bluuebunny/crossref_metadata_2025 huggingface dataset:
A Rapid Abel Inversion
Authors: Wing W. R. , Neidigh R. V.
Published: August 2005

The well-known Abel inversion performs the often necessary task of recovering the original radial functional dependence from data representing a circularly symmetric system projected into one dimension. We present a simple, rapid, graphical technique (useful in the small computer-less laboratory) for performing this inversion.
Physics Teaching by the Keller Plan at MIT
Authors: Green Ben A.
Published: August 2005

The Keller plan (a self-paced, student-tutored, mastery-oriented instructional system) has spread widely in the six years of its existence, but mainly in teaching psychology. The paper reports experience with the plan in introductory physics. The results are strongly favorable; students report that they learn material more thoroughly and more efficiently. Lectures are used sparingly and mainly for motivation. Students may take as many as 20 written tests in a semester without complaint. Sophomore tutors grade the tests on the spot and have proven to be extremely valuable. The instructor's role is not to broadcast information but to manage a system and to write the necessary tests and other materials, as well as to give personal help to individuals in unusual cases.
Operation of Electric Motors from the Atmospheric Electric Field
Authors: Jefimenko Oleg
Published: August 2005

An electret-type electric motor and a corona-type electric motor have been constructed for operation from the earth electric field. The power is delivered to the motors by means of simple earth-field antennas with radioactive or sharp-point collectors. Initial results on the operation of the motors are reported.
On Presenting the Bohr Theory
Authors: Shonle John I.
Published: August 2005

In this paper we review some of the well-known objections to the standard presentation of the Bohr theory of the hydrogen atom. A proper use of the correspondence principle avoids these objections. We present a clear set of hypotheses which can all be retained in later developments of quantum mechanics. The energy levels are derived and the limitations of the correspondence principle are discussed.
Some Uses of Computers in Introductory Electric and Magnetic Field Mapping
Authors: Merrill John R.
Published: August 2005

Past publications concerning the uses of the computer in field mappings have stressed particular geometries for the charge distributions. This note presents general methods to find and map field patterns for general distributions of charges and current loops. Two fundamental programs are presented with illustrations of the student's uses of both. Both programs use subroutines as building blocks so that the student can write programs using very simple calls to subroutines. The programs are available in BASIC as implemented on Dartmouth's time-sharing computer system.
Anniversaries in 1971 of Interest to Physicists
Authors: Barr E. Scott
Published: August 2005

During the year 1971 there are major anniversaries of the birth or death of four men whose accomplishments and influence have been of importance to the development of physics. They are Hermann Ludwig Ferdinand von Heimholtz, Sir John Frederick William Herschel, Johann Kepler, and Lord Ernest Rutherford, Baron of Nelson. Brief accounts of their careers are given here.
Racah Algebra for Pedestrians
Authors: El-Baz E. , Castel B.
Published: August 2005

A self-consistent method which introduces adiagrammatic representation of angular momentum states is presented. The method is developed to describe the Racah algebra. Both the didactic and computational aspects of the graphical, method are stressed and numerous examples of applications are given.
Another Method for the Determination of c
Authors: Trudeau J. , Loh E. C. , Hartman P. L.
Published: August 2005

A free running multivibrator suitable for the student laboratory is described, in which a solid state light emitter and a photomultiplier tube coupled to it through a long light path are used as the regenerative feedback loop. The rms frequency deviation from the mean of one such oscillator is determined to be three parts in 107 over a period of several hours. By changing the optical path, a frequency change is introduced from which the speed of light c is determined. At present, the precision is limited by the optical system, the percentage error in the value of “c” being still two orders of magnitude greater than in the best modern measurements. Various tests, sources of error, and possible improvements are discussed with the idea that this method might eventually be made of comparable precision with that of Bergstrand et al.
Hellmann-Feynman Theorems in Classical and Quantum Mechanics
Authors: McKinley William A.
Published: August 2005

Theorems giving exact expressions for the derivative of the energy with respect to a parameter in the Hamiltonian for cyclic classical mechanical problems in both the relativistic and nonrelativistic cases are derived. Comparison is made with similar well-known theorems in the quantum mechanical case. Applications of both classical and quantum derivative relations are made to deduction of parametric dependence of the energy in simple cases, deduction of a meaning to the expectation value of the Dirac operator β, and construction of a test of consistency for a well posed problem in the theory of a Dirac particle in a bound state.
Collision Rates in Photon and Relativistic-Particle Gases
Authors: Gould Robert J.
Published: August 2005

The collision rate for nonrelativistic particle gases is proportional to the magnitude of the relative velocity of the two particles. For collisions involving photons, however, this kinematic factor is, instead, the relative velocity along the direction of the photon. An exact relativistic treatment of the general problem yields a formula which contains these results as special applications. The results derived are important for calculations of certain processes in cosmic radio and x-ray sources.
Scaling and the Virial Theorem in Mechanics and Action-at-a-Distance Electrodynamics
Authors: Andersen C. M. , Von Baeyer Hans C.
Published: August 2005

As a consequence of scale invariance, a conservation law is derived in nonrelativistic mechanics with a homogeneous potential. The virial theorem is an immediate consequence of this conservation law. A slightly different scale transformation is then presented, which yields the same conservation law but which can also be applied to the relativistic Coulomb problem. Finally, both the conservation law and the virial theorem are derived for relativistic two-body theory in the Wheeler-Feynman formalism, where they provide a generalization of the expression for the energy of a two-body system with circular orbits.
An Exactly Soluble Quantum-Mechanical Three-Body Problem
Authors: Lim T. K.
Published: August 2005

An exact solution is obtained for a model three-body system in which the particles interact through pairwise, harmonic oscillator, and spin-dependent potentials, the solution being achieved by a simple transformation to an appropriate coordinate system. In particular, it is shown that the S-state wave functions of the ground state of the triton span the two-dimensional representation of the symmetric group S3, are orthogonal, and resemble closely the Irving wave forms found so successful in variational calculations.
A Course on the Physics and Chemistry of Pollution
Authors: Hodges Laurent
Published: August 2005

A course on environmental pollution which stresses physical and chemical principles is described. It presents a unified discussion of air and water pollution and solid wastes with special treatment of pesticides, thermal pollution, radioactivity, and electric power generation. Historical and current statistics have been used extensively to set pollution problems in perspective.
Use of Metastable Atom Probe for the Study of Electron Dynamics
Authors: Dickinson J. Thomas , Lockhart James M. , Zorn Jens C.
Published: August 2005

We describe a method for the study of electron trajectories which depends on the electron impact excitation of neutral argon atoms to metastable states. The metastable atom probe (MAP) allows us to determine the current density in an electron beam as a function of two arbitrary coordinates with a spatial resolution better than 0.5 mm. The probe is sensitive to the effects of all factors which influence the electron trajectories, yet the MAP operates with such low atom beam densities that the perturbation introduced by the probe is very small indeed. The application of the MAP to the study of student-built electron guns is described; in particular an experimental verification of Snell's law for electron beams is presented.
Mathematics for Physicists: A Report on the National Study of Mathematics Requirements for Scientists and Engineers
Authors: Miller G. H.
Published: August 2005

The National Study of Mathematics Requirements for Scientists and Engineers is concerned with the mathematics recommendations of a large group of outstanding scientists and engineers for their respective specializations. This report considers the recommendations of 929 physicists in eight different specializations. Course recommendations are indicated so that advisors and students as well as interested physicists may use these ratings as relative guides in the selection of courses for degree preparation or for industrial background. General trends of the data are reported.
Vectors, Spinors, and Complex Numbers in Classical and Quantum Physics
Authors: Hestenes David
Published: August 2005

Multivector calculus is shown to unite vectors, spinors, and complex numbers into a single mathematical system with a comprehensive geometric significance. The efficacy of this calculus in physical applications is explicitly demonstrated.
A Minicomputer in a Senior Modern Physics Laboratory
Authors: Finegold Leonard
Published: August 2005

A minicomputer was recently introduced in a senior modern physics laboratory. Operating in a conversational mode, it has been an excellent way both of teaching students computing and of encouraging them to use a computer routinely. The choice of computer languages is discussed, and the advantages and possible disadvantages of a minicomputer are listed.
Conservation Laws and the Dispersal Equations for Chemical and Thermal Pollution
Authors: Pomeranz Kalman B.
Published: August 2005

The dispersal of chemical pollutants by diffusion and convection in a fluid medium may be described in terms of a second-order partial differential equation for the concentration as a function of the spatial coordinates and the time. This dispersal equation is derived by applying the principle of the conservation of mass. From the conservation of energy principle an analogous equation may be derived for the dispersal of thermal energy by the processes of conduction, convection, and radiation. Special forms of these dispersal equations reduce to the standard partial differential equation for diffusion and heat conduction; and other special forms of the dispersal equation may be applied to study the cases in which the chemical material or the thermal energy is dispersed by convective motion in the fluid.
Quantizing Angular Momentum via the Simple Harmonic Oscillator
Authors: Friedman Charles P. , Taylor Edwin F.
Published: August 2005

The quantization of orbital angular momentum can be introduced simply through the model of the two- and three-dimensional simple harmonic oscillator. Most of the analysis is carried out in the familiar Cartesian coordinate system in which the simple harmonic oscillator Schrödinger equation is separable. Angular momentum eigenfunctions are constructed by superposition, and the resulting functions easily transformed into spherical coordinates. The angle-dependent parts of the solutions are the spherical harmonics, which are the orbital angular momentum eigenfunctions for all central potentials including the Coulomb potential of the hydrogen atom. The method also introduces the separation of variables technique and provides practice in applying the concepts of completeness, orthogonality, superposition of states, and alternative representations.
Brewster Angle and the Einstein Velocity Addition Theorem
Authors: Newburgh R. G. , Phipps T. E.
Published: August 2005

Linearly polarized light incident on a stationary medium at an angle whose tangent equals the relative refractive index is not reflected, provided the polarization is in the plane of incidence. Analysis of this situation for a moving medium leads to the prediction of a novel effect which is an unusual application of the phenomenon of aberration. The effect suggests a generalized experiment of the Fizeau type to determine the velocity of propagation in a moving refractive medium where the direction of propagation is not parallel to that of the motion of the medium. Such an experiment would examine the Einstein velocity addition theorem. The significance of the Fresnel drag law in relation to the Fizeau experiment is discussed, as well as Potier's principle which sets forth a universal consequence of the Fresnel law.
An Undergraduate Experiment on Nuclear Lifetime Measurement Using the Doppler Effect
Authors: Campbell J. L. , O'brien P. , Mackenzie I. K.
Published: August 2005

The Doppler broadening of gamma rays emitted during the motion of excited nuclei is measured with a high-resolution Ge(Li) detector. Results are interpreted in terms of the excited state lifetime and the processes by which the nuclei are brought to rest in condensed matter. While designed for a senior undergraduate laboratory, the experiment illustrates the principles involved in the various Doppler techniques currently used in nuclear lifetime studies and demonstrates the versatility of the Ge(Li) detector in applications other than direct energy or intensity measurement. The value 55±10 fsec obtained for the lifetime of the 477-KeV state in Li7 is in good agreement with values reported in the literature.
An Experiment on Experiments in a Senior Laboratory
Authors: Finegold Leonard , Hartley Charles L.
Published: August 2005

Two experiments were introduced in our senior modern physics laboratory to acquaint students with methods of doing complete experiments. In the “design” experiments, students individually chose, planned, designed, and listed all the apparatus, methods, and people required for a real experiment that might take several years to do. In the “ingenuity” experiments, students individually chose, planned, acquired, built, and assembled the apparatus for a relatively simple experiment and analyzed their measurements. We tested, by special laboratory examinations and other methods, if the half-class of students who had done these experiments were better than the half-class that had not.
Intensity Measurements in a Fresnel Diffraction Pattern
Authors: Boyer R. , Fortin E.
Published: August 2005

An experiment is described for the undergraduate optics laboratory to verify the law of intensity in the Fesnel diffraction of a thin wire. A He-Ne gas laser is used as a light source and a CdS photocell as a detector to scan the diffraction pattern. The agreement with the theoretical pattern is remarkably good.
Relativistic Time for Terrestrial Circumnavigations
Authors: Hafele J. C.
Published: August 2005

Relative to a clock at rest on the Earth's surface, the time recorded by an ideal clock after a circumnavigation of the Earth depends not only on the speed and altitude but also on the direction of the circumnavigation and on the rotational speed of the Earth. Such a clock may run either fast or slow, depending on the direction and ground speed for the circumnavigation. This directional dependence should be perceptible with commercial jet speeds and cesium beam clocks.
Measuring the Speed of Light with a Laser and Pockels Cell
Authors: Page Don N. , Geilker C. D.
Published: August 2005

A relatively simple experiment is described for measuring the speed of light to three significant digits in an undergraduate research project. A laser beam modulated by a 21.3-MHz signal applied to a Pockels cell is used in an interferometer arrangement patterned after Palmer and Spratt's simplification of Anderson's precision method.
Propagation of a Disturbance on a One-Dimensional Lattice Solved by Response Functions
Authors: Goodman Frank O.
Published: August 2005

Weinstock [Amer. J. Phys. 38, 1289 (1970)] has studied the problem of the propagation of a particular disturbance on a one-dimensional semi-infinite lattice of similar atoms, coupled by nearest-neighbor ideal springs; a solution to the same problem, in infinite lattice form, was given earlier in a book by Morse and Ingard [Theoretical Acoustics (McGraw-Hill, New York, 1968) p. 91]. The problem is essentially the following: Given a one-dimensional lattice that is stationary for all times t<0, what is the response of the lattice if one of the atoms (the end atom in the semi-infinite lattice case) is constrained to move with constant velocity for all t≥0? The method of response functions was developed by the author [J. Phys. Chem. Solids 23, 1269 (1962)] to solve related problems involving n-dimensional infinite and semi-infinite lattices; a summary of this method is presented for the special case of the one-dimensional lattices, and it is shown how it may be used to solve this problem in a slightly more general form.
The Origin of Exchange Interactions
Authors: Larsen Ulf
Published: August 2005

Although it is well known that the exchange interaction is a basic property of Fermi systems, the available derivations of this interaction usually involve special assumptions that tend to obscure its origin. In this paper we present a more general derivation free from these assumptions. We show that this derivation leads directly to the diagrammatic representation of perturbation theory first used by Hugenholtz. The s-d exchange Hamiltonian of Kasuya is derived as a special case for systems with localized states.
Topics in Technology and Modern Social Problems—A New Course for Science Students
Authors: Morgan M. Granger
Published: August 2005

A pilot course is described that was designed to provide advanced undergraduate science students with an opportunity to explore the way in which several fields of science and technology interface with society at large. In addition, the course was designed to allow students to explore their interests and aptitudes for career work in the science-society interface area. Enthusiastic student response has led to plans to expand the course to a full year offering and suggests that similar courses would be well received by science students at other liberal arts colleges and universities in the country.
Evolution of the Quantum States of a Harmonic Oscillator in a Uniform Time Varying Electric Field
Authors: Parker G. W.
Published: August 2005

When a system of particles in a bound state is placed in an external field the quantum state of the system depends on the manner in which the field is produced. The two limiting cases of interest are the adiabatic and impulse limits. Since the system does not approach a stationary state in either limit, in general, it is necessary to consider solutions of the time dependent Schrödinger equation. An example of this approach is provided by the problem of a harmonic oscillator in a uniform, time varying electric field for which an exact solution is easy to obtain using the Magnus expansion for the evolution operator. This operator contains the position and momentum in a particularly simple way that allows it to be interpreted in terms of position and momentum shifts produced by the field. The wavefunction of the oscillator is obtained in the adiabatic and impulse limits assuming the field to be switched on in an exponential fashion. Results obtained for these two limiting cases are then shown to be independent of the manner in which the field reaches its final steady value.
Linear Collisions
Authors: Walkiewicz T. A. , Newby N. D.
Published: August 2005

A discussion of linear collisions between two or three objects is presented. This presentation has proved to be very effective in a junior-level course in analytical mechanics. The theoretical discussion uses a geometrical approach that treats elastic and inelastic collisions from a unified point of view. This approach gives the student a physical "feeling" for the effect of imposing varying amounts of inelasticity on a two- or three-body collision. Momentum and energy constraints are used to delimit the region, in the space of final velocities, that contains all possible solutions. Experiments with a linear air track demonstrate how changing the interparticle forces produces widely differing final states og motion.
Lineair Chain with Free End Boundary Conditions
Authors: Kiwi Miguel , Rössler Jaime
Published: August 2005

The problem of energy propagation through a one-dimensional open-ended finite chain is critically re-examined. Free end boundary conditions are imposed and quantum-field-theory operators, consistent with these boundary conditions, are derived for both the local and total energy current operators, avoiding the shortcomings of previous work reported on the subject. The formal treatment is illustrated through an example, and a comparison with results obtained with cyclic boundary conditions is given.
Application of Racah Algebra to Molecular Point Groups
Authors: Cederberg J. W.
Published: August 2005

The techniques of the 3nj invariants are applied to the finite molecular point groups in the classification of states and interaction operators and the evaluation of matrix elements. The hydrogen spin-rotation of NH3 is worked out in detail as an example.
An Undergraduate Vacuum Ultraviolet Spectroscopy Laboratory
Authors: Stevenson James R. , Bartlett Roger J.
Published: August 2005

A laboratory is described that provides the student with a transitional experience between the more structured laboratories in introductory courses and the open-ended individual special problems. Vacuum ultraviolet spectroscopy has been chosen as the area of major emphasis as it provides an excellent vehicle for the student to learn a number of valuable experimental techniques. Experiments are outlined that use vacuum systems, radiation sources, dispersion, and detection systems to provide challenging laboratory experiences.
Oscillations of a Circular Membrane
Authors: Manzer A. , Smith H. J. T.
Published: August 2005

A transducer is described that enables the oscillations of a membrane to be monitored and the signal amplified so that very small vibrations may be used when measuring the eigenfrequencies. A method of identifying each mode is described.
On the “Derivation” of Einstein's Field Equations
Authors: Chandrasekhar S.
Published: August 2005

An attempt is made to clarify the physical and the mathematical reasonings that underlie Einstein's laws of gravitation. It appears that only by a mixture of physical reasonableness, mathematical simplicity, and aesthetic sensibility can one arrive at Einstein's field equations. The general theory of relativity is in fact an example of “the power of speculative thought.” The topics considered include a discussion of the principle of equivalence and the view of space-time as a geometric manifold. Two “derivations” of Einstein's equations are given: one based on physical reasonableness and the other based on a variational principle and mathematical simplicity.
A Quantum Equation of Motion with Higher Derivatives
Authors: Borneas M.
Published: August 2005

The problem of how to obtain a quantum equation of motion with higher derivatives is discussed. First the basic ideas of generalized classical mechanics with higher derivatives are reviewed. The generalized canonical conjugate momenta and a function N, corresponding to the Hamiltonian function, are constructed. Then certain reduced momenta are introduced, which in absence of higher derivatives are identical to the canonical conjugate momenta. The function N is expressed in terms of the reduced momenta. In order to obtain a quantum equation of motion, the reduced momenta in N are replaced by operators fulfilling some given conditions; thus the corresponding operator N̂ can be identified with the Hamiltonian operator. With its help, and introducing a wave function, the quantum equation of motion with higher derivatives is obtained.
The Hamiltonian of a Charged Particle in a Rotating Frame
Authors: Bow Y. F.
Published: August 2005

The transformation of the Hamiltonian of a charged particle from an inertial frame to a rotating frame in the presence of external electromagnetic fields is discussed.
A Teaching Strategy to Develop Physicist's Skills Early
Authors: Barbenza G. H. , Miguel O.
Published: August 2005

Aiming to develop from the introductory courses what can be called “physicist's skills,” we have employed a teaching strategy consisting mainly of independent study and small groups constantly supervised by the teaching staff. The Berkeley Physics Course is used as textbook, complemented with several laboratory experiments seeking the “discovery” rather than verification of physical laws.
Introducing Electron Creation and Annihilation Operators in Solid State Physics
Authors: Darby M. I.
Published: August 2005

A brief and simple introduction to the theory of many (N) electron systems that is suitable for undergraduates is given. By considering only three electrons (N = 3) it is possible to write out all the results explicitly. The manipulations of both determinantal wavefunctions and wave-functions in the number representation are considered, and the electron annihilation and creation operators are defined. It is then shown how the Hamiltonian for N electrons is written in second quantized form.
Laboratory Construction of Multilayer Dielectric Mirrors for He-Ne Laser Applications
Authors: Lashmore David S. , Baldwin Keith M.
Published: August 2005

A simple, low cost, evaporation-monitoring system for producing highly reflective, multilayer dielectric mirrors suitable for use with a helium-neon laser is described. Seventeen layer mirrors with reflectivity exceeding 99% have been constructed. Practical considerations such as substrate surface preparation and prevention of water absorption by the evaporated layers are discussed.
Matrix Elements of the Quadratic Stark Effect on Atoms with Hyperfine Structure
Authors: Schmieder Robert W.
Published: August 2005

The perturbation of atomic hyperfine levels by a weak uniform static electric field is discussed. For nearly all atoms, the effects linear in the field are identically zero, and the levels suffer small shifts proportional to the square of the field. The calculation of these shifts using ordinary second-order time-independent perturbation theory is presented. The advantages of separating the interaction into kinematical and dynamical parts and techniques for performing the separation are discussed. The algebra of irreducible spherical tensors is used to separate the interaction into parts having monopolar and quadrupolar symmetry. Some numerical values of the matrix elements of the quadrupole part are given (the monopole elements are trivial), and the shifts of the hyperfine levels due to this interaction are plotted as a function of field for some typical atoms.
Moments of a Wave Packet
Authors: Baird L. C.
Published: August 2005

The properties of a wave packet may be elucidated by a consideration of the statistical moments of the packet. The time evolution of the wave packet has an especially simple description in terms of moments.
The Second Balance Equation Associated with the Telegrapher's Equations
Authors: Chambers Ll. G.
Published: August 2005

A possible physical interpretation is given for the second balance equation associated with the telegrapher's equations.
Physics and Philosophy: A Problem for Education Today
Authors: Eger Martin
Published: August 2005

The teaching of the process of science in physics courses is discussed with reference to recent intellectual trends. Arguments and examples indicate that “process courses” must necessarily involve philosophical questions and questions of social criticism currently raised. A description is given of an interdisciplinary upper-division course for science and nonscience majors that incorporates some of the features advocated.
On the Ehrenfest Paradox
Authors: Sama Nicholas
Published: August 2005

Certain aspects of the so-called Ehrenfest paradox are discussed. It is pointed out that while the Ehrenfest description of uniform rotation is not in keeping with relativity, the “paradox” per se is independent of this fact, and rests solely upon an imprecise use of notation.
Clarification on Two Important Questions in Rigid Body Mechanics
Authors: Gruber Gary R.
Published: August 2005

In most courses on rigid body mechanics, many of the important subtleties are only superficially stated or investigated. In this article, we give two such fundamental questions (with solutions) that most students ponder upon without apparent resolution.
A Demonstration of Momentum Conservation using Bow, Arrow, and Ballistic Pendulum
Authors: Stoylov S. P. , Nsanzabera J. C. , Karenzi P. C.
Published: August 2005

The measurement of the variation of the velocity of an arrow V0 with the bending of the bow Δh using either a ballistic pendulum or the free-fall phenomenon provided in both cases coinciding linear dependences. These results create the possibility for the utilization of the bow, arrow, and ballistic pendulum for the demonstration and practical exercises of several important physical phenomena. In this paper greatest attention is paid to the demonstration of the momentum conservation principle.
Great Originals of Modern Physics
Authors: Decker Fred W.
Published: August 2005

European travel can provide an intimate view of the implements and locales of great discoveries in physics for the knowledgeable traveler. The four museums at Cambridge, London, Remscheid-Lennep, and Munich display a full range of discovery apparatus in modern physics as outlined here.
A Computer-Assisted Course In Intermediate Mechanics
Authors: Jirgal G. H.
Published: August 2005

This article describes an intermediate level mechanics course based on the solution by computer of seven problems. The nature of these problems and their solution by computer is discussed, and the sources of the programs indicated.
Geometrical Approach to Torque Free Motion of a Rigid Body Having Internal Energy Dissipation
Authors: Lamy Philippe L. , Burns Joseph A.
Published: August 2005

A geometrical approach, which differs from the classical Poinsot solution, is developed for the moment free motion of a rigid body in order to discuss the case when energy is dissipated internally. Conservation of angular momentum and conservation of energy are used, respectively, to construct two surfaces, a sphere S and an ellipsoid E, which always intersect along a closed curve C; some typical intersections are shown. The motion of the body is such that the lip of the angular momentum vector remains on a curve C. Although less complete than Poinsot solution, this geometrical description provides a check on some classical results and is particularly useful in characterizing the motion when the angular momentum is kept constant while the energy decreases; then the sphere S remains the same while the ellipsoid E shrinks. The final state, corresponding to the minimum possible energy configuration, is a pure rotation about the principal axis of maximum inertia. Many interesting problems (e.g., the rotational stability of artificial satellites, the axial alignment of asteroids, and the damping of the Chandler wobble for the Earth and pulsars) are discussed in the context of this solution.
Solution of a One-Dimensional Three-Body Problem in Classical Mechanics
Authors: Khandekar D. C. , Lawande S. V.
Published: August 2005

A one-dimensional problem of three equal particles interacting pairwise via a potential that is the sum of a quadratic and an inversely quadratic term is discussed from the point of view of classical mechanics. It is shown that the quantum energy spectrum can be obtained from the classical theory of action-angle variables and Bohr-Sommerfeld rules.
van der Waals, Boltzmann, and the Fourth Virial Coefficient of Hard Spheres
Authors: Nairn John H. , Kilpatrick John E.
Published: August 2005

The historic controversy between Van der Waals and Boltzmann concerning the correct way to calculate the fourth virial coefficient of a hard sphere gas is analyzed and put in modern notation. In this form it is easy to see what integrals would have to be evaluated in order to obtain the fifth virial coefficient by this method.
Why Did Newton See Indigo in the Spectrum?
Authors: Biernson George
Published: August 2005

The arrangement of colors in Newton's color circle suggests that it was derived from paint mixtures, not light mixtures. If this is true, we are led to conclude that what Newton called indigo represents violet in modern terminology, and what he called violet represents purple. The author hypothesizes that Newton saw seven reasonably distinct colors in the artist's paint mixture color circle (red, orange, yellow, green, blue, violet, and purple) and therefore assumed he could also see seven distinct colors in his crude spectral projections.
The First Stereoscopic Pictures of the Moon
Authors: Greenslade Thomas B.
Published: August 2005

Shortly after the announcement of the first useful photographic processes in 1839, the first photograph of the Moon was secured. This paper discusses some of the photographs of the Moon taken during the period 1840– 1864 and gives information on the processes which were used. The stereoscopic effect and the physical reasons which made stereoscopic lunar photographs possible are discussed, and some biographical material is given for two early workers in this field, Warren de la Rue and Lewis M. Rutherfurd.
On Renormalized Einstein Phonons. II. The Diagrammatic Method and Helmholtz Free Energy
Authors: Shukla R. C. , Muller E. R.
Published: August 2005

The Helmholtz free energy (F) of interacting Einstein oscillators has been presented as a simple working example of the diagrammatic method. All those diagrams (ring type in the present case) that contribute to F have been included, and the resulting series has the form of a logarithmic expansion. The summation of the series produces the wellknown formula for F.
A Suggestion on Teaching Gauss's Law in Elementary Courses
Authors: Sharon Yitzhak Y.
Published: August 2005

In introducing beginners to Gauss's law, we first emphasize the separate roles played by charges within and outside a Gaussian surface. We illustrate this in detail for the specific simple example of finite and infinite line charges. Students can thereby see more tangibly how unenclosed charges affect the flux distribution and the electric field, but not the total flux magnitude, on a Gaussian surface. The exact role of symmetry in Gauss's law applications to electric-field computations is also thereby elucidated for beginners.
Kepler's Anniversary
Authors: Postl Anton
Published: August 2005

The year 1971 marked the quadricentennial of Kepler's birth. Born in the medieval town of Weil der Stadt near Stuttgart, neither his parentage nor early education augured any future greatness as a natural philosopher or astronomer. Though he studied theology at the renowned University of Tuebingen, it was only after he was assigned to teach mathematics and astronomy in the remote Styrian town of Graz that he started on his way to fame as an astronomer. At first his own inclinations were more toward the classical and even mysterious ideals, but his later association with Tycho Brahe, the keen Danish astronomical observer, in Prague caused him to consider also the more mathematical-mechanical views. Though we owe to him the basic operational laws of planetary motion among many important contributions, he nevertheless mystifies us with his dream of a lunar voyage and his astrological views. In spite of the fact that his private life was racked with many personal problems and tragedies, he never lost his appreciation for the beauty and harmony of the universe.
On Black Body Radiation and the Attractive Force between Two Metal Plates
Authors: Mitchell D. J. , Ninham B. W. , Richmond P.
Published: August 2005

The dispersion force between two ideal metal plates is derived using a new method which places the emphasis totally on the sources of the electromagnetic radiation. Using this approach, the conceptual difficulty of how radiation in a perfectly reflecting cavity can ever achieve equilibrium with the surrounding medium is eliminated.
Galilean Invariance and the General Covariance of Nonrelativistic Laws
Authors: Rosen Gerald
Published: August 2005

The Galilean invariance of nonrelativistic laws is reviewed with particular attention given to the transformation properties of field-theoretic quantities. It is then shown that Galilean-invariant nonrelativistic laws generally manifest a broader covariance, the laws retaining their form under coordinate transformations to noninertial frames which move with arbitrary accelerative translational motion (without rotation) with respect to inertial frames.
Magnetic Fields of Current Carrying Wires—An Undergraduate Laboratory Experiment
Authors: Genova James J.
Published: August 2005

An undergraduate laboratory experiment is described which allows the student to make direct contact with his lecture course. The magnetic field of a circular loop and of a long straight wire is investigated using only a magnetic compass. As a result of this experiment the magnitude of the horizontal component of the Earth's magnetic field is determined.
Diffraction of Laser Light by Ultrasound in Liquid
Authors: Kang Pilwon , Young F. C.
Published: August 2005

Diffraction of light by a liquid carrying a sound wave enables a direct measurement of the acoustic wavelength in the liquid, and hence the acoustic velocity, if the frequency is known. The method of Debye and Sears for such measurements and an alternative method (striation or schlieren method) based on a visual display of standing wavefronts on a screen are reviewed. Measurements carried out with a He-Ne laser indicate that both methods work on the same diffraction phenomenon. Interpretation is given to the cause of image formation in the striation method, and a formula for the intensity distribution in the striation pattern is obtained. While utilizing a minimum of equipment, both methods illustrate some salient aspects of the compressional wave as well as physical optics and provide an excellent experiment for an advanced undergraduate laboratory or a lecture demonstration at an introductory level.
The Classical Limit of the Partition Function in Statistical Mechanics
Authors: McLellan A. G.
Published: August 2005

By using products of single-free-particle eigenfunctions for the container as a complete set of basis functions, a direct treatment is given of the approach to the classical limit of the partition function of an imperfect or perfect gas. This leads to a direct discussion of the case of a mixture of gases, thus making possible a natural discussion of Gibbs' paradox. The quantum correction is discussed, and the case of particles with spin is included.
Pinhole Imagery
Authors: Young M.
Published: August 2005

Despite its antiquity and apparent simplicity, the pinhole camera can be an interesting and useful device, boasting freedom from linear distortion, infinite depth of field, and wide angular field. The pinhole camera may be optimized for best resolution, and even its low aperture is largely offset by the availability of modern light sources and fast detectors. Clear understanding of this simple optical system yields a good deal of insight into physical optics and optical instruments.
Computer Solutions to the Schrödinger Equation
Authors: Chow P. C.
Published: August 2005

Numerical solution to the Schrödinger equation can be introduced to undergraduate students at the junior level. Numerov process is discussed in detail for the homogeneous differential equation and an extension of the method to inhomogeneous equations and self-consistent field calculations is briefly mentioned. An application to the simple harmonic oscillator is given as an example.
Interference between Elliptically Polarized Light Beams
Authors: Pescetti D.
Published: August 2005

Interference experiments (Young's double slit) between elliptically polarized light beams are described. The results show that when beams of light in orthogonal states of elliptical polarization are used no interference fringes are observed.
Resource Letter ERPEE-1 on Energy: Resources, Production, and Environmental Effects
Authors: Romer R. H.
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 Arthur Quinton, Chairman, Resource Letter Committee, Department of Physics, University of Massachusetts, Amherst, Massachusetts 01002.
Spreading Wave Packets—A Cautionary Note
Authors: Holstein Barry R. , Swift Arthur R.
Published: August 2005

The spreading of a quantum mechanical wave packet is studied from two apparently equivalent points of view. For certain classes of wave functions, one prescription predicts spreading while the other does not. Reasons for this anomaly are discussed.
Stimulated Emission and Bose-Einstein Statistics
Authors: Webb J. H.
Published: August 2005

Einstein's derivation of Planck's blackbody formula using the A and B coefficients for spontaneous and stimulated transition probabilities is reviewed. Application of the Einstein-Fowler equation for statistical fluctuations, 〈(ΔE)2〉 = kT2(δE/δT), shows that two terms contribute to the fluctuations, one from the particle nature of the system and one from its wave nature. When expressed in terms of the average number of quanta n̄, occupying g phase cells, the fluctuations become 〈(Δn)2〉 =  n̄ + (n̄2/g). This is exactly the first order variance 〈(Δn)2〉 of a system of n̄ particles distributed among g phase cells in Bose-Einstein statistics. If stimulated emission is omitted in the Einstein derivation, the Wien formula results, and the fluctuations become equal to the single term n̄, which is characteristic of classical statistics. Since the Planck law, which depends on both stimulated emission and stimulated absorption, gives fluctuation in accord with the Bose-Einstein statistics, whereas Wien's law, which depends on stimulated absorption alone, gives fluctuations in accord with classical statistics, it is concluded that the stimulated emission process is the mechanism responsible for the appearance of the Bose-Einstein statistics in blackbody radiation.
Calculation of Magnetothermodynamic Properties of Paramagnetic Ions in Axial Crystal Fields
Authors: Vishwamittar  , Puri S. P.
Published: August 2005

The relations between the roots and coefficients of the characteristic equation for the spin Hamiltonian have been used to derive the magnetothermodynamic properties of paramagnetic ions in axial crystal fields. The physical basis of the derivation is discussed and some illustrative examples are included.
Even and Odd Spectra of One-Dimensional Symmetrical Potential. II. Dirac Theory
Authors: Ronveaux André
Published: August 2005

The discrete spectrum of a one-dimensional symmetrical potential is studied within the framework of the Dirac theory and compared to the Schrödinger spectrum, using the variable phase approach. Separate Riccati equations characterizing the even and odd spectra are given, and transcendental inequalities yield energy bounds on the two lower states. Conditions sufficient to support one odd state are established, and some numerical results are checked for a square well potential.
Illustrating Key Problems that Can Lead Towards a Quantitative Physical Biology
Authors: Iberall A. S.
Published: August 2005

Waddington has questioned whether a theoretical biology can be formulated, analogous to theoretical physics. This paper proposes two problems that physicists might tackle. One is to account for the relation between weight specific blood flow and weight specific oxygen consumption that is found with changing activity level in mammals. An essentially unique correlation is shown to exist for all sizes of mammals over their full range of aerobic activity. The correlation applies to the entire macroorganism as well as to the local microvascular bed (e.g., in muscle). It is thus representative of design of the metabolic apparatus at an integrative cellular level. The second problem is to account for the laws of population change in complex biological species (e.g., the human). Physics reached classical maturity by relating the macroscopic properties of matter to underlying atomistic properties. The two problems posed, cast at two different systems' levels (one the organism and the other society), call for a “classical” correlation with their underlying atomistic sources (the governing processes in the microvasculature and in the individual's decision making).
An Experiment to Determine the Relative Permeability of Ferrites
Authors: Prasad B. S. N. , Shastry S. V. , Hebbar K. M.
Published: August 2005

Relative permeability μr of a ferrite rod can be determined by finding the series resonant frequencies of a simple L-C-R circuit with and without the rod inside the inductance coil. Compared to other methods employed for the determination, of permeability, this method is simple and easy to perform in the laboratory. Using the value of μr from this experiment, μ0—the absolute permeability of free space has been determined which provides a check for the correctness of this experiment.
Simple One-Dimensional Examples of Radiation
Authors: Mello P. A. , Moreno M.
Published: August 2005

A simple discussion is given to derive several qualitative properties of the radiation fields of a one-dimensional current density distribution. At the end of the paper an elementary analytical method is also given.
The Apparent Field of Gravity in a Rotating Fluid System
Authors: Fletcher R. Ian
Published: August 2005

The “gravitational” trajectories in a cylindrically bound rotating fluid are shown to generate exponential surfaces. Buoyancy, with respect to the noninertial system, is examined for the case of a rigid body submerged off-axis in the spinning fluid. Some consequences of the buoyancy and rotational forces in such a system are illustrated by the results of several experimental demonstrations.
The Twin Paradox in Special Relativity
Authors: Muller Richard A.
Published: August 2005

We resolve the twin paradox by calculating the relative ages of the twins first in the frame of the stationary twin and then in the frame of the accelerating twin. If we account for the effects of acceleration by keeping track of the instantaneous Lorentz frame of the accelerating twin, both calculations agree.
Momentum Autocorrelation Function of Noninteracting Particles in a Box
Authors: Cooper Colin A. , Davis H. Ted
Published: August 2005

The momentum autocorrelation function for noninteracting particles is evaluated in one, two, and three dimensions for microcanonical and canonical ensembles. Although the one-dimensional problem has been solved previously, it is felt that the technique used here of solving the problem by a superposition of square-wave functions is useful in that it is simpler and more physical than the previous approaches.
On Newton's Law of Gravitation
Authors: Rosenberg R. M.
Published: August 2005

Under the assumption that the gravitational force is a central force and diminishes with distance, Newton's inverse square law is shown to be the only one for which all simple finite trajectories are closed orbits.