖sn−sn+1‖, is presented. This Ising-like model is an interesting example of a graduate-level statistical mechanics problem where the eigenfunctions and eigenvalues of an integral operator, the transfer integral, can be determined exactly. This can be contrasted with the determination of eigenfunctions and eigenvalues of differential operators, such as the quantum mechanical finite-depth square well. In this problem transcendental equations leading to the eigenvalues and eigenfunctions are also obtained. The largest eigenvalue is identified and the free energy is determined. The thermodynamic properties depend on the sign of J, unlike classical Ising or Heisenberg models.
Diffraction of a Gaussian beam by a spherical obstacle
Authors: Lock James A. , Hovenac Edward A.
Published: September 2005

The Kirchhoff integral for diffraction in the near-forward direction is derived from the exact solution of the electromagnetic boundary value problem of a focused Gaussian laser beam incident on a spherical particle. The diffracted intensity in the vicinity of the particle is computed and the way in which the features of the diffraction pattern depend on the width of the Gaussian beam is commented on.
Displaying the role of repulsive and attractive intermolecular forces in fluids
Authors: Mulero A. , Cuadros F. , Pérez-Ayala M.
Published: September 2005

It is shown how computer-simulation-generated data can be used to give a qualitative understanding of the influence of repulsive and attractive forces on the microscopic and macroscopic behavior of fluids via graphical display of the radial distribution function and a video illustrating molecular structure and motion. Calculated values of pressure and potential energy are taken as macroscopic references. It is also shown qualitatively how these different descriptions are interrelated, a fundamental objective of statistical mechanics.
Chain sliding off a table
Authors: Vrbik Jan
Published: September 2005

This paper presents a detailed analysis and a numerical solution of the familiar, yet often mistreated problem, of a chain sliding off a frictionless table top under its own weight.
The random walk as an eigenvalue problem
Authors: Franceschetti D. R. , Hunke E. C. , Zhang X. , Haddock J. R.
Published: September 2005

The random walk in one dimension can be effectively used to introduce or reinforce a number of advanced mathematical and physical concepts. Here the behavior of an ensemble of particles executing random walks is discussed as an eigenvalue problem, and as a system for which entropy can be calculated in a nonequilibrium state.
Three-dimensional tunneling in quantum ballistic motion
Authors: Bracher C. , Becker W. , Gurvitz S. A. , Kleber M. , Marinov M. S.
Published: September 2005

We provide an elementary case study of field-induced quantum tunneling in a realistic three-dimensional environment which exhibits both tunneling and classically allowed motion. An analytic description is presented for ballistic motion in a uniform electric field. From there we derive simple expressions concerning the wave function for field emission from an ultrathin quantum well in the tunneling limit. At the same time a wave-packet description of the tunneling process is obtained. The tunneling time can be read off from the lateral spread of the tunneling current distribution.
Causality and negative group delays in a simple bandpass amplifier
Authors: Mitchell Morgan W. , Chiao Raymond Y.
Published: September 2005

We demonstrate a bandpass amplifier which can be constructed from common electronic components and has the surprising property that the group delay is negative in most spectral regions. A pulse propagating through a chain of such amplifiers is advanced by several milliseconds: the output waveform precedes the input waveform. Although striking, this behavior is not in conflict with causality, as demonstrated by experiments with pulses which start or end abruptly.
Applying relativistic electrodynamics to a rotating material medium
Authors: Ridgely Charles T.
Published: September 2005

We apply relativistic electrodynamics to a rotating linear medium. Covariant field equations are used to derive general field equations in a rotating coordinate system. We argue that the relation between fields in the presence of matter and those in a vacuum is necessarily dependent upon the coordinate system used. Constitutive equations are then derived in the rotating and laboratory reference frames. We find that our constitutive equations in the laboratory frame agree with Minkowski’s constitutive equations, derived on the basis of special relativity in 1908. Thus we conclude that special relativity can be used in the analysis of experiments involving rotational motion. To exemplify the use of special relativity, we derive an experimentally observed result of a 1913 experiment performed by Wilson and Wilson in which a polarizable, permeable cylinder was rotated in a uniform, axially directed magnetic field.
Nonpropagating string excitations
Authors: Berry Michael , Foley John T. , Gbur Greg , Wolf Emil
Published: September 2005

It is shown that certain force distributions applied to a finite portion of an infinitely long string do not produce any excitation outside the region of the applied force. The existence of such nonpropagating excitations is demonstrated by a simple example, and two general theorems concerning their nature are proven. Some analogies between nonpropagating string excitations and fields produced by nonradiating sources are noted.
Monte Carlo estimations of e
Authors: Mohazzabi Pirooz
Published: September 2005

Three physical processes and the corresponding Monte Carlo algorithms are outlined, in which the number e, the base of the natural logarithm, can be obtained. The value of e is estimated in each case, and the three algorithms are compared.
Crater formation in the laboratory: An introductory experiment in error analysis
Authors: Amato Joseph C. , Williams Roger E.
Published: September 2005

One of the primary objectives of the introductory physics laboratory is to teach error analysis. We describe a very simple and inexpensive experiment which exposes students to the central ideas of estimation and uncertainty, and to the evaluation of theory by graphical display of data. The task is to measure the diameter of a crater formed by dropping a small steel ball into a sand-filled container, and then to deduce the functional dependence of the crater diameter on the kinetic energy of the falling ball.
Determining the ratio of charge to mass e/m for electrons by magnetic focusing
Authors: Yang Yong-Kang
Published: September 2005

This paper describes an instrument based on Busch’s method of determining e/m for electrons. A square-wave deflection voltage is used for deflecting an electron beam. With this instrument, one can more easily and more accurately determine e/m for the electron. A comparison is made experimentally and theoretically among several ways of deflecting an electron beam.
Physics in the laundromat
Authors: McDonald Kirk T.
Published: September 2005

The spin cycle of a washing machine involves motion that is stabilized by the Coriolis force, similar to the case of the motion of shafts of large turbines. This system is an example of a stable inverted pendulum.
Short-range repulsion and symmetry of two-body wave functions
Authors: Yang Jun , Zelevinsky Vladimir
Published: September 2005

We calculate the stationary wave functions for two identical particles moving in a common one-dimensional potential well and interacting through a repulsive delta-potential. We show how a symmetric noninteracting state ψm,n(+), where the particles occupy the single-particle orbitals m and n, evolves as a function of the interaction strength. In the limit of very strong repulsion, the energy levels coincide with those for the adjacent antisymmetric states ψm,n+1(−). The spatial probability distributions also coincide, revealing an apparent change of statistics. However, the relative momentum wave functions are different demonstrating memory of original statistics.
Toward an understanding of the spin-statistics theorem
Authors: Duck Ian , Sudarshan E. C. G.
Published: September 2005

We respond to a recent request from Neuenschwander for an elementary proof of the Spin-Statistics Theorem. First, we present a pedagogical discussion of the results for the spin-0 Klein–Gordon field quantized according to Bose–Einstein statistics; and for the spin-12 Dirac field quantized according to Fermi–Dirac statistics and the Pauli Exclusion Principle. This discussion is intended to make our paper accessible to students familiar with the matrix solution of the quantum harmonic oscillator. Next, we discuss a number of candidate intuitive proofs and conclude that none of them pass muster. The reasons for their shortcomings are fully discussed. Then we discuss an argument, originally suggested by Sudarshan, which proves the theorem with a minimal set of requirements. Although we use Lorentz invariance in a specific and limited part of the argument, we do not need the full complexity of relativistic quantum field theory. Motivated by our particular use of Lorentz invariance, if we are permitted to elevate the conclusion of flavor symmetry (which we explain in the text) to the status of a postulate, one could recast our proof without any explicit relativistic assumptions, and thus make it applicable even in the nonrelativistic context. Such an argument, presented in the text, sheds some light on why it is that the ordinary Schrödinger field, considered strictly in the nonrelativistic context, seems to be quantizable with either statistics. Finally, an argument starting with ordinary-number valued (commuting), and with Grassmann-valued (anticommuting), oscillators shows in a natural way that these must relativistically embed into Klein–Gordon spin-0 and Dirac spin-12 fields, respectively. In this way, the Spin-Statistics Theorem is understood at the expense of admitting the existence of the simplest Grassmann-valued field.
The restitution coefficient: A new interpretation
Authors: Falcone G. , Piperno F.
Published: September 2005

The restitution coefficient, used up to now to describe binary inelastic collisions between macroscopic bodies, is interpreted here as a measure of the limiting value of the recoil angle in binary inelastic collisions at microscopic scale. The description of inelastic collisions in terms of this new quantity enables us to dramatically simplify several basic equations for the kinematics of binary inelastic collisions. As an application, the hard sphere cross section when elastic and inelastic processes are correlated is also shown.
Assessing student learning of Newton’s laws: The Force and Motion Conceptual Evaluation and the Evaluation of Active Learning Laboratory and Lecture Curricula
Authors: Thornton Ronald K. , Sokoloff David R.
Published: September 2005

In this paper, we describe the Force and Motion Conceptual Evaluation, a research-based, multiple-choice assessment of student conceptual understanding of Newton’s Laws of Motion. We discuss a subset of the questions in detail, and give evidence for their validity. As examples of the application of this test, we first present data which examine student learning of dynamics concepts in traditional introductory physics courses. Then we present results in courses where research-based active learning strategies are supported by the use of microcomputer-based (MBL) tools. These include (1) Tools for Scientific Thinking Motion and Force and RealTime Physics Mechanics laboratory curricula, and (2) microcomputer-based Interactive Lecture Demonstrations. In both cases, there is strong evidence, based on the test, of significantly improved conceptual learning.
On approximate formulas for the electrostatic force between two conducting spheres
Authors: Sliško Josip , Brito-Orta Raúl A.
Published: September 2005

A series expression for the electrostatic force between two charged conducting spheres having equal radii and charges is derived using the method of electrical images. This expression is a special case of that for two spheres with arbitrary charges and radii, found by Maxwell using zonal harmonics. Keeping in mind the use of approximate formulas for the interpretation of classroom measurements of the electrostatic force between spheres, we comment on two incorrect approximate formulas and examine the contribution of the first few non-Coulomb terms of the correct formula by comparing with values obtained using a computational approach.
“The Boundaries of Nature: Special and general relativity and quantum mechanics, a second course in physics:” Edwin F. Taylor’s acceptance speech for the 1998 Oersted Medal presented by the American Association of Physics Teachers, 6 January 1998
Authors: Taylor Edwin F.
Published: September 2005

Public hunger for relativity and quantum mechanics is insatiable, and we should use it selectively but shamelessly to attract students, most of whom will not become physics majors, but all of whom can experience “deep physics.” Science, engineering, and mathematics students, indeed anyone comfortable with calculus, can now delve deeply into special and general relativity and quantum mechanics. Big chunks of general relativity require only calculus if one starts with the metric describing spacetime around Earth or black hole. Expressions for energy and angular momentum follow, along with orbit predictions for particles and light. Feynman’s Sum Over Paths quantum theory simply commands the electron: Explore all paths. Students can model this command with the computer, pointing and clicking to tell the electron which paths to explore; wave functions and bound states arise naturally. A second full-year course in physics covering special relativity, general relativity, and quantum mechanics would have wide appeal—and might also lead to significant advancements in upper-level courses for the physics major.
Quantum measurement theory and the Stern–Gerlach experiment
Authors: Hannout M. , Hoyt S. , Kryowonos A. , Widom A.
Published: September 2005

The Stern–Gerlach experiment was one of the early illustrative examples of the Bohr view of quantum mechanics. In the Bohr view, a measurement is an interaction between a quantum object and an apparatus which acts in a classical fashion. There are still open problems with this concept, many of which enter into the discussion of the original Stern–Gerlach measurement.
Circular orbits inside the sphere of death
Authors: McDonald Kirk T.
Published: September 2005

A wheel or sphere rolling without slipping on the inside of a sphere in a uniform gravitational field can have stable circular orbits that lie wholly above the “equator,” while a particle sliding freely cannot.
Resource Letter Sol-1: Solitons
Authors: Degasperis Antonio
Published: September 2005

This Resource Letter provides a guide to the literature on the theory of solitons and its relevance in physics. Journal articles and books are cited for the following topics: the history of solitons, construction of soliton equations and of soliton solutions, solitons and mathematics, quantum solitons, solitons in physics and near-integrable equations.
Density functional theory of one-dimensional two-particle systems
Authors: Neal H. L.
Published: September 2005

We consider the density functional theory from the point of view of one-dimensional two-particle systems, where the particles are either spin-1/2 fermions or spin-0 bosons. The basic equations are derived and applied to the system of two coupled harmonic oscillators. An exact density functional solution is constructed from the exactly known single-particle density for this system. We demonstrate how this solution may be applied to other two-particle systems to calculate the exact single-particle density and energy.
Recession parameters versus cosmic time
Authors: Lement Bernard S.
Published: September 2005

Theoretical relations for such recession parameters as the Earth–galaxy (L) and Earth–photon (Lp) separation distances, Hubble parameter (H), universe density ratio (Ω), scale factor (R), and expansion factor distance (A) are given as functions of cosmic time (t). These relations are based on the standard flat, closed, and open models of the universe with the Einstein cosmological constant Λ=0. Comparisons are made of these models using selected values of Ho and Ωo, which for each model indicate an age of the universe that is consistent with ages reported for the oldest stars.
Casimir force on a loaded string
Authors: Cooke James H.
Published: September 2005

We derive the Casimir force in its simplest setting, a massless string loaded with point masses. The derivation is simple enough for presentation to students immediately after they study this system in mechanics. There is no problem with infinities, since the loaded string has only a finite number of degrees of freedom. After the short derivation, we review a number of questions which may arise in class discussion. In particular, we point out the hazards of a popular heuristic explanation of the Casimir force.
Electrons in a shell
Authors: Budker Dmitry
Published: September 2005

The spatial distribution of electrons inside an empty spherical shell with an impenetrable wall is considered. It is shown that with a large number N of nonrelativistic electrons, the electrons are concentrated near the wall in a layer of thickness δ∼N−1/5a2/5aB3/5, where a is the radius of the shell, and aB is the Bohr radius.
The Mössbauer effect explained
Authors: Vandegrift Guy , Fultz Brent
Published: September 2005

Direct integration of Schrödinger’s equation yields the transition probability for the Mössbauer effect, assuming that the bound nucleus receives a sudden impulse of momentum from a gamma particle. Generalization from two coupled oscillators to a linear chain introduces the discrete Fourier transform, in real variables. This chain of coupled oscillators can be used to suggest how very low order collective modes can remain unexcited by the impact.
A unidirectional photorefractive ring resonator oscillating at 633 nm
Authors: Lin Hong , Weir David W. , Yousuf Adnan , Bergman Sharon
Published: September 2005

We have constructed an optical resonator using a photorefractive crystal as the gain medium. The orientation of the crystal and the angle between the signal and the pump beam are chosen to obtain optimal two-wave coupling. The average output power of the resonator is proportional to the power of the pump beam for a small cavity loss, but this linear relation is broken when the cavity loss is increased. The transverse beam pattern of the signal can be controlled by intracavity apertures.
A course in tools and procedures for Physics I
Authors: Allie Saalih , Buffler Andy
Published: September 2005

A one-semester course covering the tools, skills, and procedures that are required to engage meaningfully with first-year university physics is described. The course forms part of the Science Foundation Programme at the University of Cape Town which was set up to provide access to a science degree for students who have been educationally disadvantaged, part of the legacy of racial discrimination in South Africa. The course comprises three basic elements: a theoretical component, a laboratory-based experimental component, and a communication skills component. The theory component consists of the various mathematical techniques used in a calculus-based Physics I course, grouped into cognate areas so that each technique is presented immediately in the full range of contexts that will be encountered later on. Part of the theory component involves written explanations of the mathematical formalism. The focus of the communication skills component is on report writing which follows as a natural consequence of the laboratory tasks which have been restructured as problems necessitating an experimental investigation. The implementation of cooperative tutorial groups, which forms an integral part of the learning environment, is also discussed.
Thomas scattering: Just kinematics
Authors: Bitensky I. S.
Published: September 2005

Capture of a particle by a fast projectile during a sequence of two binary elastic collisions, called Thomas scattering, is considered using a velocity diagram method. It turns out that this process occurs at an angle depending just on the masses of the particles involved. Therefore, it can be described solely by kinematics. The velocity diagram method gives a very simple way to see relationships between the velocities of the colliding particles and can be used successfully to analyze the kinematics of elastic collisions.
Accidental degeneracy and hidden symmetry: Rectangular wells with commensurate sides
Authors: Lemus R. , Frank A. , Andrés M. V. , Leyvraz F.
Published: September 2005

Two-dimensional quantum square wells and rectangular billiards with commensurate sides are simple systems which exhibit accidental degeneracies. We show that a recent analysis for square wells can be similarly applied to rectangular wells with commensurate sides.
Electric potential in the classical Hall effect: An unusual boundary-value problem
Authors: Moelter Matthew J. , Evans James , Elliott Greg , Jackson Martin
Published: September 2005

The classical Hall effect presents a surprisingly unusual and challenging problem in electrostatics, with boundary conditions that are not of Dirichlet, Neumann, or of mixed Dirichlet and Neumann type. These unusual boundary conditions create several difficulties not normally encountered in standard problems, and ultimately lead to expansion of the electric potential in a nonorthogonal basis set. We derive the boundary conditions for the potential in a rectangular geometry, construct a solution for the potential, and discuss the relation between this problem and problems of the standard mixed type. We also address a commonly encountered misconception about the current distribution.
A classroom jumping ring
Authors: Schneider Carl S. , Ertel John P.
Published: September 2005

We present the design of a compact alternating current jumping ring apparatus which can electromagnetically launch conducting rings across a classroom. Jump energy and height are calculated for core and thin ring length, radius, thickness, and material. The effects of core saturation, permeability, hysteresis and demagnetizing field, ring shielding, and convective derivative are described. Rings with even small phase lag can pass by the magnetic pole of the primary in one-quarter of a cycle. Large ring size relative to skin depth delays the ring current close to the 180 deg of Lenz’s law. Contactless jump height measurement enables ring resistivity determination. Demonstrating the effects of voltage, frequency, conductivity, permeability, and geometry contributes to understanding electromagnetism in the classroom.
Correlation coefficient for incompatible observables of the quantum harmonic oscillator
Authors: Campos Richard A.
Published: September 2005

We explore, using elementary examples of harmonic-oscillator superposition states, the quantum-mechanical measures of covariance and correlation coefficient for two noncommuting observables. A Schrödinger cat state which provides perfect correlation or anticorrelation of the position and momentum operators is presented. We employ quantum and classical phase-space distributions as graphical illustrations of correlation coefficients for the two theories.
Introducing quantum mechanics: One-particle interferences
Authors: Scarani Valerio , Suarez Antoine
Published: September 2005

One-particle quantum interference is presented using probably the simplest setup. This review of experimental facts may be useful as a short self-contained introduction to quantum mechanics, highlighting the dependence of interference on indistinguishability.
Anomalous dispersion of dye solutions observed in a prismatic cuvette
Authors: Erdélyi Miklós , Hilbert Margit , Bor Zsolt
Published: September 2005

An experimental setup is described which uses a prismatic dye cuvette and a dispersion glass prism. The two prisms are oriented so as to ensure wavelength-dependent deflection in two perpendicular planes. The dispersion of the solvent material was subtracted by using an immersion cuvette filled with the solvent liquid of the dye solution. The setup displays the contribution of the dye material to the refractive index of the solution as a function of the wavelength. The setup is simple, inexpensive, does not use toxic or hazardous materials or high temperature ovens, and thus can be a very useful means to demonstrate the effect of anomalous dispersion at different levels of education.
A current sheet model for the Earth’s magnetic field
Authors: Stump Daniel R. , Pollack Gerald L.
Published: September 2005

As an example in magnetostatics we consider the main magnetic field of the Earth and its current sources. The measured field on the surface is accurately given, in tables of the International Geological Reference Field, in terms of Gaussian coefficients. By applying Maxwell’s equations to these data we calculate the extended field, inside the Earth, and give graphical representations of it. We also construct a simple theoretical model of the source of the field, in which the field is the result of currents flowing on the surface of a sphere inside the Earth. The current sources which give the observed field are calculated in terms of vector spherical harmonics. The stream function and currents are displayed on a Mercator projection for a sphere whose radius is half the Earth’s radius. Interesting properties of vector operations on the Mercator plane are analytically and graphically described.
The hydrogen atom as an entangled electron–proton system
Authors: Tommasini Paolo , Timmermans Eddy , de Toledo Piza A. F. R.
Published: September 2005

We illustrate the description of correlated subsystems by studying the simple two-body hydrogen atom. We study the entanglement of the electron and proton coordinates in the exact analytical solution. This entanglement, which we quantify in the framework of the density matrix formalism, describes correlations in the electron–proton motion.
Landau resonance mechanism for plasma and wind-generated water waves
Authors: Vekstein G. E.
Published: September 2005

A profound analogy between the Landau damping of plasma waves and the resonant mechanism of wave generation on a water surface by wind is discussed. A new simple derivation of the former effect is presented which explicitly demonstrates the essential role of the integrals of motion (the vorticity for an inviscid fluid, and the particle distribution function for a collisionless plasma) in these phenomena.
Mutual entrainment of two nonlinear oscillators
Authors: Heath T. , Wiesenfeld K.
Published: September 2005

We present an example of how two nonidentical oscillators can synchronize due to dynamical nonlinear interactions. This highlights a classic distinction with coupled linear oscillators, a difference which is important to the functioning of several systems in physics and biology. We illustrate the phenomenon using an electronic circuit appropriate for an advanced undergraduate physics lab.
Scattering of a Gaussian wave packet by a reflectionless potential
Authors: Kiriushcheva N. , Kuzmin S.
Published: September 2005

The specific features of scattering of the Gaussian wave packet by the simplest of all reflectionless potentials, the Sech-squared well, are considered. The results of numerical computation show that a wave packet that has passed through this potential overtakes a free wave packet and is both higher and narrower than a free wave packet; in other words, the scattered wave packet accelerates inside the well and preserves its shape better. Comparisons with scattering by the square well and by a series of reflectionless potentials are also presented. Possible applications of the Sech-squared as well as other reflectionless potentials are discussed.
Bound and unbound wave functions at short distances
Authors: Fäldt Göran , Wilkin Colin
Published: September 2005

There exists a simple relationship between a quantum-mechanical bound-state wave function and that of nearby scattering states, when the scattering energy is extrapolated to that of the bound state. This relationship is demonstrated numerically for the case of a spherical well potential and analytically for this and other soluble potentials. Provided that the potential is of a finite range and that the binding is weak, the theorem gives a useful approximation for the short-distance behavior of the scattering wave functions. The connection between bound and scattering-state perturbation theory is established in this limit.
Elementary theoretical description of the heavy symmetric top
Authors: Schönhammer K.
Published: September 2005

A simple theoretical description of a symmetric top with one stationary point and subject to the action of the gravitational force is presented without the use of Lagrangian mechanics. Also no use is made of the Euler angles. The fact that the vectors of the angular momentum l, the angular velocity ω, and the symmetry axis ẽ3 are coplanar every instant of time is used to derive a closed set of equations for ẽ3 and l. The frequencies of pure “slow” and “fast” precession are calculated without solving the differential equations and a simple interpretation of the latter is given. Using energy conservation, the well-known differential equation for the angle θ between the symmetry axis and the surface normal is derived. The combination of precession and nutation is discussed for small nutation amplitudes.
An experiment to demonstrate the angular Doppler effect on laser light
Authors: Dholakia K.
Published: September 2005

Two simple and related experiments are outlined that allow the student to investigate the frequency shift experienced by a laser light beam when passing through a rotating half-wave retardation plate. The shift arises due to the energy exchange between a rotating optical element, in this case a half-wave plate, and a circularly polarized light beam. The shift is directly proportional to the rotation frequency of the optical element. The shift may be interpreted as an angular Doppler effect for light.
Representation of arbitrary charge–current densities by polarization and magnetization fields
Authors: Goedecke G. H.
Published: September 2005

It is shown that any electromagnetic charge–current distribution may be expressed in terms of polarization and magnetization fields, plus a static charge density of one sign if the total charge q is nonzero, and that the standard Maxwell equations reduce, in general, to the conventional form used for material media plus a static Gauss law if q≠0. Examples considered include a capacitor, a point charge and an oscillating point electric dipole in arbitrary motion, and lumpy media composed of oscillating point electric dipoles or other particles.
Brightness at night
Authors: Pesic Peter
Published: September 2005

The average brightness of the night sky can be used to determine a general relation between the number density of stars and their average lifetime. Plausible values for stellar lifetimes then imply that a single-galaxy cosmology is inadequate, even without observations of external galaxies. This is the positive content of the old riddle of why the sky is dark at night. Although Kelvin gave the correct resolution to this riddle he did not realize that it requires a far larger universe than he had assumed.
Physics of the Theremin
Authors: Skeldon Kenneth D. , Reid Lindsay M. , McInally Viviene , Dougan Brendan , Fulton Craig
Published: September 2005

We discuss some of the interesting physics behind the design and operation of the Theremin electronic musical instrument. To complement the theory we present details of a parallel effort to construct two versions of this remarkable instrument. One of these designs remains fairly faithful to the traditional beat frequency oscillator approach that first inspired Theremin’s invention, while the other contains more modern electronics that helps make more reliable the setting up and use of the instrument. The emphasis on the physical principles continues into a comparison of the two instruments. Following completion, the Theremins have been extensively used in public and schools science exhibitions and in lecture demonstrations.
Quantum computing
Authors: Scarani Valerio
Published: September 2005

The main features of quantum computing are described in the framework of spin resonance methods. Stress is put on the fact that quantum computing is itself nothing but a reinterpretation (fruitful indeed) of well-known concepts. The role of the two basic operations, one-spin rotation and controlled-NOT gates, is analyzed, and some exercises are proposed.
Mechanical force in laser cooling and trapping
Authors: Shimizu Yukiko , Sasada Hiroyuki
Published: September 2005

Laser cooling and trapping are based on the mechanical force an electromagnetic wave (EMW) exerts upon an atom. The force is generally explained as the result of the conservation law of the linear momentum of a photon and the atom. In contrast, we have directly derived the force from primary electromagnetism in order to clarify its origin. We regarded the atom as an electric dipole moment induced by the EMW, and examined the interaction between the dipole moment and the EMW. We applied a semiclassical theory in which the atom is quantized as a two-level system but the electromagnetic field is not; no photon is introduced. The results are consistent with the commonly accepted explanation, and explicitly demonstrate the contribution of the electric and magnetic fields to the force, in particular, the significance of the longitudinal magnetic field for the dipole force in laser trapping.
Probability and quantum mechanics
Authors: Velleman Daniel J.
Published: September 2005

We discuss the use of probability theory in quantum mechanics, and suggest that there are some interpretations of quantum mechanics in which probabilities may be used inappropriately.