bluuebunny/crossref_metadata_2025 huggingface dataset:
Many oscillations of a rigid rod
Authors: Cromer Alan
Published: March 2005

The many oscillations of a rigid rod—pendular, bifilar, torsional, coupled, nonlinear (including pure x3), and chaotic—provide interesting opportunities for experimental and theoretical investigations in introductory, intermediate, and advanced mechanics courses. Because of the rod’s simple geometry, precise expressions for the periods of its oscillations can be calculated, allowing comparisons between theory and experiment to within 0.5%. At this level of precision, the finite diameter of the pin upon which the rod oscillates has an observable effect on the period. A derivation is given of this effect, and applied to a ring oscillating on rods of various diameters. The large-angle oscillations of the bifilar pendulum are shown to depart by a measurable amount from the large-angle oscillations of the physical pendulum. The unequal-arm bifilar pendulum couples torsional and pendular modes in a calculable way. The vertical bifilar pendulum is a double pendulum with calculable coupled oscillations for small amplitudes and chaotic oscillations for large amplitudes. Other oscillators that can be built from a rigid rod, including an x3 oscillator, are described.
Women in astronomy: Inclusion in introductory textbooks
Authors: Larsen Kristine M.
Published: March 2005

The reasons for identifying the contributions of women astronomers in introductory textbooks are discussed. The rates of inclusion of ten women astronomers are studied and analyzed. The evolution of inclusion over the past four decades is explored.
Parametric instability of a pendulum
Authors: Curzon F. L. , Loke A. L. H. , Lefrançois M. E. , Novik K. E.
Published: March 2005

The pendulum, which can rotate in a vertical plane about a horizontal axis, consists of a tube with a pneumatically propelled internal slider which is driven periodically from one end of the tube to the other without changing the pendulum’s angular momentum. The resultant parametric oscillations can be observed in great detail, in both linear and nonlinear regimes, because of the multisecond time scales which characterize the system. It is shown that, in addition to the expected conditions for instability to occur, there is also an amplitude threshold caused by sliding friction in the pendulum’s bearings.
Reflection of wave packets from a quantum well with a tunneling transmission resonance
Authors: Edgar A.
Published: March 2005

The reflection of wave packets from a quantum well bounded by rectangular potential barriers, and which has a tunneling transmission resonance, is discussed. Numeric solutions to Schrödinger’s time-dependent equation show that the shape of the probability function ψψ* for a reflected wave packet can be quite different from that of the incident packet. Either a symmetric double hump or an asymmetric shape are possible for the reflected ψψ*, depending on the sharpness of the resonance. These shapes are explained analytically in terms of the reflection coefficient.
Statics of a ladder leaning against a rough wall
Authors: Mendelson Kenneth S.
Published: March 2005

A ladder leaning against a wall is an example of a statically indeterminate structure for which the equations of equilibrium are insufficient to determine the reaction forces. In such problems the reaction forces also depend on the elasticity of the system and the way in which the system was set up. Introductory physics texts usually make the ladder problem tractable by assuming that the wall is frictionless. This paper argues that the correct condition is that the frictional force at the top of the ladder is equal to the coefficient of static friction times the normal force, i.e., the maximum possible static friction at the wall. The stability of the ladder against falling depends on the frictional force at the bottom of the ladder which would normally be less than its maximum possible value independently of conditions at the top of the ladder.
Fractal dimension of the strange attractor of the bouncing ball circuit
Authors: Clark B. K. , Martin R. F. , Moore R. J. , Jesse K. E.
Published: March 2005

We address the problem of distinguishing regular, chaotic, and random behavior using an electronic circuit modeling of a ball bouncing on an oscillating table. We calculate the correlation dimension of the system from time series data taken from the circuit, and show that this system seems amenable to correlation dimension analysis. In particular we find dimensions of 1.07 for regular data and 1.7 for chaotic data, while random data give no finite dimension. We conclude that the system apparently has a chaotic attractor of low dimension. The experiment and data analysis make a useful module to introduce advanced undergraduate students to nonlinear systems.
A three-particle problem in one dimension
Authors: Martinez J. C.
Published: March 2005

The problem of three particles of identical mass interacting with each other via a delta-function potential is studied within a simple framework inspired by the 2-particle system. We discuss the S matrix and the possibility of bound states arising for both bosons and fermions.
The new morning of the world
Authors: Rhodes Richard
Published: March 2005

A lecture delivered at the annual conference of the American Association of Physics Teachers, Spokane, Washington, 9 August 1995.
Potential distribution in the van der Pauw technique
Authors: de Vries D. K. , Wieck A. D.
Published: March 2005

The van der Pauw technique for resistivity and Hall measurements is illustrated on large-scale models of conductive polyethylene, which can be used to visualize the potential distribution in arbitrarily shaped two-dimensional samples. The equipotential lines in a square sample and the dependence of measured voltages on the aspect ratio of these samples are studied. We give examples of the use of conformal mapping in two-dimensional conduction.
A new statement of the second law of thermodynamics
Authors: Macdonald Alan
Published: March 2005

A new statement of the second law of thermodynamics is given. The law leads almost effortlessly, for very general closed systems, to a definition of absolute entropy S, a demonstration that ΔS≥0 in adiabatic processes, a definition of temperature, and a demonstration that dS≥δQ/T in quasistatic processes. Entropy is given a clear physical meaning.
Excited-state solutions for an infinite family of one-dimensional potentials
Authors: Reed B. Cameron
Published: March 2005

A method of generating analytically and numerically exact ground and excited-state wave functions and energies of an infinite family of one-dimensional potentials is described. Explicit application to a sixth-order polynomial potential is presented.
Emil Cohn’s electrodynamics of moving bodies
Authors: Darrigol Olivier
Published: March 2005

A now forgotten figure, Emil Cohn was one of the leading experts in electrodynamics at the turn of the century. Unsatisfied with Lorentz’s electron theory, he proposed an alternative electrodynamics of moving bodies based on a modification of Maxwell’s macroscopic field equations that managed to account for all relevant electrodynamic and optical experiments, including that of Michelson and Morley. Some of his insights foreshadow aspects of Einstein’s relativity theory, especially the elimination of the ether and the criticism of Lorentz’s implicit distinction between true and measured coordinates of space and time. However, Cohn did not believe in the general validity of the relativity principle, and did not require a revision of the usual concepts of space and time.
Two student experiments on electrical fluctuations
Authors: Kraftmakher Yaakov
Published: March 2005

Variants of student experiments on electrical fluctuations are described. Thermal noise is measured over a wide temperature range using incandescent lamps. A common resonant circuit serves as the load of a thermionic diode when measuring shot noise. The quality factor of this resonant circuit must be measured while the diode current passes through it. Boltzmann’s constant and the electron charge are evaluated from the data obtained. Finally, a simple circuit is recommended as a rms voltmeter for measuring noise voltages.
Fermi’s golden rule and Bardeen’s tunneling theory
Authors: Reittu H. J.
Published: March 2005

A simple way to derive Bardeen’s tunneling theory is introduced. With a low rate of tunneling of, for example, electrons from one electrode to another through a wide vacuum gap, the appearance of the second electrode can be regarded as a perturbation. Then Bardeen’s formula for tunneling follows exactly from Fermi’s golden rule, supposing that this perturbation appears suddenly at some instant of time. Bardeen’s theory is illustrated by assuming a smoothly variable barrier shape, including the rectangular one as a limiting case. This exactly solvable example clarifies the sensitivity of the tunneling probability to the barrier shape and the energy of the tunneling particle.
Bouncing due to the ‘‘infinite jerk’’ at the end of a circular track
Authors: Theron W. F. D.
Published: March 2005

It is shown that conditions exist such that an elastic wheel rolling down a circular track onto a horizontal pavement will bounce off the pavement due to the sudden change in acceleration referred to as infinite jerk.
When will discrete eigenstates be nondegenerate?
Authors: Chau H. F.
Published: March 2005

By means of supersymmetric quantum mechanics, we provide a new simple proof that discrete eigenstates, i.e., bound states, of any one-dimensional quantum system satisfying the time-independent Schrödinger equation without internal degrees of freedom are nondegenerate. Using the same idea, we show that the ground state of an N-dimensional time-independent Schrödinger equation without internal degrees of freedom is nondegenerate, too. Reasons why degeneracy is possible for excited states when N≳1 are also discussed.
The partial ring pendulum
Authors: Wagner David L. , Walkiewicz Thomas A. , Giltinan David A.
Published: March 2005

The use of a set of partial ring pendula of equal radii as the basis for an interesting laboratory experiment is discussed. Sources of systematic errors are analyzed and theoretical calculations are presented for nonidealized partial rings. These calculations are found to be in good agreement with experimental results within measured uncertainties.
Nonlinear crosstalk in a multichannel fiber-optic communication system
Authors: Shi Hong , Lin Yan , Carney Sean , Zygmunt Aaron , Thompson John R.
Published: March 2005

Nonlinear mixing between the longitudinal modes of multimode laser pulses is used to illustrate the effects of nonlinear crosstalk in multichannel communication systems. The results of the experiments are compared with a simple theoretical model that was described in a recent article. The article concludes with suggestions for experiments in nonlinear fiber optics for undergraduate and masters students.
Dimensionality as a perturbation parameter in the generalized hydrogen atom
Authors: Hagen C. R.
Published: March 2005

A recent suggestion has been made that the hydrogen bound state spectrum should not depend on the number of spatial dimensions. It is pointed out here that the uncertainty principle implies that such differences must exist and that a perturbation expansion in the dimensionality parameter yields a precise quantitative confirmation of the effect.
Pascal’s demonstration experiment: Weighing the atmosphere
Authors: Brown J. B. , Dore J. C. , Isenberg C. , Rogers S. J.
Published: March 2005

A full-scale re-enactment of an historic experiment carried out by Pascal in 1646 to demonstrate the principles of barometric pressure to an outdoor audience can provide a dramatic event today for a university open day or a town festival. The script for such a performance is given together with practical details for its production.
Inexpensive laser cooling and trapping experiment for undergraduate laboratories
Authors: Wieman Carl , Flowers Gwenn , Gilbert Sarah
Published: March 2005

We present detailed instructions for the construction and operation of an inexpensive apparatus for laser cooling and trapping of rubidium atoms. This apparatus allows one to use the light from low power diode lasers to produce a magneto-optical trap in a low pressure vapor cell. We present a design which has reduced the cost to less than $3000 and does not require any machining or glassblowing skills in the construction. It has the additional virtues that the alignment of the trapping laser beams is very easy, and the rubidium pressure is conveniently and rapidly controlled. These features make the trap simple and reliable to operate, and the trapped atoms can be easily seen and studied. With a few milliwatts of laser power we are able to trap 4×107 atoms for 3.5 s in this apparatus. A step-by-step procedure is given for construction of the cell, setup of the optical system, and operation of the trap. A list of parts with prices and vendors is given in the Appendix.
Experiment to demonstrate diffusion doping
Authors: Jones E. D.
Published: March 2005

Single crystals of CdS possess a translucent yellow color but when indium is diffused into the crystal from the vapor in an evacuated silica capsule it becomes opaque. This type of diffusion is linearly dependent on the indium concentration and produces a sharp interface between the diffused and undiffused regions of the crystal. The process of diffusion doping can be demonstrated by studying the variation of the depth of the interface with anneal time and temperature, using an optical microscope. In addition, as CdS possesses a hexagonal crystal structure of the ‘‘wurtzite’’ type, this is a sensitive method for studying diffusion anisotropy along the two principal crystal directions, and the sharpness of the interface can be demonstrated by the dispersion produced by a narrow beam of white light. This article describes how these properties can be incorporated into an undergraduate student experiment, or an open ended project for demonstrating Fick’s laws and the process of diffusion doping.
Time-dependent generalizations of the Biot–Savart and Coulomb laws: A formal derivation
Authors: Heras José A.
Published: March 2005

A formal derivation of Jefimenko’s formulas for the time-dependent generalizations of the Biot–Savart and Coulomb laws is presented. Maxwell’s equations and the free-space retarded Green function for the scalar wave equation are the basic ingredients of this derivation.
Electric polarizability and the solution of an inhomogeneous differential equation
Authors: Maize M. A. , Burkholder Chad A.
Published: March 2005

In this paper, we are going to illustrate the effectiveness of the method of the inhomogeneous differential equation in obtaining the energy shift of a quantum level in second order perturbation theory. The energy shift will be used to calculate the electric polarizability due to the interaction between a static electric field and a charged particle moving under the influence of a one-dimensional delta potential. Both relativistic and nonrelativistic problems will be treated.
Dominant color reversals and chromaticity cusps in interferometric color mixing
Authors: Kiess Thomas E. , Berg Richard E.
Published: March 2005

White light was injected into a Michelson interferometer to obtain color fringes, which show a succession of dominant colors that we have analyzed quantitatively. For a given interferometric path length difference, ΔL, the resulting color fringe was sent to a diffraction grating spectrometer and light-sensitive detector, to record its spectral composition. This data enabled us to depict the color in the two-dimensional color space of the x–y C.I.E. chromaticity diagram. In this analysis, we show the dominant color in the progression of color fringes in interferometric color mixing to reverse the direction with which it sweeps through the visible spectrum, as ΔL is monotonically increased. This phenomenon is represented by spiraling with cusps and reversals of curvature in the C.I.E. x–y plane. Our measurements agree favorably with a theoretical model showing cusp behavior. We show the cusps to signify a transition from in- to out-of-phase behavior in the relative growth of x and y. This result is robust, persisting for many trial spectral power distributions (SPDs) of the incident ‘‘white light’’ illuminant.
Answer to Question ♯30 [‘‘How are positrons moderated?,’’ Thomas D. Rossing, Am. J. Phys. 63(12), 1065 (1995)]
Authors: Weber M. , Lynn K. G.
Published: March 2005

The positrons from β+ decaying sources loss energyat a much faster rate than they annihilate. As the energy of the positrons drops, core excitations, plasmon excitation, electron/hole pair creation, and phonon scattering are the dominant processes of further energy loss.
The Richtmyer Memorial Lecture: Bose–Einstein Condensation in an Ultracold Gas
Authors: Wieman Carl E.
Published: March 2005

The following article is a written version of the Richtmyer award lecture given to the annual meeting of the American Association of Physics Teachers in January 1996. I discuss the basic idea of Bose–Einstein condensation in a gas and how it has been produced and examined. To cool the atoms to the point of condensation we use laser cooling and trapping, followed by magnetic trapping and evaporative cooling. These techniques are explained, along with the signatures of Bose–Einstein condensation that we observe. I also discuss how very similar laser cooling and trapping techniques have been incorporated into undergraduate laboratory experiments.
Feynman’s derivation of the Schrödinger equation
Authors: Derbes David
Published: March 2005

R. P. Feynman’s ‘‘path integral’’ approach to quantum field theory emerged from his discovery that the Schrödinger equation could be derived from an expression of P. A. M. Dirac’s involving the action. Feynman gave the history of his discovery in his Nobel lecture, but withheld most of the details; when he did publish the discovery, he did not provide the framework. This article provides some historical background and puts both of Feynman’s presentations together.
On the electromagnetically damped mechanical harmonic oscillator
Authors: McCarthy Lance
Published: March 2005

The development of a mechanical, damped, forced, harmonic oscillator system with computer data acquisition and analysis was undertaken. The original aim was to make accurate comparisons of experimental data with the standard textbook analyses, especially with regard to the phase difference between the displacement response and the driving force, and to the functional form of the displacement response versus frequency curve. Accurate measurements of the phase and amplitude for the displacement responses for the system developed indicated that for real systems with damping, the conventional analysis needs to be revised. If electromagnetic damping is used, the effective restoring forces must include the electromagnetic forces resulting from the interaction of the ‘‘eddy’’ currents with the damping magnetic field, and this can be considered as increasing the effective spring constant. When viscous damping is used, fluid adhering to the damping system changes the effective oscillating mass. Both of these effects will change the resonant frequency. Experimental data and analysis are presented to confirm the revised theoretical treatment.
Demonstration of the evanescent wave through absorption
Authors: Weigand R. , Guerra J. M.
Published: March 2005

A simple and didactical method is proposed to make evident the presence of the evanescent wave due to total reflection by introduction of an absorption factor in the optically less-dense medium. The method permits taking precise quantitative measurements on the totally reflected beam and calculating the path length travelled by the evanescent wave in the optically less-dense medium.
Scattering from a nonsymmetric potential in one dimension as a coupled-channel problem
Authors: Nogami Y. , Ross C. K.
Published: March 2005

We study the partial-wave description of scattering of a particle from a one-dimensional potential in quantum mechanics. There are two partial waves, with even and odd parity. They are decoupled if the potential V(x) is symmetric, i.e., V(x)=V(−x). If V(x)≠V(−x), however, the two partial waves are coupled. This coupled-channel problem can be handled in terms of two eigenphases and a mixing parameter. This method enables us to shed new light on the transmission and reflection probabilities at threshold.
Analysis of idealized Zeeman quantum beat experiments in the advanced laboratory
Authors: Gemmen Gregory J. , Rouze N.
Published: March 2005

An expression for the time-dependent intensity of light scattered in idealized Zeeman quantum beat experiments commonly found in advanced teaching laboratories is presented. The development of this expression illustrates the separation of geometrical and dynamical factors via the Wigner–Eckart theorem. The experiment is also interpreted in terms of a pictorial description of a rotating electron cloud, and an experimental procedure to illustrate this rotation is described.
On the concept of absorption for a Fabry–Perot interferometer
Authors: Monzón J. J. , Sánchez-Soto L. L.
Published: March 2005

We argue that the Fabry–Perot interferometer should be modeled as a transparent medium between two absorbing coatings of finite thickness. Using the scattering-matrix formalism, we show that the transmittance obeys an Airy function, but not the reflectance, because of absorption and the coupling between the multiply reflected waves in the coatings. The model allows us to compute the absorptance in each coating and to explain a number of previous experimental results. The Stokes relations are generalized for this model.
Equation poems
Authors: Prentis Jeffrey J.
Published: March 2005

One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.
Rolling and slipping down Galileo’s inclined plane: Rhythms of the spheres
Authors: Crawford Frank S.
Published: March 2005

In ‘‘Two New Sciences’’ (TNS) Galileo presents a number of theorems and propositions for smooth solid spheres released from rest and rolling a distance d in time t down an incline of height H and length L. We collect and summarize his results in a single grand proportionality P: d1/d2=(t21/t22)(H/L)1/(H/L)2. (P) From what he writes in TNS it is clear that what we call P is assumed by Galileo to hold for all inclinations including vertical free fall with H/L=1. But in TNS he describes only experiments with gentle inclinations H/L<1/2. Indeed he cannot have performed the vertical free fall (H=L) experiment, because we (moderns) know that as we increase H/L, P starts to break down when H/L exceeds about 0.5, because the sphere, which rolls without slipping for small H/L, starts to slip, whence d starts to exceed the predictions of P, becoming too large by a factor of 7/5 for vertical free fall at H/L=1. In 1973 Drake and in 1975 Drake and MacLachlan published their analysis of a previously unpublished experiment that Galileo performed that (without his realizing it) directly compared rolling without slipping to free fall. In the experiment, a sphere that has gained speed v1 while rolling down a gentle incline is deflected so as to be launched horizontally with speed v1 into a free fall orbit discovered by Galileo to be a parabola. The measured horizontal distance X2 traveled in this parabolic orbit (for a given vertical distance fallen to the floor) was smaller than he expected, by a factor 0.84. But that is exactly what we (moderns) expect, since we know that Galileo did not appreciate the difference between rolling without slipping, and slipping on a frictionless surface. We therefore expect him to predict X2 too large by a factor (7/5)1/2=1/0.84. He must have been puzzled. Easy ‘‘home experiments’’ with simple apparatus available to Galileo (no frictionless air tracks, strobe lamps, or electronic timers!) allow the student to use his/her musical ear (for rhythm and tempo) to study vertical free fall as well as balls rolling down steep or gentle inclines, with or without slipping, and perhaps appreciate Galileo’s dilemma.
Thomas precession and the Liénard–Wiechert field
Authors: Philpott R. J.
Published: March 2005

The role of the Thomas precession in the dynamic formation of the electric field lines of a moving charged particle is demonstrated. A simple derivation of the Thomas precession formula is given, based only on the Lorentz contraction of moving bodies. A simple and physically appealing construction is developed for determining points on a field line. Field line diagrams are generated and discussed. These diagrams vividly reveal the existence and magnitude of the Thomas precession.
A technique for experimentally observing the polarization ellipse
Authors: Fernando P. C. B. , Samarasinghe S.
Published: March 2005

This paper describes a simple direct technique for obtaining experimentally the shape of the polarization ellipse of an elliptically polarized wave. A simple construction which recognizes and corrects for the distortion introduced by the analyzer is the key to the extraction of the ellipse from the experimentally obtained polar diagrams.
Christiaan Huygens’ discovery of the center of oscillation formula
Authors: Erlichson Herman
Published: March 2005

Christiaan Huygens was the first person to discover the general formula for the center of oscillation length of a physical pendulum. He was motivated to do this work by his interest in constructing accurate pendulum clocks. It is remarkable that Huygens arrived at his brilliant solution about a quarter of a century before the publication of the first edition of Newton’s Principia. This paper analyzes Huygens’ little-known derivation in detail. We take particular note of Huygens’ ingenious idea of having the moving physical pendulum ‘‘theoretically explode’’ into constituent pieces which then rise until their kinetic energy is exhausted.
Graphics simulation of a soap film catastrophe model
Authors: Tilley John , Lovett David R.
Published: March 2005

A soap film model is described that demonstrates catastrophic changes of the film pattern caused by continuous changes in configuration. The scope of the model is extended by the use of computer graphics both to animate the pattern changes of the films and to plot the corresponding movement on energy-configuration and other curves. Such energy-configuration curves are identical to those of systems that experience first-order and second-order phase changes.
The intrinsic magnetic moment of elementary particles
Authors: Gould Robert J.
Published: March 2005

In a purely nonrelativistic formulation, a Hamiltonian is obtained for the description of states of a charged particle with spin, interacting with an external electromagnetic field. For the specific cases of spin-1/2 and spin-1, the simplest choices for the Hamiltonian functions lead to a value for the (lowest order) intrinsic magnetic moment equal to the Bohr magneton in both cases. This is the same as is obtained in treatments that start from a relativistic formulation, as in the Dirac theory. The nonrelativistic and relativistic formulations both employ the ‘‘minimal coupling principle,’’ but the resulting Hamiltonians with couplings are, for very general considerations, not completely determined. However, the corresponding ambiguity that occurs in the nonrelativistic theory is also present in the relativistic formulation. The simpler nonrelativistic theory is more transparent in exhibiting these features of the problem and dispels the notion that spin (and the associated magnetic moment) require relativistic formulations for a proper understanding.
Approach to thermal equilibrium in a system with adiabatic constraints
Authors: Crosignani Bruno , Di Porto Paolo , Segev Mordechai
Published: March 2005

The problem of prediction of the equilibrium state in an isolated composite system with an adiabatic internal wall is a delicate problem, whose solution is easily seen to be not entirely determined in the frame of elementary thermodynamics. We show how this indeterminacy can be removed by introducing a suitable kinetic model, in which the influence of the finite velocity of the wall on the change of momentum of the gas molecules impinging on it plays a relevant role. An interesting feature of the entropy behavior of the system is discussed.
Derivation of relativistic force transformation equations from Lorentz force law
Authors: Jefimenko Oleg D.
Published: March 2005

Relativistic transformation equations for the 3-vector force are derived from the Lorentz force law by using the well-known transformation equations for electromagnetic fields and velocity. The derivation is a simple alternative to the conventional derivation based on relativistic expressions for energy and momentum.
A critical exponent of an aniseed-based liquor
Authors: Mayorga A. , Thompson D.
Published: March 2005

We present the results of a simple experiment suitable for the undergraduate laboratory in which the onset of turbidity when an aniseed-based liquor is diluted with water is observed. The optical transmission shows the behavior typical of the order parameter in a second-order phase transition. The changes in the transmission are due to the precipitation of terpenes and the amount of precipitated terpenes also shows critical behavior of the form n=k′(c−cc)y, where c is the fraction of water in the solution. The critical exponent is determined to be y=1.01±0.06.
Angular momentum states of the diatomic molecule
Authors: Hornkohl James O. , Parigger Christian
Published: March 2005

An exact equation for the angular momentum states of the diatomic molecule is derived. The eigenstates of the idealized Hund’s cases (a) and (b) are then calculated from the exact result. Example calculations of the matrix elements of the rotational Hamiltonian in the Hund’s case (a) basis are given and Hönl–London factors for (a)↔(a) and (b)↔(b) transitions are calculated. All calculations are carried out within the fully standard theory of angular momentum. Previous discussions of diatomic angular momentum states have invariably employed special methods such as consistently applied anomalies, and it is not generally known that such methods are unnecessary.
Specific heat revisited
Authors: Pizarro C. A. , Condat C. A. , Lamberti P. W. , Prato D. P.
Published: March 2005

The correlation between potential shape and specific heat is generally absent from textbook discussions. We present a detailed analysis of the specific heat contribution due to independent particles subject to one-dimensional classical and quantum model potentials. For the classical models, we use phase space concepts to develop a clear physical interpretation of the temperature dependence of the specific heat. For the quantum models, we make the interpretation in terms of the differences in quantum levels.
Design and measurements of variably nonuniform acoustic resonators
Authors: Denardo Bruce , Bernard Miguel
Published: March 2005

We describe the design, construction, and acoustical measurements of resonators with nonuniform cross-sectional areas that are easily altered to yield different resonance frequencies. These resonators are useful as educational demonstrations of symmetry breaking and of an effect of nonuniformity upon standing waves. Resonators that yield two, three, and four pitches are considered, where the relative frequencies are designed to correspond to musical intervals. Agreement is within 2% in all cases and 1% for most. The data reveal a breakdown of the theory, which is shown to be a result of additional kinetic energy, and thus effective inertia, near a discontinuity in cross-sectional area. The data also reveal that it is more accurate accurate to employ the end correction of an infinite flange rather than that of a thin-walled tube.
Impurity level lifetime measurements using a lock-in amplifier
Authors: Edmondson Kenneth , Agoston Steve , Ranganathan Radha
Published: March 2005

Lifetimes of metastable levels of chromium in ruby are determined using an unusual technique. The fluorescence from the chromium is measured using an ac technique in which the excitation is modulated and the fluorescence is detected synchronously. The novelty lies in the measurement of the dependence of the signal on the modulation frequency and extracting the lifetime from the frequency dependence. The experiments and data analysis demand a detailed understanding of the methods of lock-in amplification and synchronous detection and hence they can serve as a useful primer on the subject. The observed values for the lifetimes show excellent agreement with previous measurements.
Load distribution in moving furniture
Authors: Xiong-Skiba P.
Published: March 2005

Static equilibrium conditions are applied to the case of moving a piece of furniture. Assume that two people are carrying a piece of furniture down a hill with a uniform speed. The load distribution on both people is found to be a function of the slope of the hill, the difference in the heights of the two people, the length of the furniture, and, more importantly, the force angle that the person at the upper end applied relative to a horizontal line. Some interesting features are revealed through this analysis. For example, contradictory to our common sense, the person at the lower end does not always carry more ‘‘weight.’’ This problem was found to be effective in helping students develop the static equilibrium concept.
Disentanglement formulas: An alternative derivation and some applications to squeezed coherent states
Authors: DasGupta Ananda
Published: March 2005

An alternative derivation of the disentanglement formulas for exponential operators, also known as the Baker–Campbell–Housdorff formulas is given for several Lie algebras. The method is especially suited to Lie algebras having no nontrivial center. We also look at some results that can be obtained by the use of these formulas in the case of squeezed coherent states.
Acceleration of gravity for the earth model as an ellipsoidal mass with nonuniform density
Authors: Maialle Marcelo Z. , Hipólito Oscar
Published: March 2005

We present a model calculation of the acceleration of gravity in an ellipsoidal mass with nonuniform density. Using parameters resembling that of the earth’s dimensions and mass density, we are able to account for most of the observed variation of the acceleration of gravity at the pole and the equator which is not related to rotational effects. The nonuniformity of the density of mass, when considered with the ellipsoidal flattening of the earth, is one of the most important factors to be considered when explaining the difference of the acceleration of gravity at the pole and equator. A simple model of a flattened earth with a uniform mass density does not give a reasonable explanation for this variation of the gravitational acceleration.
Visualizing the solutions for the circular infinite well in quantum and classical mechanics
Authors: Robinett R. W.
Published: March 2005

The classical and quantum mechanical problem of a particle in the infinite circular well has recently surfaced in two quite different manifestations: (i) the observation of ‘‘electron standing waves’’ in circular ‘‘corrals’’ of atoms adsorbed on surfaces and (ii) as a benchmark example of an integrable system for comparison to the classical and quantum chaotic behavior of the ‘‘stadium billiards’’ problem. Motivated by this, we review the quantum and classical probability distributions for both position and momentum for this familiar problem, focusing on the visualization of the quantum wave functions and classical trajectories as well as the semiclassical connections between the two.
Electromagnetism with magnetic charge and two photons
Authors: Singleton D.
Published: March 2005

The Dirac approach to include magnetic charge in Maxwell’s equations places the magnetic charge at the end of a string on which the the fields of the theory develop a singularity. In this paper an alternative formulation of classical electromagnetism with magnetic and electric charge is given by introducing a second pseudo-four-vector potential, Cμ, in addition to the usual four-vector potential, Aμ. This avoids the use of singular, nonlocal variables (i.e., Dirac strings) in electrodynamics with magnetic charge, and it makes the treatment of electric and magnetic charge more symmetric, since both charges are now gauge charges.
Conchoid of Nicomedes from reflections and refractions in a cone
Authors: Szmulowicz Frank
Published: March 2005

Reflections and refractions of a sheet of light from a truncated cone are shown to produce the ancient figure of the conchoid of Nicomedes when imaged on the basal plane. The idea can be easily demonstrated using a truncated cone (here a glazed flower pot is used) and a laser pointer. This result may be of interest in the area of nonimaging optics.
Computer simulated holography and computer generated holograms
Authors: Trester Seymour
Published: March 2005

The success of calculating and displaying the Fraunhofer diffraction patterns for various apertures using the fast Fourier transform algorithm on an IBM compatible personal computer has been well documented in the recent literature. In this paper the technique is extended to the simulation of optical holography on the computer. Using this method, Fourier transform holograms are easily generated. Their optically reconstructed images are compared to the ones reconstructed and displayed by the computer. These computer generated images allow for a quantitative verification of the holographic theory presented and can serve as the basis of a tutorial on this subject suitable for advanced undergraduates. The calculations and graphics were accomplished using the mathcad(R) for windowsTM software package.
Cryogenic heat engine
Authors: Ordonez C. A.
Published: March 2005

A classroom demonstration is described which illustrates how a cryogenic fluid, liquid nitrogen, can be used to run an open-cycle engine and do work. A brief analysis on the utility of liquid nitrogen for doing work shows some surprising results in comparison with lead/acid batteries. The specific energy (the work per unit mass) is found to be higher for liquid nitrogen while the energy cost is found to be about an order of magnitude lower.
A coordinate independent approach to the kinematics of rotating frames
Authors: Dede K. M. , Demény A. , Darai J. Kuti
Published: March 2005

Generalization of the laws of dynamics to noninertial frames is based on the kinematic transformation formula for accelerations relative to different frames. A new approach is proposed to treat this problem. The relationship between accelerations relating to different frames of reference R and R′ is stated in the form a=a′+aP+2ω×v′ which is derived in this paper from fundamental geometrical properties, without referring to any actual coordinate system. Here aP is the ‘‘conveyer acceleration,’’ that is the acceleration (relative to R) of the point P of R′ where the material point is found at the given instant. The conventional detailed transformation formula follows then from the well-known kinematic formula of rigid bodies, after having chosen a translational point in R′ serving as the origin of the coordinate system K′: aP=a0+ω×(ω×r′)+β×r′.
Elementary relativistic string mechanics
Authors: Rumpf Helmut
Published: March 2005

The basic properties of the relativistic string, including its simplest modes of motion, are shown to be derivable in an elementary manner directly from the postulate of constant tension. The full set of equations of motion can be derived from the same principle by employing slightly more advanced mathematical concepts. Finally a heuristic derivation of the Nambu–Goto action is presented.
Resource Letter CD-1: Causality and determinism in physics
Authors: Jones Roger
Published: March 2005

This Resource Letter provides a guide to the literature on causality and determinism in physics. It first surveys the literature of a long history of attempts to construct a systematic account of causality, attempts that constitute options for the use of the concept in physics. It then surveys the status of determinism in classical, relativistic, and quantum theories.
Using a linear approximation for single-surface refraction to explain some virtual image phenomena
Authors: Galili Igal , Goldberg Fred
Published: March 2005

There are many examples of interesting optical phenomena involving virtual images arising from refraction at the interface(s) between air and some transparent solid or liquid. However, because it is cumbersome to interpret analytical expressions or to sketch diagrams using Snell’s law of refraction, students rarely explore and develop a qualitative understanding of these phenomena. In this paper we introduce a simple-to-use linear approximation for single-surface refraction and show how it leads to qualitatively correct descriptions of some interesting but complex optical phenomena. In particular, we analyze the virtual images formed when looking at objects through both rectangular blocks and triangular prisms. The refraction images observed through a triangular prism are particularly interesting pedagogically and also provide a physical means to distinguish between objects located just outside and just inside, or on, the prism’s surface.
Viscous and nonviscous models of the partially filled rolling can
Authors: Jackson K. A. , Finck J. E. , Bednarski C. R. , Clifford L. R.
Published: March 2005

We examine the motion of soft drink cans rolling down an incline as a function of the amount of water in the can. Our observations show this behavior to be remarkably complex. We introduce models suggested by the experimental results which describe the limiting cases of a nonviscous fluid and an infinitely viscous fluid, and compare the results of the model calculations to our observations.
Low-cost differential scanning calorimeter
Authors: Mañosa Lluís , Bou Marc , Calles Carme , Cirera Albert
Published: March 2005

We present a simple and inexpensive calorimetric system that has been implemented in the undergraduate students laboratory of thermodynamics at the Physics Faculty of the University of Barcelona. It is shown that, after proper calibration, the system enables measurement of the relevant thermodynamic quantities at a first-order phase transition. As an example, the solid–liquid phase transition of water can be studied: Students find that both the change in specific heat and the latent heat (and its temperature dependence) coincide within the experimental scatter with the values given in the literature.
Direct calculation of the electric field induced by a time-varying magnetic induction
Authors: Sampaio Ray V. , Suave Rogério N.
Published: March 2005

This paper deals with the problem of obtaining the electric field near a region of magnetic flux, whose geometry has cylindrical symmetry. We derive an expression for a direct calculation of the induced electric field vector in geometric situations where a slowly varying magnetic field is confined to a long solenoid of arbitrary cross section. We check our result in a standard case, then we use it in a nontrivial case to confirm its utility. The developed expression can also be used to provide numerical evaluation of the field within the class of cylindrical symmetry.
Richard Feynman’s popular lectures on quantum electrodynamics: The 1979 Robb lectures at Auckland University
Authors: Dudley J. M. , Kwan A. M.
Published: March 2005

The subject of quantum electrodynamics (QED) was the subject of QED—The Strange Theory of Light and Matter, the popular book by Richard Feynman which was published by Princeton University Press in 1985. On p. 1, Feynman makes passing reference to the fact that the book is based on a series of general lectures on QED which were, however, first delivered in New Zealand. At Auckland University, these lectures were delivered in 1979, as the Sir Douglas Robb lectures, and videotapes of the lectures are held by the Auckland University Physics Department. We have carried out a detailed examination of these videotapes, and we discuss here the major differences between the original Auckland lectures and the published version. We use selected quotations from the lectures to show that the original lectures provide additional insight into Feynman’s character, and have great educational value.
Charge density on a conducting needle
Authors: Griffiths David J. , Li Ye
Published: March 2005

We attempt to determine the linear charge density on a finite straight segment of thin charged conducting wire. Several different methods are presented, but none yields entirely convincing results, and it appears that the problem itself may be ill-posed.
The libration limits of the elastic pendulum
Authors: Davidović D. M. , Aničin B. A. , Babović V. M.
Published: March 2005

The motion of the elastic pendulum is ruled by coupling between the pendulum mode and the harmonic oscillator mode. The bob of the pendulum executes trajectories in a domain of the vertical plane, the shape and size of which are set by the initial conditions and the total energy of the pendulum. The limits of this libration, in exact resonance, are studied using parabolic coordinates. Other Hamiltonians, with similar interaction terms, exhibit similar libration limits.
Analytical construction of electrostatic field lines with the aid of Gauss’ law
Authors: Kalotas T. M. , Lee A. R. , Liesegang J.
Published: March 2005

With the aid of a little-known application of Gauss’ law, we calculate analytical expressions for field line equations for certain configurations of charge which possess either axial or one-dimensional translational symmetry. The method is first demonstrated via the simple symmetric dipole and then extended to a number of other examples.
The gravitational Aharonov–Bohm effect with photons
Authors: Harris Edward G.
Published: March 2005

The analogy between general relativity and electromagnetism suggests that there is a gravitational analog of the Aharonov–Bohm effect. There is indeed such an effect. Since gravitation couples to all fields, the effect should exist for photons. There is a close connection with the Sagnac effect. Both the electromagnetic field and the gravitational field are classical fields, so the effect could have been predicted in the interval between the publication of the theory of general relativity in 1915 and the discovery of quantum mechanics in the mid 1920s.
Chaos in a simple impact oscillator: The Bender bouncer
Authors: Walker James S. , Soule Terence
Published: March 2005

We present a computer study of an impact oscillator known as the Bender bouncer. It consists of a driven mass on a linear spring, with damping proportional to the velocity, and an infinitely massive, elastic barrier. If it were not for the barrier, the system would be the simple mass on a spring so familiar to students of freshman physics. With the barrier in place, the system displays a remarkable range of behaviors, including energy amplification, chaos, sensitivity to initial conditions, and fractal basins of attraction. The fact that such interesting behavior occurs with such a small modification of a freshman physics problem makes the system especially well suited for presentation to students.