bluuebunny/crossref_metadata_2025 huggingface dataset:
Crystal Symmetry and Macroscopic Laws. II
Authors: Callen Herbert , Callen Earl , Kalva Zdenek
Published: August 2005

In an earlier paper [Amer. J. Phys. 36, 735 (1968)] of the same title one of us described a particularly simple method by which symmetry considerations can be applied to determine the possible forms of macroscopic laws. In this sequel we clarify the role of time-reversal symmetry, describe more fully the criteria for the occurrence of spontaneous electric and magnetic moments, discuss the application of the method to magnetically ordered systems, and correct a number of errors in the tables.
Propagation of a Longitudinal Disturbance on a One-Dimensional Lattice
Authors: Weinstock Robert
Published: August 2005

Propagation of a particular longitudinal disturbance on a semi-infinite one-dimensional lattice of identical mass particles coupled by identical massless ideal springs is studied. With all but one of the particles at rest and all the connecting springs at equilibrium length at t = 0, the end particle is constrained to move with fixed longitudinal velocity for all t ≥ 0. Use is made of a method in which an infinite system of differential equations of motion is replaced by a single ordinary differential equation; the time-dependent Fourier coefficients of the equation's solution are the respective displacements from equilibrium of the individual lattice particles. These displacements and the corresponding velocities are expressed in terms of definite integrals. The results of velocity computations are presented along with asymptotic velocity distributions on the lattice and are discussed in relation to a simplified propagation description posited in a recent introductory textbook. The case of a semi-infinite elastic continuum subject to essentially the same initial and boundary conditions is worked out as a limit of the solution of the problem for the lattice.
A Useful Form of the Minkowski Diagram
Authors: Parker Leonard , Schmieg Glenn M.
Published: August 2005

We give a diagrammatic representation of the diagonal form of the special Lorentz transformation. The null coordinates x±ct are plotted along a single set of orthogonal axes. Special Lorentz transformations are then represented only by a change of scale along those orthogonal axes. This diagram, which we call a null coordinate diagram, and the Minkowski diagram are closely connected. To demonstrate the use of the null coordinate diagram, we apply it to the linear Doppler effect, time dilation, and Lorentz contraction.
Matrix Interaction for EPR Spectrum in a Paramagnetic Crystal under External Stress
Authors: Brenman M.
Published: August 2005

Using a method based only in group theory, and having in mind that many of today's experiments in EPR are done with paramagnetic crystals under external stress, we want to give those starting to work with this technique some idea how to write down a complete expression for the total interaction without assuming any model such as the spin Hamiltonian. This matrix interaction will have more parameters than the spin Hamiltonian, and we will decide the contribution of each one solely by experiment. We show the results of some experiments in transition and rare earth ions, and the equivalence between spin Hamiltonian parameters and the matrix interaction one.
Possible Origins of Internal Symmetry
Authors: Penney Robert V.
Published: August 2005

It is argued that the existence of the Pauli and Touschek transformations for the four-component neutrino field is a simple consequence of the fact that the basic wave function is a direct sum of two elementary spinors.
Electromagnetic Momentum, Energy, and Mass
Authors: Rohrlich F.
Published: August 2005

Electromagnetic systems of finite mass (m > 0) and of zero mass (m = 0) are considered. For both cases the electromagnetic energy and momentum are computed and are shown to lead to essentially different formulas. An invariant expression for the electromagnetic mass in m > 0 systems is derived. All m > 0 results are then specialized to the electrostatic case. Historical and present day confusion in the literature is discussed.
A Variation on Melde's Experiment
Authors: Blair J. Morris
Published: August 2005

A modification of the conventional driven vibrating string experiment is described which makes use of steel wires of various diameters and shows the effects of the stiffness of the wire on the tension required to make the wire resonate with the driving force.
Integral Equation Formulation of One-Dimensional Quantum Mechanics
Authors: James Philip B.
Published: August 2005

The transformation of the one-dimensional Schrödinger equation to an integral equation is described. Several interesting problems are analyzed using this formulation. The level of the material is such as to be appropriate for a senior level undergraduate course in quantum mechanics.
Lippmann Color Photography for the Undergraduate Laboratory
Authors: Schwall Robert E. , Zimmerman Peter D.
Published: August 2005

With the advent of holography in the undergraduate laboratory and the availability of very fine grain, essentially panchromatic emulsions, it has become relatively easy to produce color photographs by the Lippmann method. An experiment developed in the advanced physics laboratory at Stanford is described here. The elementary theory of the Lippmann process is presented along with a procedure for producing monochromatic plates using a hydroquinone developer and a procedure for producing natural color plates using a pyrogallol developer.
A Coulomb's Law Balance Suitable for Physics Majors and Nonscience Students
Authors: Larson Curtiss O. , Goss Everett W.
Published: August 2005

The PSSC soda straw balance is adapted to make it applicable to a study of Coulomb's law. Because of the inherent simplicity of the balance, it is well suited to nonscience students as well as physics majors. A calculation is made to determine a correction for the redistribution of charge as conducting spheres of finite radius are brought near each other in the Coulomb's law experiment. Typical data are presented to illustrate the value of this simple balance as a teaching device.
Multiple Reflection in Potential-Barrier Scattering
Authors: Beam J. E.
Published: August 2005

The standard quantum mechanical problem of scattering of an incident plane wave by a rectangular potential barrier in one dimension is examined from a point of view which emphasizes the multiple-scattering contributions to the reflected and transmitted, waves. This approach is used to gain insight into the phenomenon of resonant scattering of a wave packet by a potential barrier.
The Evolution of the Two-Dimensional Maxwell-Boltzmann Distribution
Authors: Novak John , Bortz Alfred B.
Published: August 2005

A computer simulation of a two-dimensional ideal gas has been studied in order to observe the time development of the speed distribution function. The results described here are effective in demonstrating to naturally skeptical freshmen that the Maxwell-Boltzmann distribution indeed occurs in nature. The results are also useful to demonstrate the statistical nature of the second law of thermodynamics.
Determination of Interference Patterns from Laser Produced Schlieren Interferometry
Authors: Penner S. S. , Davidor W. , Bien F.
Published: August 2005

The known expression for the Doppler frequency shift may be used in the derivation of the relation for interference-intensity patterns in Young's modified double-slit arrangement with a monochromatic source. Alternately, the statement that the interference-fringe maxima formed in the observation plane must move downward as a density gradient ahead of a collimating lens moves upward are sufficient to establish Doppler's law for the effect of velocity on frequency shift. The theoretical result has actually been confirmed by Schwar and Weinberg in experiments that were designed to demonstrate the use of schlieren interferometry with a laser source in velocity measurements on flames.
The Computer in General Physics Instruction
Authors: Stannard C.
Published: August 2005

This paper describes an experimental use of computer terminals for instructional purposes in a university-level general physics course over a 2-yr period. Programs have been written to simulate physical problems otherwise difficult for the student to investigate. The student specifies all of the important parameters and observes the calculated result which can be displayed in graphical form. Prior to the simulated experiment, a tutorial series of questions in a multiple choice format is used to familiarize the student with the problem and to help him make an intelligent parameter selection. Similar questions can be used to guide the analysis of the results after the calculations and to allow him to repeat the simulation with variations of any or all parameters. In the particular example given here, the student can launch a satellite into orbit with his own choice of parameters. The program ensures that be cannot consider physically meaningless values. The results of computer managed instruction (CMI) programs, student reactions to them, estimates of their cost and the present and future impact of the computer on our physics curriculum are discussed.
Radiation from a Uniformly Accelerated Charge
Authors: Atwater H. A.
Published: August 2005

The radiation from a uniformly accelerated charge is calculated by transformation of the covariant field tensor with the use of a transformation law which is designed to preserve the velocity of light in the accelerated frame. Both the accelerated charge as seen by a resting observer and a charge at rest as seen by a uniformly accelerated observer are shown to exhibit radiation under these conditions.
A Note on the Uniform Field Approximation when Guard Rings Are Used
Authors: Asano Kazutoshi , Dipert Arnold W. , Hendricks Charles D.
Published: August 2005

The uniform electric field approximation of parallel plates with guard rings is well recognized. However, near corners a high electric field exists in some circumstances, and it can give rise to electron or ion emission. A theoretical study of this field intensity, for example, shows that for a 10-mm electrode separation, 2-mm gap between an electrode and a guard ring, and a 0.005-mm corner radius, the electric field is as high as 5.4 times the uniform field found between infinite plane electrodes.
Elementary Treatment of Relativistic Cross Sections
Authors: Terrall J. R.
Published: August 2005

The primary purpose of this paper is to show that, when relativity must be taken into account, there is no need to revise the ordinary definition of a cross section. Rather, a slight rearrangement of factors will obtain Lorentz invariant quantities. To demonstrate invariance is quite simple. Next, the reaction rate density can easily be written down just by bringing together, from a particle viewpoint, the various factors we know on physical grounds should be present. Again, by judicious grouping, the result can be expressed as a product of factors that are separately invariant. We go on to discuss the Lorentz transformation of an angular distribution (without explicitly using the Lorentz transformation equations), the relativistic normalization of wave functions, and finally, the connection of our simple approach with S-matrix theory.
An Alternative to Perturbation Theory
Authors: Niblack W. K. , Nigam B. P.
Published: August 2005

A matrix method alternative to perturbation method is proposed. The method is applicable even when some of the off-diagonal elements of the Hamiltonian are large, it does not require a nondegenerate “unperturbed Hamiltonian.” The method proposed is not a perturbation theory in the usual sense, since it does not require the interaction potential to be small, and its convergence or lack of convergence can be determined during the course of the calculations, since the method depends on an iterative procedure.
Recent Progress Toward a Theory of Tensor Operators in the Unitary Groups
Authors: Louck James D.
Published: August 2005

The theory of tensor operators in the unitary groups is developed in a form which parallels the familiar Racah-Wigner angular momentum calculus. The presentation is principally an attempt to synthesize published results into a comprehensive whole.
Resource Letter Neu-1 History of the Neutrino
Authors: Lederman Leon M.
Published: August 2005

Prepared at the request of the AAPT Committee on Resource Letters.

This is one of a series of Resource Letters on various topics, intended to guide college physicists to literature and other teaching aids that may help them improve course content in specified fields of physics. No Resource Letter is meant to be exhaustive and complete. In time, there may be more than one letter on some of the main subjects of interest. Comments and suggestions concerning the content and arrangement of letters as well as suggestions for future topics will be welcomed and should be addressed to Professor Joel E. Gordon, Chairman, AAPT Committee on Resource Letters, Department of Physics, Amherst College, Amherst, Mass. 01002.

Notation: An asterisk (*) before an item number indicates items of particular fundamental importance.

Reprints: Individual reprints of this Resource Letter may be obtained by sending 25 cents (in cash) per copy, together with a stamped and self-addressed envelope, to the Executive Secretary, American Association of Physics Teachers, 335 East 45th Street, New York, N. Y. 10017.
Approach to a General Physics Course for Natural Science Students
Authors: Barón Máximo , de Ransemberg Perla A.
Published: August 2005

On the basis of past experience in the physics department (Facultad de Ciencias Exactas y Naturales, Univ. de Buenos Aires) a general physics course for natural science students was organized by making a careful selection of subject content, organizing lab and discussion periods, and devoting a number of lecture hours to discuss papers selected from current literature.
Theory of a Ball Rolling on a 1/ρ Surface of Revolution
Authors: Andersen C. M. , von Baeyer Hans C.
Published: August 2005

The equations of motion for a ball rolling without slipping on a 1/ρ surface of revolution are derived and applied to the case of the ball scattered by the surface. Our result is a simple integral for the scattering angle. In the limiting case that the ball is small, the integrand is a known function. In the general case it contains several power series.
Robert Grosseteste on Refraction Phenomena
Authors: Eastwood Bruce S.
Published: August 2005

This translation of the treatise by Robert Grosseteste (1167–1253) On the Rainbow (1235) categorizes the then-known types of optical phenomena as results of direct, reflected, and refracted light. His discussion of optics as a geometrical science, concerned therefore with explanation rather than description alone, introduces the following subjects: real visual rays, the law of refraction in terms of the law of reflection, the position of an image in refraction in terms of image-position in reflection, the rainbow, and color theory. Whereas all these discussions show the primitive state of the science, the law of refraction and the attribution of refraction to the rainbow are notable as the first influential attempts along these lines in the history of optics.
Liquid Crystals and Newton's Rings
Authors: Jeppesen Myron A. , Hughes William T.
Published: August 2005

Studies of the birefringence of liquid crystals by means of Newton's rings are described. Some results for 4-4′-dihexoxyazoxybenzene are given. These experiments are suitable for student laboratories.
On the Operational Definition of Radiation in Wheeler-Feynman “Action-at-a-Distance” Electrodynamics
Authors: Leiter Darryl
Published: August 2005

The basic structure of Wheeler-Feynman “action-at-a-distance” electrodynamics is reviewed in an attempt to better understand the details of how the process of radiation is described in this theory. In action-at-a-distance electrodynamics, radiation is not associated with a single current, but instead involves both an “emitter” charge and a “receiver” charge in its definition. We study this process in detail and show the exact manner in which this definition of radiation can be made to agree with the conventional Maxwell-Lorentz definition of radiation. As a practical example of this definition of radiation, the Rayleigh-Jeans blackbody radiation law is derived within the Wheeler-Feynman electrodynamic framework.
Characteristics of Compressible Fluids and the Effects of Heat Conduction and Viscosity
Authors: Horie Y.
Published: August 2005

The behaviors of the characteristics of compressible fluids are known to be singular when the parameters of usual heat conduction and viscosity laws become zero. The understanding of existing resolutions requires a fair amount of sophistication in mathematics. Presented here is an heuristic explanation appealing to simple physical reasoning.
Dimensionality Effects on the Fermi Gas
Authors: Kapron Felix P.
Published: August 2005

It is shown how the elementary properties of one-, two-, and three-dimensional free electron gases may be obtained as special cases of a general formulation. The exercise is suitable for a student and furthermore suggests that the concept of nonintegral dimensionality may serve to describe finite geometries as intermediate between the usual integral types.
Graphical Method of Teaching Elementary Collisions
Authors: Rutledge Harley D.
Published: August 2005

A graphical method of teaching elementary collisions is explained. The traditional method consists of an introduction to the conservation laws of linear momentum and energy followed by a treatment of two-body collisions with a few special cases as examples. The new method yields universal solutions to head-on collision problems with the target at rest by the use of parameters and graphical analysis at a mathematical level that students can understand. The time required for classroom presentation is little more than that of the traditional method. The author concludes that the graphical method is better than the traditional method because of increased student interest and comprehension. The results suggest an experiment utilizing a linear air track or similar apparatus.
Algebraic Solution of the Kepler Problem Using the Runge-Lenz Vector
Authors: Collas Peter
Published: August 2005

The Runge-Lenz vector is used to obtain the equation for the Kepler orbits algebraically and the frequency of small oscillations of a particle about a stable circular orbit. The invariance of the Hamiltonian under the Lie algebras generated by the components of the Runge-Lenz and angular momentum vectors is discussed.
Core Course for Science Majors Combining Material from Physics, Chemistry, and Biology
Authors: Pickar Arnold D.
Published: August 2005

In view of the increasing interdependence of the sciences and of the growing curricular demands upon students of science, a new program encompassing material from introductory majors-level courses in physics, chemistry, and biology has been developed. This core course is a two-year sequence which is designed to prepare students to undertake an advanced undergraduate program in any of these fields beginning in their sophomore year. The syllabus and special features of the course are discussed and several of the ongoing problems are reviewed.
Remark on the Harmonic Radius Vector
Authors: Buchdahl H. A.
Published: August 2005

This note is concerned with certain questions relating to the definition of, and the uniqueness of, the “harmonic radius vector” as introduced by Fock within the general theory of relativity.
“Glorified Shadows” in Molecular Scattering: Some Optical Analogies
Authors: Kong Pilwon , Mason E. A. , Munn R. J.
Published: August 2005

Optical analogies are extensively used in understanding quantum-mechanical phenomena. In the present paper, we show that such analogies are useful in discussing the “glorified shadows” seen in molecular-beam experiments. These analogies provide additional insight into the phenomena and have considerable pedagogical value.
A Discriminating Laboratory in Elementary Mechanics
Authors: McFarlane W. K.
Published: August 2005

A new laboratory was tried out for a first course in physics, the subject matter being entirely Newtonian mechanics with calculus. The aim was to teach experimental methods from design of the experiment to final report, as well as to communicate some basic physical ideas. The use of experiments to discriminate between rival theories was emphasized. A high standard of maturity was expected. Except for one section, teaching assistants handled the instruction. The laboratory was successful in most of its aims and got moderately favorable reactions from the students.
Diagonalization and Renormalization of the One-Boson Lee Model
Authors: Trubatch S. L.
Published: August 2005

Renormalization in simple quantum mechanical systems is illustrated by diagonalizing the Hamiltonians for the displaced harmonic oscillator and the one-boson Lee model. The diagonalizing transformation for the one-boson Lee model is found by generalizing its dressing transformation. The renormalized fermion masses in the diagonalized Hamiltonian are found to be q numbers.
Undergraduate Laser Diffraction Experiments Using Large Objects
Authors: Berko Stephan , Lee Yon G. , Wright Fulton , Rosenfeld Jon
Published: August 2005

Apparatus by which students can conveniently observe diffraction and interference phenomena from large objects is described.
Radiative Lifetimes of Some Electronic States of Helium
Authors: Chin-Bing Stanley A. , Head Charles E. , Green Albert E.
Published: August 2005

In this paper, we describe our measurements of the radiative lifetimes of the 33P, 33D, 41D, and 43D electronic states of helium, using a low-energy positive ion accelerator. The lifetimes in nanoseconds are 33P (111±5), 33D (14±3), 41D (34±4), and 43D (32±1). In addition, we discuss the desirability and feasibility of introducing undergraduates to this type of research.
The Potential of a Point Charge between Capacitor Plates
Authors: Glasser M. L.
Published: August 2005

The potential of a point charge between two grounded conducting plates is expressed as a definite integral, simplifying a previous formula due to Pumplin. The potential is obtained exactly in closed form along a line passing through the charge.
Thermoelectric Power Experiment for the Advanced Laboratory
Authors: Greenslade Thomas B.
Published: August 2005

Apparatus suitable for measurements of the thermoelectric power of wires in the temperature region from 77 to 300 K is described. An outline of the theoretical treatment of thermoelectric power is presented and typical results are given for aluminum, gold, and iron. This experiment has been used in the undergraduate advanced laboratory.
The Merry-Go-Round and Schwarzschild Coordinates: A Comparison
Authors: Laurent B. E.
Published: August 2005

The behavior of the Schwarzschild metric inside the gravitational radius is compared to the behavior of the flat space metric in rotating coordinates when rω > 1. In both cases the time is imaginary and the spatial line element indefinite with regard to sign. In both cases the physical interpretation is the same: Observers at rest (in the coordinate system) do not exist.
Euler Potentials
Authors: Stern David P.
Published: August 2005

The representation of a magnetic field by the cross product of the gradients of two scalars has recently seen wide use in plasma physics and in the study of energetic particles in space. The properties of such a representation are reviewed and examples of its application are given.
Circuit Response Using Fourier Series with Experimental Verification
Authors: Jones H. W. , Wallingford J. S.
Published: August 2005

As an illustration of a general method for calculating the circuit response of a network subjected to a periodic signal, the case of an RC circuit driven by a square-wave generator is worked out in complete detail for three values of a circuit parameter. A computer is used to add a sufficient number of Fourier sinusoidal terms and to plot out the circuit response. A criterion for the number of terms needed is given. For comparison, the exact solution is also presented. Experimental verification is achieved by photographing the screen of an oscilloscope which is connected across the proper circuit element. The resulting photographs are enlarged (in effect) to the exact size of the computer plots onto transparent film. An overlay of the transparencies on the computer plots give excellent agreement.
A “Derivation” of Maxwell's Equations
Authors: Krefetz Elliott
Published: August 2005

Herein is presented a student-teacher oriented examination of how one might arrive at Maxwell's equations via a number of reasonable assumptions.
Further Developments in Generalized Classical Mechanics
Authors: Rodrigues Ligia M. C. S. , Rodrigues P. R.
Published: August 2005

Transformation theory for mechanics with higher derivatives is investigated. Poisson brackets previously introduced are proved not to be invariant under canonical transformations. A new definition of Poisson brackets is proposed and it is found to be invariant. Hamilton-Jacobi theory is established.
Stokes Parameters for Quantum Systems
Authors: Collett Edward
Published: August 2005

The classical Stokes polarization parameters are extended to treat quantum systems. This is accomplished by using the semiclassical radiation theory and considering only radiation by the dipole mechanism. The identification of the Stokes parameters with the density matrix elements is noted. The Stokes parameters for a number of familiar quantum systems which undergo dipole radiation are then calculated.
Methods of Proof and Applications of the Virial Theorem in Classical and Quantum Mechanics
Authors: Killingbeck J.
Published: August 2005

This article reviews the assumptions made in deriving the classical and quantum forms of the virial theorem and gives some alternative methods of derivation. A study is made of the use of the virial theorem in approximate calculations on classical and quantum systems, with emphasis on variational processes which involve a change of length scale. A detailed example is provided by the use of the virial theorem in computing the approximate frequency of a classical anharmonic oscillator.
Handed Products and Axial Vectors
Authors: Gelman Harry
Published: August 2005

Two closely similar cross products of two vectors are considered. It is shown both formally and pictorially that only one of these transforms as an axial vector, the other transforming as a polar vector, under proper and improper spatial rotation. It is pointed out, however, that because the difference between the products has not generally been recognized, the conventional right-handed cross product has been almost universally assumed to transform as an axial vector, whereas, in fact, it transforms as a true vector. It is also shown that just as there are two cross products, there are also two closely similar curl operations, one leading to an axial vector, the other to a vector. Free-space electrodynamics is considered as an example of a physical theory in which curls and cross products appear. It is shown that with the appropriate set of conventions, the magnetic field can be regarded as a vector rather than as an axial vector.
Brillouin Scattering in Toluene
Authors: Johnson D. C. , Shine R.
Published: August 2005

An experiment on Brillouin scattering, which is suitable for an undergraduate laboratory, is described. A measurement is made of the change in frequency of light scattered through 90° by toluene. The result is used to calculate the velocity of the corresponding phonon.
Information Theory and the Approach to Equilibrium
Authors: Robertson Harry S. , Huerta Manuel A.
Published: August 2005

After a general discussion of thermodynamic equilibrium and the information-theoretic formulation of equilibrium statistical mechanics, illustrative calculations are presented of the evolution to equilibrium of a finite segment (the system) of an infinite coupled harmonic-oscillator chain, most of which is regarded as the heat bath. The reduced Liouville function ρN is used to define the information-theoretic version of the Gibbs entropy as SN = −kB  ∫  ρN ln(hρNN)dΓN. This entropy evolves to a proper equilibrium value as |t| → ∞ from time-reversible dynamics, because ρN spreads from an initially sharp distribution to a diffuse one characteristic of the heat bath in equilibrium. The approach is regarded as generally valid, in principle, although the procedure is most easily carried out in the treatment of coupled harmonic-oscillator systems.
Experiments in Magnetohydrodynamics
Authors: Rayner J. P.
Published: August 2005

Three student experiments in magnetohydrodynamics (MHD) are described which show that the electrical conductivity of the local water supply (∼3×10−3 mho/m) can be sufficient to produce observable effects. Measurements are made of the distribution of induced voltage along a diverging duct, the power extracted from a duct under load, and the change in the pressure gradient along a duct produced by an applied MHD body force.
Pacific Northwest Association for College Physics, a Many-Body Problem
Authors: Johnson Wilbur V.
Published: August 2005

On 7 May 1966, physics instructors from nearly 50 institutions, meeting in Seattle for the Third Northwest Conference on College Physics, voted to establish a regional association of physics faculties in Alaska, Idaho, Montana, Oregon, and Washington. Formally designated the Pacific Northwest Association for College Physics, the resulting organization has worked steadily since then for the improvement of physics teaching and research in the area. The following article describes the status of college physics in the Northwest, briefly discusses the structure and role of the Association, and summarizes the programs it has sponsored or is planning.
Intensity Correlations from Pseudothermal Light Sources
Authors: Haner A. B. , Isenor N. R.
Published: August 2005

An experiment for observing intensity correlations from pseudothermal light sources is described. Analog rather than digital electronics is used. Results are obtained that show clearly the relation between amplitude interference and intensity interference. Gaussian, two-slit, and uniform-brightness disk sources are used. The application of this experiment to the understanding of stellar-intensity interferometry is pointed out.
Least Squares Fitting of Data to Pseudolinear Relationships
Authors: Steinbach Wayne R. , Cook David M.
Published: August 2005

A general method is presented for applying the principle of least squares to determine the constants C, D, E, and k that optimize the fit of experimental data to a relationship between a dependent variable y and an independent variable x expressible either in the form h(y) =  Cf(x) + Dg(x) + E or in the form h(y) = Cf(k; x) + Dg(k; x) + E, where h, f, and g are arbitrary functions of the indicated arguments. Analysis of the first form is essentially identical with analysis of a bilinear form, and an analytic solution can be obtained; analysis of the second form involves an iterative process in which the value of k is assumed, tried, and successively revised until the principle of least squares is satisfied to a specified accuracy. The resulting formulation makes the broad utility of the principle of least squares more apparent than is often the case, stresses particularly the importance of weighting to the correct application of the principle and can be easily specialized to cover a wide variety of commonly occurring relationships such as straight lines, quadratic polynomials, exponentials, power laws, Gaussian curves, the Lorentz line shape, and sinusoidal functions.
Some Applications of Detailed Balancing
Authors: Oster Ludwig
Published: August 2005

The principle of detailed balancing is used in a consistent manner to derive equilibrium distribution functions, such as the Maxwell-Boltzmann and Saha-Boltzmann distributions, and the Bose-Einstein and Fermi-Dirac distributions. The same technique is then applied to matter at very high temperatures at which radiation and elementary particles are in thermodynamic equilibrium, that is, to situations postulated in supernova explosions and the early stages of an evolutionary universe.
Resource Letter PD-1 on Particle Detectors
Authors: Trower W. Peter
Published: August 2005

This is one of a series of Resource Letters on various topics, intended to guide college physicists to literature and other teaching aids that may help them improve course content in specified fields of physics. No Resource Letter is meant to be exhaustive and complete. In time, there may be more than one letter on some of the main subjects of interest. Comments and suggestions concerning the content and arrangement of letters as well as suggestions for future topics will be welcomed and should be addressed to Professor Joel E. Gordon, Chairman, AAPT Committee on Resource Letters, Department of Physics, Amherst College, Amherst, Mass. 01002.
Experiments in Pulsed Ultrasonics
Authors: Palmer S. B. , Forster G. A.
Published: August 2005

Apparatus is described to generate and detect pulsed ultrasonics in solids and liquids over the frequency range 1–20 MHz. The equipment should be useful for demonstration purposes in teaching laboratories because of its low cost and ease of construction. Experiments are suggested for velocity of sound, elastic constant and ultrasonic attenuation measurements on various materials over a wide temperature range (1–400 K) and results on polycrystalline chromium obtained with this apparatus are presented.
Physics and the Vertical Jump
Authors: Offenbacher Elmer L.
Published: August 2005

The physics of vertical jumping is described as an interesting and “relevant” illustration for motivating students in a general physics course to master the kinematics and dynamics of one dimensional motion. The equation for the height of the jump is derived (1) from the kinematic equations and Newton's laws of motion and (2) from the conservation of energy principle applied to the potential and kinetic energies at two positions of the jump. The temporal behavior of the reaction force and the center of gravity position during a typical jump are discussed. Mastery of the physical principles of the jump may promote understanding of certain biological phenomena, aspects of physical education, and even of documents on ancient history.
Classroom Use of Interactive Computer Graphics
Authors: Hearn Dwight D. , Reed Alan
Published: August 2005

A computer graphics laboratory and its classroom use are described. Specific lecture demonstrations in relativity and quantum physics are also discussed.
Particle Identity Entropy and Maxwell-Boltzmann Counting
Authors: Boyer Timothy H.
Published: August 2005

The entropy SMB found from Maxwell-Boltzmann counting in classical statistical mechanics may be regarded as a sum of terms SMB = SQ + Sident, where SQ is the extensive entropy of thermodynamics and Sident is an entropy connected solely with the identity of particles. The failure to separate out Sident is seen to occasion one form of Gibbs's paradox.
Concerning Einstein's, Podolsky's, and Rosen's Objection to Quantum Theory
Authors: Hooker C. A.
Published: August 2005

Professor J. Jauch, in his recent book, Foundations of Quantum Mechanics, claims to resolve the paradox of Einstein, Podolsky, and Rosen. Jauch's approach is representative of that adopted by the majority of physicists. I argue that, although Jauch does exhibit a consistent quantum formalism for dealing with situations of the type involved in the original paradox, that formalism, so far from doing away with the paradox, serves only to highlight the difficulties of providing an acceptable physical understanding of it. The paradox must remain, therefore, as a central clue in the search for a more adequate understanding of quantum theory.
Inequalities of J. W. Gibbs
Authors: Falk H.
Published: August 2005

This paper contains a unified presentation of Gibbs' inequalities and some of their quantum-statistical generalizations.
One-Dimensional Model of a Diatomic Ion
Authors: Lapidus I. Richard
Published: August 2005

A one-dimensional model of a diatomic ion with δ-function atomic potentials is solved exactly. A molecular orbital calculation is also carried out and compared with the exact solution. The model provides a simple illustration of the general techniques which are used in more complicated and realistic calculations of molecular energy eigenvalues and eigenfunctions.
On Hidden Variables and Quantum Mechanical Probabilities
Authors: Wigner Eugene P.
Published: August 2005

An argument, due originally to J. S. Bell, is somewhat simplified and made more specific. It deals primarily with a quantum mechanical system consisting of the spins of two spin-12 particles. It shows that a description of the quantum mechanical measurement of the spin components of these two particles by means of hidden parameters is impossible if we assume that the parameters determining the outcome of the measurement of the spin of each particle are independent of the direction in which we decide to measure the spin of the other particle. The mathematical reason for the impossibility is analyzed.
Hamiltonians and Wave Equations for Particles of Spin 0 and Spin 12 with Nonzero Mass
Authors: Arunasalam V.
Published: August 2005

The formal mathematical structure of the truly Hamiltonian formulations of nonrelativistic and relativistic quantum mechanics is critically examined for both spin 0 and spin 12 particles with nonzero mass. It is shown that the relativistic quantum mechanics can, in principle, at least be fitted into a truly covariant Hamiltonian procedure where the Hamiltonian is a Lorentz-invariant world scalar (and is the negative of 12 the rest energy of the particle, regardless of its spin). In particular, a truly covariant Hamiltonian theory of the electron is presented. It will be seen that the Lorentz-invariant Dirac theory of the electron does not fall within the framework of a truly covariant Hamiltonian procedure. Further, the dynamical variables associated with the translational degree of freedom of the particle (such as the position, the canonical momentum, and the velocity four-vectors of the relativistic quantum mechanics) correspond precisely to the same variables of the truly covariant formulation of relativistic classical mechanics. The mathematical structure of relativistic quantum mechanics is seen to be rather similar to that of nonrelativistic quantum mechanics for both spin 0 and spin 12 particles with nonzero mass.
Energy-Momentum Conservation for Collision, Creation, and Annihilation Processes: Geometrical Derivation from a Very Simple Classical Action Principle
Authors: Dorling J.
Published: August 2005

It is shown by a geometrical argument that the action principle δ  ∑ i m0i  ∫  dτi = 0 (m0i is the rest mass of the ith particle taking part in the process; dτi is an infinitesimal element of proper-time along the ith particle's trajectory; the integrals are over all trajectories between any two spacelike hypersurfaces) leads directly to energy-momentum conservation for collisions and creation and annihilation processes. This action principle could be interpreted as a principle of maximum total “particle time” if the rest masses were thought of as the frequencies of certain periodic processes defined along the particle trajectories.
A Unified Approach to Introductory Physics Based on the Conservation Laws
Authors: Perry Bradley , Miller Charles
Published: August 2005

A new approach to introductory physics based on the conservation laws has been developed at Trinity College and used for the last three years. Classical and quantum physics are presented together as different levels of a unified and consistent description of the world. This approach has been incorporated into a one-semester course which lays a foundation for several different continuations.
Exact Partition Function for the Two-Dimensional Ising Model
Authors: Glasser M. Lawrence
Published: August 2005

We present a relatively simple derivation, based on Burgoyne's combinational method, of the Onsager formula for the partition function of the two-dimensional square Ising model.
A Simple Experiment on Fresnel Diffraction
Authors: Haskell Richard E.
Published: August 2005

An experiment is described in which the Fresnel diffraction pattern of a single slit can be displayed directly on an oscilloscope. The experiment requires a minimum amount of equipment and space. Results of the experiment are presented and compared with theoretical calculations carried out on a digital computer.
Resource Letter Scy-2 on Superconductivity
Authors: Ginsberg D. M.
Published: August 2005

Prepared at the request of the AAPT Committee on Resource Letters.

This is one of a series of Resource Letters on different topics, intended to guide college physicists to some of the literature and other teaching aids that may help them improve course contents in specified fields of physics. No Resource Letter is meant to be exhaustive and complete; in time there may be more than one letter on some of the main subjects of interest. Comments and suggestions concerning the content and arrangement of letters as well as suggestions for future topics will be welcomed. Please send such communications to Professor Joel Gordon, Chairman, Resource Letter Committee, Department of Physics, Amherst College, Amherst, Massachusetts.

Notation: The letter E after an item number indicates elementary level; the letter I indicates intermediate level; and the letter A indicates advanced material. An asterisk (*) indicates items particularly recommended for introductory study.

Additional copies: Available from the Executive Secretary, American Association of Physics Teachers, 335 East 45 Street, New York, N. Y. 10017. When ordering, request Resource Letter Scy-2 and enclose 25 cents per copy (not in stamps), together with a self-addressed stamped envelope.
Computers in the Physics Curriculum
Authors: Blum Ronald , Bork Alfred M.
Published: August 2005

The use of computers in the physics curriculum has been steadily expanding. The facilities now available to physics educators can be classified as interactive, semi-interactive, or non-interactive, according to the time required for the student to communicate with the computer. Interactive facilities, with times of the order of seconds, make possible educational use of the computer in a variety of modes: as a calculator, simulator, tutor, administrator, or producer of materials. The computer generally, and each mode in particular, is discussed in terms of its relevance to the teaching and learning of physics.
The Velocities of Light
Authors: Smith Richard L.
Published: August 2005

The definitions, the physical significances, the interrelationships, and the observability of seven velocities of light are discussed. One of the seven, the centrovelocity, is a new velocity which is introduced here. It is suggested that this velocity can be used for the description of the transport of electromagnetic radiation since it does not have any of the short comings of the standard definitions of the group velocity or the velocity of energy transport.
Sensitive Small Area Photometer
Authors: Levenson M. D.
Published: August 2005

A simple photometer capable of measuring small light intensities over small areas is described. The device is intended to be used in a student laboratory to measure the light intensities in a diffraction experiment from single or multiple slits. The photometer is inexpensive, rugged, and easy to construct. Typical experimental results are presented along with the theoretical predictions.
Einstein's Priority in Recognizing Time Dilation Physically
Authors: Rindler W.
Published: August 2005

It is shown that, contrary claims notwithstanding, apparently no one before Einstein in 1905 ventured the idea that all clocks in motion might go slow. And thus, however logical it would have been, there never existed a theory based on the axioms of length contraction and time dilation relative to the ether.
A Double Pendulum “Art Machine”
Authors: Romer R. H.
Published: August 2005

A double pendulum apparatus is described, with which a great variety of figures similar to Lissajous figures can be drawn. This apparatus has great appeal to users of all sorts. In addition to the use of this apparatus for drawing figures, several more advanced physical subjects can be studied with the aid of this instrument.
Relativistic Bohr Model with Finite-Mass Nucleus
Authors: Cushing James T.
Published: August 2005

An elementary but rigorous treatment is given of the Bohr model of hydrogenlike atoms in which first-order corrections are made for both the finite mass of the nucleus and for the relativistic motion of the electron. Particular attention is paid to the approximations necessary to obtain the energy levels first given by Sommerfeld.
A Quantum Shuffling Game for Teaching Statistical Mechanics
Authors: Black P. J. , Davies P. , Ogborn J. M.
Published: August 2005

A game is described in which students can use random numbers according to simple rules to simulate an Einstein model of a crystal and produce a Boltzmann distribution. Computer films exploit the game further to show heat flow rom hot to cold as a random process and to establish other results as a basis for further teaching on entropy. The theoretical status of the game is discussed in detail, and possible developments of other games are briefly considered.
Optical Simulation of the Origin of Contrast in the Electron Microscope
Authors: Ast Dieter G.
Published: August 2005

A simple setup is described that simulates an electron microscope imaging a two-dimensional lattice. The diffraction pattern in the back focal plane is large enough to be easily observed and manipulated. The origin of contrast can be demonstrated by filtering out the image contributions of the individual Fourier components. The experiment can be used to demonstrate Abbe's theory of the microscope, origin of phase contrast, and two-dimensional Fourier transforms.
The Reduction of the Dirac Equation to a Nonrelativistic Form
Authors: Moss R. E.
Published: August 2005

The positive and negative energy solutions of the Dirac equation for a free electron are completely decoupled using the method of small components. It is shown that this separation is formally equivalent to that obtained with the Foldy-Wouthuysen transformation but that the separation is achieved much more economically with the method of small components. The method may also be used to relate operators in the relativistic and nonrelativistic representations.
Inexpensive Pulsed Nuclear Magnetic Resonance Spectrometer
Authors: Du Bois R.
Published: August 2005

A compact and inexpensive fixed frequency pulsed nuclear magnetic resonance spectrometer is described. The apparatus is entirely self-contained and all units are bench made.
Size, Shape, and Orientation of Sonar Targets Measured Remotely
Authors: Chapman Seville
Published: August 2005

Interference principles permit remote measurement of size, shape, and orientation of sonar targets. Each pair of scatterers on the target creates a Fourier component in the intensity pattern in space. Fourier-type wave analyses of the pattern observed either (A) over about half a radian of aspect angles at two closely spaced frequencies, or (B) over about half an octave of frequencies at two closely spaced aspects yield amplitude and phase for each wave number. For pairs of scatterers, in method (A) transverse width between scatterers comes from wave numbers of amplitude peaks, radial depth from phase shift with frequency change. In method (B) depth comes from peaks, width from phase shift with change of aspect angle. Combining the n(n−1)/2 oriented separations from n scatterers, a unique outline drawing is obtained. Presumably dolphins use this process. Both methods have been demonstrated acoustically at about 14 kHz with an experimental setup costing $250. Five small speakers with maximum separation 90.3 cm act as scattering sources. Computer analysis yields all dimensions within a few centimeters or degrees for four- or five-source objects.