bluuebunny/crossref_metadata_2025 huggingface dataset:
Dielectric loss measurements on raw materials
Authors: Mwanje J.
Published: March 2005

This paper describes a relatively simple experiment which can be performed by undergraduate students to study the dielectric properties of materials. Values of the dielectric loss tangent can be determined at low frequencies from Lissajous figures formed on an oscilloscope. Sample results for mineral rock specimens are presented. Some of these specimens show Debye-type relaxation peaks at frequencies in the region of 1 to 500 Hz. Such losses can be reasonably represented by an equivalent circuit.
Reflection of rarefaction wave in one-dimensional gas flow
Authors: Sundelius Björn
Published: March 2005

A one-dimensional gas flow is generated by a piston which moves at a constant velocity out of a pipe filled with gas. The piston causes a rarefaction wave which is reflected against the closed end of the pipe. According to the theory as described by Landau and Lifshitz the reflection process is governed by the solution of a linear partial differential equation with the adiabatic exponent γ as a parameter. Explicit solutions are obtained for γ=5/3 and γ=7/5, corresponding to the theoretical values for monoatomic and diatomic ideal gases, respectively. In this paper an explicit solution for arbitrary γ is given and applied specifically to the case γ=4/3, corresponding to a polyatomic ideal gas.
Raising and lowering operators and spectral structure: A concise algebraic technique
Authors: de la Peña L. , Montemayor R.
Published: March 2005

We show that it is possible to give to any (linear and Hermitian) operator with discrete spectrum, acting on a Hilbert space, a canonical form in terms of the commutator and anticommutator of a pair of adequately constructed raising and lowering operators. This construction enables one to investigate in a very compact way the (discrete) spectrum of the given operator, which becomes determined by a set of consistency conditions. We apply the method to several important problems of quantum mechanics.
Plane electromagnetic waves in material media: Are they transverse waves?
Authors: Halevi P.
Published: March 2005

We study the polarization properties of electromagnetic waves in material media, such as a solid, a liquid, a gas, or a plasma. The waves are excited by direct incidence of light at the surface of the medium, at an arbitrary angle of incidence. Contrarily to a common misconception, the electric field E, the magnetic field B, and the wave vector q are not perpendicular to each other (as is the case in vacuum). In fact, because of dissipative and/or free-charge effects, these three quantities must be represented by complex vectors. We find that, at any given point, the tips of the electromagnetic vectors Re E and Re B describe ellipses as a function of time. The planes of these ellipses are not parallel; neither plane is normal to the direction of the refracted beam (Re q); and Re E is not perpendicular to Re B. Thus electromagnetic waves in material media are not transverse waves, in general. The only exception is the case of normal incidence of light. In the special case of p(s)-polarized incidence Re B(E) is linearly polarized and transverse, while Re E(B) has ’’longelliptical’’ polarization. By this we mean that the direction of propagation of the light is parallel to the plane of the polarization ellipse (itself parallel to the plane of incidence).
Exercise in probability and statistics, or the probability of winning at tennis
Authors: Fischer Gaston
Published: March 2005

The relationships between the probabilities p, x, s, and M, of winning, respectively, a point, a game, a set, or a match have been derived. The calculations are carried out under the assumption that these probabilities are averages. For example, x represents an average probability of winning a game when serving and receiving, and the same value of x is assumed to hold also for tie-break games. The formulas derived are for sets played with a tie-break game at the level of 6–6, as well as for the traditional rule requiring an advantage of two games to win a set. Matches to the best of three and five sets are considered. As is to be expected, a small advantage in the probability p of winning a point leads to advantages which are amplified by large factors : 2.5 for games, 7.1 for sets with tie-break at 6–6, 10.6 for matches to the best of three sets, and 13.3 for matches to the best of five sets. When sets are decided according to the traditional rule, the last three factors become, respectively, 7.4, 11.1, and 13.8. The theoretical calculations are compared with real and synthetic tennis scores and good agreement is found. The scatter of the data is seen to obey the predictions of a normal distribution. Some classroom problems are suggested at the end.
Air column resonance spectra using basic laboratory equipment
Authors: Jewett J. W.
Published: March 2005

Common laboratory apparatus and readily available materials are used to generate resonance spectra of air columns. Frequency measurements of the harmonics of a column match very well with theoretical calculations. Three additional experiments are described, involving the end correction to the column length, tone holes in the side of the column and the addition of a bell to the end of the column.
False paradoxes of superposition in electric and acoustic waves
Authors: Levine Richard C.
Published: March 2005

When acoustic or electromagnetic waves cancel by destructive interference, the wave impedance reflected to the sources of the wave energy changes so that the input power is reduced correspondingly. Because this rather subtle point is not discussed in most instructional treatments of wave physics, misconceptions concerning the apparently ’’missing’’ energy are widespread, as reflected in semipopular science writing. This paper presents an analysis of the cases of destructive and constructive wave interference, and analogous problems for lumped electrical and mechanical systems.
The use of room reverberation time measurements in physics of music courses
Authors: Zych D. A. , Earle Thomas
Published: March 2005

Room reverberation measurements and their interpretation are an important part of a musical acoustics course which has proved successful with nonscience students at the State University of New York College at Oswego. This paper describes these measurements in detail along with a variety of ways they can be used in the classroom.
Photoacoustic effect and the physics of waves
Authors: McDonald F. Alan
Published: March 2005

The photoacoustic effect is the basis for photoacoustic spectroscopy, a rapidly developing technique for studying optical absorption in many solid and liquid samples which are difficult to study by conventional means. Understanding of the effect requires knowledge of both acoustic and thermal waves, making this an interesting problem in the application of fundamental wave concepts and techniques. Both qualitative and quantitative discussions are presented for use as classroom examples at various levels.
Photovoltaic experiment using light from a solar simulator lamp
Authors: Chow R. H.
Published: March 2005

A photovoltaic cell experiment utilizing the convenience of a solar simulating type lamp is described. The circuit for obtaining the cell characteristic drives an X-Y plotter to graph continuously the characteristics from short circuit current to the open circuit voltage. Calibration methods and their limitation are discussed for estimating the irradiance to determine the light conversion efficiency of the cell. The diode junction nature of the cell is clearly supported by the agreement between experiment and theory. The experiment should be exceptionally suitable for an undergraduate physics laboratory experiment.
Demonstration for observing J0(x) on a resonant rotating vertical chain
Authors: Western A. B.
Published: March 2005

A simple example of mechanical resonance using a light chain rotating about a vertical axis is described. The equation of motion for the chain can be reduced to Bessel’s function of the first kind of order zero [J0(x)]. Stable lobe patterns are formed with eigenfrequencies and internode spacing which agree well with the zeros of J0(x).
Isotope shift in the spectrum of helium
Authors: George Simon , Voelker Mark
Published: March 2005

The arc spectrum of helium 42He has been photographed using an Ebert 3.4-m plane grating spectrograph in the fourth and fifth orders. The spectrum of 32He using a He–Ne laser is then superimposed on the above spectrum. An iron arc spectrum is used for calibration. The wave numbers due to four singlet-singlet transitions in 32He and 42He are reduced with the help of a photoelectric-setting comparator. The observed wave number differences of these four pairs resulting from the isotope shift are compared with published values in research journals. The presence of 32He in the laser provides the 32He light source and the widespread availability of helium–neon lasers makes this a convenient and inexpensive experiment in the undergraduate optics and spectroscopy laboratory or in the modern physics curriculum.
Magneto-optical experiments on rare earth garnet films
Authors: Tanner B. K.
Published: March 2005

Experiments to measure several macroscopic magnetic properties of thin rare earth garnet films used in the manufacture of magnetic bubble devices are described. Using the magneto-optic Faraday effect to measure the net component of magnetization normal to the film the shape of hysteresis loop, coercive field, Curie temperature, anisotropy field and the variation of magnetization with temperature can be determined. The results of the latter two measurements agree very well with theoretical predictions. As inexpensive or standard laboratory equipment is used the experiments are ideally suited to use in an undergraduate teaching laboratory.
Solutions of the Hamilton–Jacobi equation in the Coulomb potential and the quasiclassical approximation
Authors: Brojan J. B.
Published: March 2005

New solutions of the Hamilton–Jacobi equation with the Coulomb potential are presented. They correspond to quantum-mechanical scattering states and Green’s functions and can be applied in quasiclassical approximations. As an example, the quasiclassical limit of bremsstrahlung is considered.
Magnetic multipoles in theory and practice
Authors: Smith D. G.
Published: March 2005

The general expression for the magnetic moment of arbitrary order of a circular current loop about any point on its axis is derived, and used to obtain the magnetic moments of systems of current loops. A magnetic multipole apparatus suitable for the physics teaching laboratory is described. The apparatus enables the student to measure the magnetic field configuration of a single large coil and of systems of one or more small coils, and results obtained with it are presented. The potential role of the nuclear magnetic octupole moment in nuclear structure studies is indicated by deriving the M3/M1 ratio of three spheroidal current distributions.
Simple ultra-low-cost undergraduate holography using a modified Michelson interferometer
Authors: Rudmin J. W. , Taylor G. R. , Hand P. M. , Ashworth J. N. , Wehr P. H.
Published: March 2005

A technique is presented for producing holograms using equipment which is already in the possession of the great majority of college physics departments. The equipment is a slightly modified Michelson interferometer, a helium–neon laser, and a long focal-length lens. The only materials which must be purchased are the photographic supplies. With the modified Michelson interferometer, production of consistently high-quality holograms has been achieved by inexperienced undergraduates after a few hours of labor.
Undergraduate experiment: Half-lifes Thorium 232 and Radon 220
Authors: Cussenot J. R. , Fabry M.
Published: March 2005

An elecroscope is employed along with the laws of secular equilibrium to give accurate values for the α-decay rates of 232Th and 220Rn. (AIP)
Finite rotations and angular velocity
Authors: Peres Asher
Published: March 2005

The angular velocity vector is not the time derivative of the vector which represents a finite rotation. The relationship between the two is derived explicitly.
Gravitational deflection of relativistic massive particles
Authors: Silverman Mark P.
Published: March 2005

The deflection of relativistic massive particles in a spherically symmetric gravitational field is analyzed according to general relativity and compared with results obtained according to Newtonian and special relativistic theories of gravity. The examples chosen highlight the striking disparity in the predictions of the three theories and show that deflection experiments on massive particles can provide an alternative test of the equivalence principle in general relativity.
Concepts of nonequilibrium thermodynamics in discrete model of heat conduction
Authors: Lurié David , Wagensberg Jorge
Published: March 2005

Examples of thermodynamic evolutions toward stationary states are exhibited in a one-dimensional heat conduction problem. A computer simulation technique is employed to solve the Fourier partial differential equation and compute the evolution of the three terms in the entropy balance equation. Some concepts of linear nonequilibrium thermodynamics are analyzed in the framework of the model: the meaning of the entropy balance equation, the disticntion between free and fixed forces, the role of the Onsager’s relations, and the relationship between the structural adaptation of a linear system to the externally imposed constraints and the entropic concept of ’’order.’’
Experimental studies of the He–Ne laser: resonators and self-locking
Authors: Ruddock I. S.
Published: March 2005

He–Ne laser experiments suitable for an undergraduate laboratory are described. The topics covered are cavity stability, self-mode-locking coherent interactions between pulses and laser medium, and spontaneous transverse mode locking.
Kinetic theory derivation of the adiabatic law for ideal gases
Authors: Sobel Michael I.
Published: March 2005

We show how the adiabatic law for ideal gases can be derived from the assumption of a Maxwell–Boltzmann (or any other) distribution of velocities—in contrast to the usual derivation from thermodynamics alone. We also discuss the higher-order effect that leads to one-body viscosity. We give a more elementary derivation of the adiabatic law suitable for introductory classes.
Space-age ticktock
Authors: Baird Leemon C.
Published: March 2005

The author makes a study as to why space-age electronic watches are capable of fantastic accuracy.(AIP)
Black hole thermodynamics in an undergraduate thermodynamics course
Authors: Parker Barry R. , McLeod Robert J.
Published: March 2005

An analogy has been drawn between black hole physics and thermodynamics. In this paper the analogy is mathematically broadened. Equations similar to the standard partial differential relations of thermodynamics are found for black holes. The results can be used to supplement an undergraduate thermodynamics course.
Redundancy and superfluity for electromagnetic fields and potentials
Authors: Rosen Joe
Published: March 2005

Redundancy (the correspondence of different specifications to the same physical situation) and superfluity (the existence of specifications corresponding to no physical situation) in the description of classical electromagnetism by fields and by potentials are discussed for the vacuum case. The amount of information specifying a physical situation is found for each description and is shown to be the same for both.
Factors influencing the learning of classical mechanics
Authors: Champagne Audrey B. , Klopfer Leopold E. , Anderson John H.
Published: March 2005

The study described in this paper investigates the combined effect of certain variables on student achievement in classical mechanics. Our purposes are (1) to describe the preinstructional knowledge of mechanics, mathematical skills, and reasoning skills of a sample of college physics students, (2) to correlate these variables with the student’s success in learning classical mechanics, and (3) to develop an hypothesis about the relationships between these variables and student achievement in mechanics. We also offer some proposals for improving the teaching of classical mechanics.
Time evolution of the dynamical variables of a stochastic system
Authors: de la Peña L.
Published: March 2005

By using the method of moments, it is shown that several important and apparently unrelated theorems describing average properties of stochastic systems are in fact particular cases of a general law; this method is applied to generalize the virial theorem and the fluctuation–dissipation theorem to the time-dependent case.
Integral formulation of the boundary value problem in waveguides
Authors: Sancho M.
Published: March 2005

An integral approach to the boundary value problem in waveguides is presented. This approach is deduced from the Kirchhoff’s integral formulation of the electromagnetic field. Several monodimensional cases of simple analytical solution are exposed showing the suitability of such approach as a complement of the usual differential formulation from a lecturer’s point of view. Finally, the basis for the numerical solution of more general problems is given, including the example of the isosceles right triangular guide.
Considerations about equivalent models in a classical one-dimensional system
Authors: Trapote A. G.
Published: March 2005

A series of equivalent models for a classical, conservative, one-dimensional system is developed. Next, with respect to such models, we obtain a set of related results about some specific, interesting, and outwardly unconnected subjects in mechanics. For instance, dissipative functions, variable mass, generalized velocity-dependent potentials, ’’hidden motions’’, and noninertial situations. A comparative analysis allows us to deduce certain formal analogies with particular relativistic statements.
Investigation of student understanding of the concept of velocity in one dimension
Authors: Trowbridge David E. , McDermott Lillian C.
Published: March 2005

This paper describes a systematic investigation of the understanding of the concept of velocity among students enrolled in a wide variety of introductory physics courses at the University of Washington. The criterion selected for assessing understanding of a kinematical concept is the ability to apply it successfully in interpreting simple motions of real objects. The primary data source has been the individual demonstration interview in which students are asked specific questions about simple motions they observe. Results are reported for the success of different student populations in comparing velocities for two simultaneous motions. It appears that virtually every failure to make a proper comparison can be attributed to use of a position criterion to determine relative velocity. Some implications for instruction are briefly discussed.
Probability interpretation of quantum mechanics
Authors: Newton Roger G.
Published: March 2005

The paper draws attention to the frequency meaning of the probability concept and its implications for quantum mechanics. It emphasizes that the very meaning of probability implies the ensemble interpretation of both pure and mixed states. As a result some of the ’’paradoxical’’ aspects of quantum mechanics lose their counterintuitive character.
Do free quantum-mechanical wave packets always spread?
Authors: Klein James R.
Published: March 2005

The spreading or shrinking of free three-dimensional quantum-mechanical wave packets is studied, and several results are presented. A seeming paradox concerning the time evolution operator and nonspreading wave packets is discussed, and the necessity of taking into account the appropriate mathematical structure of quantum mechanics is emphasized. Implications for the teaching of quantum mechanics are given.
Three-particle symmetry classifications according to the method of Dirac
Authors: Hussar P. E. , Kim Y. S. , Noz Marilyn E.
Published: March 2005

It is shown that the method of Dirac is an effective way of teaching three-particle symmetry classifications to students in the first-year quantum mechanics class, who wish to understand the symmetry properties associated with elementary particles before or without learning group theory. According to the method spelled out for the N-particle case by Dirac in Secs. 55 and 56 of his classic book Principles of Quantum Mechanics, explicit calculations are carried out for three particles. It is shown that this method leads to the three-particle wave functions and their symmetric combinations as given by Feynman et al. In the following paper, the general principles derived here are applied to the quark model of hadrons.
Quark model in the quantum mechanics curriculum
Authors: Hussar P. E. , Kim Y. S. , Noz Marilyn E.
Published: March 2005

The formalism for understanding the quark model is developed purely within the framework of the first-year quantum mechanics curriculum. It is shown that the mathematics presented in the preceding paper is sufficient for dealing with the essential features of the quark model, including the construction of the spin, unitary spin and spatial wave functions, and the combination of them. The totally symmetric three-quark baryonic wave functions are discussed in detail. The two-body mesonic states are also discussed. A brief review of the experimental efforts to identify the quark model multiplets is given.
Model experiment of two-dimensional Brownian motion by microcomputer
Authors: Mishima Nobuhiko , Petrosky Tomio Yamakoshi , Minowa Hiroaki , Goto Suteo
Published: March 2005

A model experiment, which is designed to display graphically by the use of a microcomputer, is proposed. In this model experiment, the direction of a thermal particle colliding with a Brownian particle and the scattering angle of it are determined by using random numbers. Parameters, which are important for determining Brownian motion, such as the mean speed of the thermal particle, can be selected at will, and the experimental results can be graphically displayed moment by monent. A flow chart and a program for the experiment are provided. A means is provided to deepen student’s understanding through mutual dialog between the students and computer.
Photographing a relativistic meter stick
Authors: Gibbs Robert E.
Published: March 2005

A ’’gedanken photograph’’ of a relativistic meter stick is analyzed at a level appropriate for undergraduate students. While an image of the correct Lorentz contracted length can be obtained, that image is distorted, since it does not represent all parts of the stick at one instant of time, but different parts of the stick at different times. Aspects of the photographic process are also analyzed in the frame of the moving meter stick.
Does the Fizeau experiment really test special relativity?
Authors: Clément Gérard
Published: March 2005

The motivation and interpretation of the Fizeau experiment are reviewed, and its status as a test of special relativity is discussed. It is shown, with the aid of a simplified, purely mechanical, model of the propagation of light in matter, that the experiment actually cannot discriminate between Galilean and relativistic kinematics.
Dynamics of circular motion with friction
Authors: Franklin Lloyd P. , Kimmel Paul I.
Published: March 2005

The velocity of a block as it traverses a circular surface with friction is calculated. Numerical and analytical solutions by dynamical and energy methods are presented and compared. Equations for the velocity, acceleration, and work done against friction are derived and their implications discussed.
Teaching the principles of radioactive dating and population growth without calculus
Authors: Celnikier L. M.
Published: March 2005

A dice playing game is proposed, by which means mathematically unsophisticated students and school children can learn empirically the principles of radioactive dating and population growth.
Feynman path integral and gauge invariance
Authors: Kobe Donald H.
Published: March 2005

Gauge invariance in both quantum and classical mechanics is investigated using the Feynman path integral formulation of quantum mechanics. The Feynman path integral expresses the wave function in terms of the Lagrangian. A gauge transformation in classical mechanics is the addition of a total derivative of a gauge function to the Lagrangian. A gauge transformation of the second and first kind in quantum mechanics is obtained by adding and subtracting, respectively, a total derivative to the Lagrangian in the Feynman path integral.
Reply to L. D. Firth, ’’Regarding magnetic flux quantization’’
Authors: Higbie J.
Published: March 2005

The author explains the pedagogical value of his previous calculation.(AIP)
Man’s size in terms of fundamental constants
Authors: Press William H.
Published: March 2005

Why are we the size we are, instead of some very different size? Simple physical scaling laws and three ’’requirements’’ dictate that our size be of order (h/2/mee2)(e2/Gmp 2)1/4. They also ’’predict’’ the mass and radius of the Earth. The three requirements are: (i) We are made of complicated molecules; (ii) we breathe an evolved planetary atmosphere; (iii) we are about as big as we can be without breaking.
Thermodynamic laws of neutrino and photon emission
Authors: Walsh P. J. , Gallo C. F.
Published: March 2005

From the analogous properties of neutrinos and photons as quantized energy waves, the generalized ’’blackbody’’ radiation law for the total power radiated Rν per unit area per unit frequency ν is derived as Rν?k3/c2h2) × T3{(hν/kT)3/ [exp(hν/kT)−1] +3(hν/kT)3/ [exp(hν/kT)+1]}, where c is the speed of light, h is Planck’s constant, k is Boltzmann’s constant, and T is the absolute temperature. The first term in the brackets is the usual Planck radiation law for photon emission. The second term is the corresponding expression describing blackbody neutrino and antineutrino emission, which contains a factor of 3 because three different types of neutrinos are presently suspected. Otherwise the photon and neutrino terms only differ in the sign of the unity term due to the different spin statistics of photons compared with neutrinos. For photons, the spin =h/ and Bose–Einstein statistics apply, while for neutrinos the spin =h//2 and Fermi–Dirac statistics are appropriate. The wavelength (λm) at which the maximum energy is radiated is λmT=2.898 μ kK for photons and λmT=2.859 μ kK for neutrinos, while the total power radiated per unit area is R=T4 (σp+σn), where σp=5.67 W/cm2(kK)4 for photons and σn = 14.88 W/cm2(kK)4 for three types of neutrinos. Note that kK represents kilo degrees Kelvin. As is well known, the form of the blackbody law for photons demands the possibility of stimulated emission by light flux, thus allowing light to be amplified. On the other hand, the neutrino blackbody law demands that neutrino radiating transitions are suppressed in the presence of a neutrino flux. There are applications of these neutrino concepts in particle physics and astrophysics. It appears that neutrino blackbodies or graybodies may exist in nature associated with black holes, the formation of neutron stars, and the formation of the universe itself.
Quantum dynamics and a semiclassical description of the photon
Authors: Henderson Giles
Published: March 2005

Nonstationary, superposition wave functions are used with computer graphics to reveal the dynamic quantum trajectories of several molecular and electronic transitions. These methods are then coupled with classical electromagnetic theory to provide a conceptually clear picture of the emission process and emitted radiation localized in time and space.
Relativistic transformation of solid angle
Authors: McKinley John M.
Published: March 2005

We rederive the relativistic transformations of light intensity from compact sources to show where and how the transformation of solid angle contributes. We discuss astrophysical and other applications of the transformations.
Interval-based representations of complex tones
Authors: Lawson Dewey Tull
Published: March 2005

A novel graphic representation is presented for complex musical spectra. Based on component intervals rather than the component tones themselves, this representation offers pedagogical and analytical advantages, particularly when musical transposition is involved. Examples are given of the use of this kind of plot in representing complex intervals and chords, discussing perceptual data, and carrying out various types of consonance analysis.
Electromagnetic momentum in static fields and the Abraham–Minkowski controversy
Authors: Lai H. M.
Published: March 2005

Using a simple but quantitative example and requiring the conservation of total angular momentum, we have shown that Minkowski’s D×B/4πc cannot be accepted and that there is no inconsistency to accept Abraham’s E×H/4πc, as the general expression for the electromagnetic field momentum density in a stationary nonmagnetic medium.
Quantum pendulum
Authors: Aldrovandi R. , Ferreira P. Leal
Published: March 2005

The problem of the mathematical pendulum is discussed in its classical, semiclassical, and quantum aspects. The energy spectrum and the eigenfunctions are presented under the usual requirement of single valuedness of the solutions.
Localization of interference fringes
Authors: Simon J. M. , Comastri Silvia A.
Published: March 2005

If one considers the interference of two extended sources and if one is able to observe fringes only at certain points in space one says that the fringes are localized on those points. As an example we show how the localized fringes may be found in a device used to observe Newton’s rings. Moreover we give a proof of the general method used to determine the localized fringes position. This proof is suitable for undergraduate optics courses. We also analyze the visibility of fringes.
Plasmon surface polariton dispersion by direct optical observation
Authors: Swalen J. D. , Gordon J. G. , Philpott M. R. , Brillante A. , Pockrand I. , Santo R.
Published: March 2005

Simple optical techniques are described for the direct visual observation of the plasmon surface polariton dispersion curve, ω vs κ, and of the shift in the dispersion curve from overcoatings of different thicknesses. To see the dispersion curve, a collimated beam of white light is dispersed by a prism, and then focused by a cylindrical lens onto the base of a second prism coated with a thin metal film. With this arrangement the attenuated total reflection spectrum is obtained with all the visible frequencies spatially resolved. The shift of the dispersion curve for coatings of different thicknesses is illustrated in a separate experiment using a specially constructed Langmuir wedge. This demonstrates the usefulness of plasmon surface polaritons for monitoring coatings with thicknesses of the order of nanometers.
Another simple model for energy emission by black holes
Authors: Celnikier L. M.
Published: March 2005

The qualitative results of Hawking and Page concerning the stability of black holes against energy emission are obtained by a direct application of Heisenberg’s uncertainty principle.
Diagrams for quantum oscillators
Authors: Ferrell Thomas L.
Published: March 2005

Diagrams are constructed for matrix elements associated with perturbed harmonic oscillators in quantum mechanics. The diagrams are shown to enable efficient computation of energy shifts and transmission probabilities. An intuitive approach to the diagrammatic technique is used so that introductory quantum courses can incorporate the methods presented.
Undergraduate electron-spin-resonance experiment
Authors: Willis James S.
Published: March 2005

For institutions which have an electron-spin-resonance spectrometer available to them, potassium azide (KN3) is a material which provides a unique opportunity for a student to conduct an experiment which extends from the phase of sample preparation (crystal growth, sample mounting, and orientation) through data taking to the stages of calculation and theoretical explanation. Through the desires and imagination of the teacher, the level of sophistication can be varied widely, but at any level the student can have the satisfaction of doing a complete experiment which reenforces the lessons of many courses in physics. This paper describes the basic procedures of this experiment and gives sample results for instructor reference.
Student microwave experiments involving the Doppler effect
Authors: Weber F. Neff , Helminger Paul , Moulds Delores Lynn
Published: March 2005

An attempt to improve on an earlier article reported in this Journal has lead to the use of the Doppler effect with microwaves in the measurement of the acceleration due to gravity of falling objects. The experiments described add to the repertoire of quantitative student microwave experiments.
Alternative form of the hydrogenic wave functions for an extended, uniformly charged nucleus
Authors: Ley-Koo E. , Castaño E. , Finotello D. , Nahmad-Achar E. , Ulloa S.
Published: March 2005

An exact closed solution for the hydrogenic wave functions for an extended, uniformly charged nucleus was reported in this Journal some time ago. We present an alternative form of such wave functions which allows numerical results to be obtained more easily. We illustrate the use of this alternative form by its application to muonic atoms throughout the periodic table.
Terminal velocity of a shuttlecock in vertical fall
Authors: Peastrel Mark , Lynch Rosemary , Armenti Angelo
Published: March 2005

We have performed a straightforward vertical fall experiment for a case where the effects of air resistance are important and directly measurable. Using a commonly available badminton shuttlecock, a tape measure, and a millisecond timer, the times required for the shuttlecock to fall given distances (up to almost ten meters) were accurately measured. The experiment was performed in an open stairwell. The experimental data was compared to the predictions of several models. The best fit was obtained with the model which assumes a resistive force quadratic in the instantaneous speed of the falling object. This model was fitted to the experimental data enabling us to predict the terminal velocity of the shuttlecock (6.80 m/sec). The results indicate that, starting from rest, the vertically falling shuttlecock achieves 99% of its terminal velocity in 1.84 sec, after falling 9.2 m. The relative ease in collecting the data, as well as the excellent agreement with theory, make this an ideal experiment for use in physics courses at a variety of levels.
The Doppler effect: A consideration of quasar redshifts
Authors: Gordon Kurtiss J.
Published: March 2005

For a collection of moving sources with velocities randomly distributed, the classical Doppler effect predicts that half of the sources appear redshifted and half appear blueshifted. When relativistic speeds are involved, the transverse Doppler effect introduces a preponderance of redshifts over blueshifts. In this article it is shown that the size of the effect (i.e., the ratio of redshifts to blueshifts) can be calculated in a straightforward manner. For quasars, redshifts as large as 3.5, corresponding to velocities of 0.91c, have been observed. At this speed, randomly directed motions will produce almost an order of magnitude more redshifts than blueshifts. This consideration should be mentioned in discussions of whether quasars are ’’local’’ rather than ’’cosmological’’ objects.
Fiber optic wink-around speed of light experiment
Authors: Blackburn James A.
Published: March 2005

A recycling oscillator has been designed in which a fiber optic data link closes the loop. The repeated emission and detection of infrared pulses is termed a ’’wink-around system’’ in correspondence with the sing-around methods used in ultrasonics. Electronic delay elements reduce the system frequency to about a megahertz. The difference in period for two fiber lengths yields a value for the speed of light in the cable.
Electrostatics in the plane
Authors: Liboff Richard L.
Published: March 2005

Electrostatic laws are obtained for charges constrained to lie in a plane. The corresponding electric field E in the plane obeys neither Poisson’s equation nor Gauss’ law. A vector field Λ is constructed which does satisfy these equations and which is a functional of the charge density. Various limiting forms of the coupling dyad M are obtained. where E=MΛ.
Diamagnetism, gauge transformations, and sum rules
Authors: Friar J. L. , Fallieros S.
Published: March 2005

The dependence of conventional definitions of the atomic diamagnetic susceptibility on the gauge adopted for the description of the magnetic field is illustrated. The demonstration of the gauge invariance of the complete magnetic susceptibility leads to a discussion of the connection between gauge transformations and sum rules.
Estimate for the gaps between the energy levels of a particle in a bounded interval
Authors: El-Batanouny F. M.
Published: March 2005

In the present paper we obtained an estimate for the gaps between the energy levels of a particle moving in a bounded interval subjected to a potential field U(x). As a consequence, the validity of the correspondence principle in this case is discussed.
Separability of center of mass and relative motion of hydrogen in very strong magnetic fields
Authors: Palmer William F. , Taylor Robert J.
Published: March 2005

While hydrogen does not strictly separate into center of mass (CM) and relative motion in a magnetic field, a judicious gauge choice does lead to a simple Hamiltonian whose form in a state of zero translational motion of the center of mass is that of a charged particle in a magnetic field plus a Coulomb potential.
Real and hybrid atomic orbitals
Authors: Cook D. B. , Fowler P. W.
Published: March 2005

It is shown that the Schrödinger equation for the hydrogenlike atom separates in both spheroconal and prolate spheroidal coordinates and that these separations provide a sound theoretical basis for the real and hybrid atomic orbitals. Thus the real and hybrid atomic orbitals have as sound a pedigree as the more familiar complex orbitals based on the separation of the Schrödinger equation in spherical polar coordinates.
Monochromators as light stretchers
Authors: Rubin B. , Herman R. M.
Published: March 2005

A known but often overlooked property of optical monochromators is discussed in view of its currents applications. It is shown that grating and prism monochromators hold on to light for time durations proportional to the resolving power. The dispersing ability of monochromators extends to pulses of arbitrarily short duration, in contrast to a somewhat common belief concerning interference.
Broken symmetry of the charged planar rotator in electric and magnetic fields
Authors: Silverman Mark P.
Published: March 2005

An exact solution to the problem of the Stark and Zeeman effects of the charged two-dimensional rotator is given. The energy spectrum is shown to exhibit an unusual degeneracy-breaking pattern. Group theory is used to account for the contrasting symmetry properties of the electric and magnetic field solutions. An examination of the physical properties of the system by means of perturbation theory leads to a clarification of an important point concerning the use of degenerate perturbation theory and the analytical continuity of perturbation wave functions.
General properties of lossless beam splitters in interferometry
Authors: Zeilinger A.
Published: March 2005

The author uses spinor algebra to investigate general properties of lossless beam splitters in interferometry.(AIP)
Circular motion with sliding friction
Authors: Lapidus I. Richard
Published: March 2005

This note considers the motion of a block starting from rest at any position on a vertical semicircular track. (AIP)
Simplified approach to brachistochrone problems
Authors: Aravind P. K.
Published: March 2005

The derivation of the brachistochrone as first developed by Jean Bernoulli is examined.(AIP)
An improved approximate closed-form solution to the error function
Authors: Busen Karl M.
Published: March 2005

An improved approximate closed-form solution to the error function is presented. (AIP)
More on the restricted three-body problem
Authors: Zapolsky Harold S.
Published: March 2005

The author provides an insight into libration points of the restricted three-body problem.(AIP)
Fundamental units and dimensionless constants in a universe with one, two, and four space dimensions
Authors: Lapidus I. Richard
Published: March 2005

The author considers the usefulness of dimensional analysis of fundamental units and dimensionless constants by examining such units and constants in one- , two- , and four-dimensions.(AIP)
Polarization and intensity fluctuations in He–Ne lasers
Authors: Fortin E. , Singh D.
Published: March 2005

The authors discuss polarization and intensity fluctuations in helium-neon lasers polarized by using permanent magnets. (AIP)
Physics of the tennis racket II: The ’’sweet spot’’
Authors: Brody H.
Published: March 2005

The term sweet spot is used in describing that point or region of a tennis racket where the ball should be hit for optimum results. There are several definitions of this term, each one based on different physical phenomenon. In this paper the different definitions are discussed and methods are described to locate the points corresponding to each one.
The cat landing on its feet revisited or angular momentum conservation and torque-free rotations of nonrigid mechanical systems
Authors: Essén Hanno
Published: March 2005

This paper explains the connection between rotation and the law of conservation of angular momentum and points out that macroscopic angular momentum need not be conserved if it can be transferred to spin. Exact equations giving the rotational motion induced by a given internal motion are derived and discussed.
Simple explanation of a well-known collision experiment
Authors: Herrmann F. , Schmälzle P.
Published: March 2005

A well-known collision experiment can be carried out with an arrangement of several identical elastic balls each suspended by two threads and in contact with one another: a certain number of the balls is displaced from its equilibrium position and then released, so as to collide with the remaining balls at rest. After the collision, the same number of balls moves away to the other side as had initially been displaced. It is shown that, contrary to common belief, the conservation laws of energy and momentum alone are not sufficient to explain this behavior. Indeed, a further condition must be satisfied by the system of balls; namely, it must be capable of dispersion-free energy propagation.
Modern spectroscopy with a spectrometer by the optogalvanic effect
Authors: Arnett Kenneth , Anderson Richard , Alexander Ralph
Published: March 2005

An experiment involving the optogalvanic effect suitable for the advanced physics laboratory is described. This experiment complements the usual basic experiment in atomic spectroscopy where spectra are recorded on photographic film with a spectrograph or with a monochromator and photomultiplier. The optogalvanic effect used the atoms being studied as the detector and a tunable dye laser as the source. Linewidths observed are those of the dye laser that are considerably smaller than those obtained with the usual laboratory monochromator. The student is introduced to the techniques of spectroscopy with pulsed dye lasers and to a spectrum for which LS coupling does not hold.
Singly refracting biaxial crystals: A curiosity in Maxwell’s electrodynamics
Authors: Sastry G. P. , Chowdhury D.
Published: March 2005

The little-known fact that a biaxial crystal with a tensor permittivity εij as well as a tensor permeability μij can have a single refracted extraordinary ray for arbitrary angles of incidence on arbitrary cuts of the crystal, provided it satisfies the material condition ε1/μ1 = ε2/μ2 = ε3/μ3, is demonstrated from first principles and the consequences are examined in some detail.
Flashlamp-pumped dye laser as an undergraduate lab project
Authors: Alfrey Anthony J.
Published: March 2005

State-of-the-art dye lasers have been exhaustively discussed previously in the literature, however, few of these articles provide the essential bare details necessary to construct a simple working dye laser. This discussion presents an overview of the construction techniques of dye lasers suitable for student projects. Ease in construction, low cost, and tuneable output in the visible range make such lasers ideal for the junior-level lab. Skills required to complete a dye laser include basic optics, electricity, and modern physics usually covered at the sophomore level.
Coriolis force revisited
Authors: Neuberger Jacob
Published: March 2005

The author shows that if air resistance is proportional to the velocity, the Coriolis projectile problem is solved.(AIP)
Thermodynamics of blackbody radiation
Authors: Kelly Robert E.
Published: March 2005

The thermodynamics of homogeneous, isotropic, unpolarized electromagnetic radiation in a cavity with volume and temperature controllable as the independent variables is analyzed. Internal energy, pressure, chemical potential, enthalpy, Gibbs free energy, heat capacities, expansivity, and compressibility are all derived from the Helmholtz free energy. Topics treated are the third law, isothermal, adiabatic, and free expansion, throttling process, phase equilibrium, stability, and the Carnot cycle.
Physics of living in space: A new course
Authors: Holbrow C. H.
Published: March 2005

A new course uses the prospect of living in space to motivate students to learn some basic physics and also to grapple with some larger questions about the differences between pure science and technology. Among the special features of this course are a set of exercises (two done with a computer graphics terminal), a treatment of dynamics that defines mass from the conservation of momentum rather than from Newton’s second law of motion, and a strong emphasis on weightlessness, rocket propulsion, orbital mechanics, and other aspects of physics relevant to how one might build an orbiting city in space and live there.
Euler angles, direction cosines, and angular momentum
Authors: Jo/rgensen Flemming
Published: March 2005

The line of nodes en for the Euler angles (φ, ϑ, χ) is orthogonal to the plane of the two z axes e°z and ez. In the present paper we introduce two vectors, f°z and fz, in the plane of the z axes such that the set (f°z, en, fz) is biorthogonal to (e°z, en, ez). These new vectors are so easily visualized that their components can be written down by inspection of the figure illustrating the definition of the Euler angles, and thus the direction cosine e°r ⋅ es can be obtained simply. This derivation makes no use of matrices. The total angular momentum J for a system of particles, where the Euler angles are used as coordinates for overall rotation, is shown in a simple manner to be J = f°zpφ+enpϑ+fzpχ, where (pφ, pϑ, pχ) are the momenta conjugate to (φ, ϑ, χ).
Simple solution method for the Korteweg–de Vries equation
Authors: Malfliet W.
Published: March 2005

A simple method is presented to solve the Korteweg–de Vries equation. If one assumes that the solution can be written as a product of two functions, it is shown that each of them can be related to the same Schrödinger equation. The well-known multisoliton solution then appears in a convenient way, if one deals with discrete eigenvalues.
Permutation operator: An explicit representation
Authors: Grau Dietrich
Published: March 2005

Recently Schmid has derived an explicit representation of the permutation operator in terms of coordinate and momentum operators expressed as an infinite series. Here we give an alternative derivation yielding a closed expression ? = exp(i?), which in several respects is more satisfactory.