bluuebunny/crossref_metadata_2025 huggingface dataset:
Resource Letter ECAN-1 on the Electronic Charge and Avogadro's Number
Authors: Anderson David L.
Published: August 2005

Prepared at the request of the AAPT Committee on Resource Letters; supported by a grant from the National Science Foundation.

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 Arnold Arons, Chairman, Resource Letter Committee, Department of Physics, Amherst College, Amherst, Massachusetts.

Notation: The letter E after an item number indicates elementary level, useful principally for freshman liberal arts through sophomore physics courses; the letter I indicates intermediate (junior, senior) level; and the letter Aindicates advanced material principally suited for senior, graduate study. An asterisk (*) indicates items particularly recommended for introductory study.

Additional copies: Available from American Institute of Physics, 335 East 45 Street, New York, New York, 10017. When ordering, request Resource Letter ECAN-1 and enclose a return envelope.
Kepler's Third Law and the Mass of the Moon
Authors: Miller Franklin
Published: August 2005

A noncalculus derivation of Newton's modification of Kepler's third law is given for two bodies of arbitrary masses revolving in elliptical orbits around their center of mass. Using this law and readily available astronomical data, an approximate value of the mass of the moon is calculated. At present, a precise determination of the moon's mass requires knowledge of the very small shifts of the earth from its mean orbit due to center of mass effects, although lunar probes will some day be useful for this purpose.
Intensity of Electron Beams
Authors: Helmer J. C.
Published: August 2005

The theories of D. Langmuir and J. R. Pierce on the thermal limitations of electron beam current density have a simple interpretation through geometrical optics and the law of photometric brightness. The brightness law together with Abbe's sine law are sufficient for the design of most electron beams for laboratory experiments. Application of the theory is illustrated for the design of low voltage, high-intensity beams as used in low-energy electron-diffraction experiments.
Propagators in Nonrelativistic Quantum Mechanics
Authors: Beauregard Laurent A.
Published: August 2005

A discussion of propagators (Green's functions) and methods for calculating them for the simplest systems in nonrelativistic quantum mechanics is given from several points of view. The relevance of such techniques to partition function calculations is pointed out. Finally, a simple perturbation theory is given for the case of the free particle.
Drake, Galileo, and the Law of Inertia
Authors: Losee John
Published: August 2005

Stillman Drake has argued that Galileo believed that inertial motion is rectilinear motion, and that certain of Galileo's references to uniform circular motion were part of a strategy against the Aristotelian geocentrists. Drake's arguments are examined and are found to be unconvincing.
Studies of Laser Light Scattered by a Moving Surface
Authors: Morgan Joseph , Lysiak R. J.
Published: August 2005

Visible light from a helium-neon laser was directed onto a white-card surface capable of rotation, and the granularity characteristics of the scattered light were observed. Photographs are given showing the degree of granularity observed under various rotational speeds. It is indicated that the visible granularity, due to the extremely high degree of coherence of the laser light, disappears from view as a consequence of persistence of vision when the light is scattered by a moving surface. Additional observations relating to the phenomenon of granularity are also presented and discussed.
Vector Differential Operations Derived from Physical Definitions
Authors: Bevc Vladislav
Published: August 2005

Vector differential operations can be introduced through their physical definitions which are independent of coordinate systems. It is shown how the components of the gradient of a scalar function and the curl of a vector can be calculated directly form their physical definitions.
Collateral Readings in the Philosophy and History of Physics for the Introductory Science and Engineering Physics Course
Authors: Erlichson Herman
Published: August 2005

The standard introductory course for the science and engineering students is too often completely crammed with formulas and problems and gives the beginning student no idea whatsoever of the excitement of physics, and of its philosophy, history, and research frontier. Several new introductory courses have made a fresh start and attenpted to introduce the excitement of research physics. However, very little effort has been expended on the other problem, that of making the beginning student aware of the philosophy and history of physics. This objective can be accomplished by a series of selected readings in the original literature and in the literature of the philosophy of physics. The author of this paper has experimented for several years with collateral reading of this nature in the introductory course and the results have been excellent.
Resource Letter PA-1 on Particle Accelerators
Authors: Blewett John P.
Published: August 2005

Prepared at the request of the AAPT Committee on Resource Letters; supported by a grant from the National Science Foundation.

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 Arnold Arons, Chairman, Resource Letter Committee, Amherst College, Department of Physics, Amherst, Massachusetts.

Notation: The letter E after an item number indicates elementary level, useful principally for freshman liberal arts through sophomore physics courses; the letter I indicates intermediate (junior, senior) level; and the letter A indicates advanced material principally suited for senior, graduate study. An asterisk (*) indicates items particularly recommended for introductory study.

Additional copies: Available from American Institute of Physics, 335 East 45 Street, New York, New York 10017. When ordering, request Resource Letter PA-1 and enclose a stamped return envelope.
Graduate-Record Examination Advanced Physics Test as a Predicator of Performance
Authors: Michels Walter C.
Published: August 2005

The performances of 124 physics graduate students in two departments have been compared with their Graduate Record Examination scores. It is indicated that the currently used forms of the Advanced Physics Test and the Quantitative Aptitude Test are satisfactory devices for predicting a meaningful probability that a student will be a successful candidate for the doctorate. Both tests, however, fail to distinguish among “fair,” “good,” and “excellent,” students. The GRE scores furnish information of significance for the admission of students to graduate departments but they cannot be counted upon to determine which students show highest promise or to which a limited number of fellowships or other financial aids should be awarded.
Language for Making Movies on a Computer
Authors: Cralle Robert K.
Published: August 2005

A report of the state of the art, the hardware, and software necessary for a computer language which allows an easy and immediate display of visualizable solutions, designs, etc., of physical systems and immediate visual response to orders to change any features of the display.
Physicists and Teachers
Authors: Strassenburg Arnold A.
Published: August 2005

A resume of the Commission on College Physics' role in programs to prepare physics teachers at all levels. The recommendations of the CCP Informal Conference on Teacher Training, Washington, D. C. 9–10 October 1965 are extensively reported.
Central Force Motion without Calculus
Authors: Parke William C. , Bergmann Otto
Published: August 2005

A method is described which enables one to derive the orbital equations for a body moving under the influence of a conservative force in terms of “central coordinates” and, for the important case of a 1/r2 force, to derive the equations of motion using only energy and angular momentum conservation without appealing to calculus. The method is applied to more general central forces where its usefulness is discussed, and it is shown that forces depending on a negative power of the radial distance to the body, allow the dependence of the scattering cross section on the incoming velocity of the body to be easily found. The relations between central coordinates and the ordinary Cartesian and polar coordinates are exhibited.
Effective Mass Concept in Solids: A Classical Analogy
Authors: Rivera C. , Infante C. , Claro F.
Published: August 2005

The purpose of this work is to explain the electron effective mass concept under the action of a periodic potential field in solids, in the context of classical mechanics. In this manner, the effective mass is expressed by a second-rank tensor as it appears in solids, and it can also be translated to the quaternion language.
Dispersion Relations in the One-Boson Lee Model
Authors: Scarfone Leonard , Brooks G. Lantry
Published: August 2005

The one-boson Lee model is used as a simple example for demonstrating how the methods of dispersion theory can be used to calculate state vectors, wavefunction renormalization constants, and self-energies without having to solve eigenvalue equations. This method of solution has been applied successfully to the original Lee model; in this paper we give some analogous calculations at a more elementary level. The same point of view was taken in a previous paper where the Lehmann-Symanzik-Zimmermann formalism was used to solve the first nontrivial sector of the one-boson case.
Use of a Classical Rotation Operator in Quantum Mechanics
Authors: Talpe Jan
Published: August 2005

A classical operator exp(α x), for the rotation of a vector about an angle α, is presented. Some properties are derived and its usefulness is illustrated in a quantum-mechanical calculation. The operator easily dispenses from specifying coordinates in three dimensional configurations, extending in this way the usefulness of rotors and cross products.
The Leibniz-Clarke Controversy: Absolute versus Relative Space and Time
Authors: Erlichson Herman
Published: August 2005

There is an increasing current interest in the philosophy and history of physics. This paper discusses an interesting and important (but relatively little known among physicists) controversy in the history of theories of space and time, the Leibniz-Clarke correspondence. Leibniz represents the relativist view of space and time. Clarke, a disciple of Newton, upholds the absolute space and time of Newtonian mechanics.
Concerning a Kind of Truncated Quantized Linear Harmonic Oscillator
Authors: Buchdahl H. A.
Published: August 2005

In quantum mechanics the linear harmonic oscillator representatives of the canonical observables q and p are certain well-known infinite square matrices, qmn and pmn, with denumerable sets of rows and columns. It is pedagogically useful to investigate various problems which arise when one considers the finite matrices Qmn and Pmn which result when qmn and pmn are truncated after the Nth row and column, where N( 2≥2)  is some preassigned positive integer. So that the enquiry may be more instructive, it begins with an abstract formulation of the problem of the “truncated harmonic oscillator.” Formally, the latter has the usual Hamiltonian H = 12( Q2+P2 ) , but Q and P are not canonical—their commutator [Q,P] now differing from i by a certain projection operator. The spectrum of H and the (finite) basis { |n〉}  generated by H are found by standard methods, though there are now some complications which are absent from the theory of the linear harmonic oscillator. The diagonalization of Q and P presents no difficulties if full use is made of the classical theory of Hermite polynomials. The spectrum of Q is the set of N zeros hs of the Nth Hermite polynomial. Although the wavefunctions 〈 Q′|n〉  are therefore functions of the discrete variable hs, one can formally contemplate them as functions of a continuous real variable h; and some curious intimations of Schrödinger representation appear. The analog of a component of orbital angular momentum is considered, and its spectrum obtained. Finally, the asymptotic limit N → ∞ is briefly discussed, in order thus explicitly to dispel the impression that this limit might somehow represent the “usual” linear harmonic oscillator.
Force on a Wire in a Magnetic Field
Authors: English A. C.
Published: August 2005

An analysis is given of the force acting on a metal or semiconductor wire carrying a current in a magnetic field in terms of the Hall field, diffusion forces, and electron gas pressures.
Electric Field of an Accelerating Charge
Authors: Tessman Jack R. , Finnell Joseph T.
Published: August 2005

The method of J. J. Thomson of analyzing the kink in the electric-field lines is used to obtain the expression for the electric field of a charged particle undergoing a parallel acceleration while moving at any velocity v less than c. Thomson originally applied the method to a slowly moving charge and thereby obtained a result correct to zeroth order in v/c. The technique is rigorously and directly applicable, without approximation, to a charge moving with large velocity. Thus one can obtain the acceleration field of a fast-moving charge without resorting to more elaborate treatments such as the use of the Lienard-Wiechert potentials.
Spark Chambers: A Simplified System for the Observation of Particle Trajectories in Two Types of Chambers
Authors: Sachs A. M.
Published: August 2005

A complete, simplified system has been designed and constructed for two types of spark chamber demonstrations: (1) A multiplate chamber for observation of penetrating cosmic rays; and (2) a “curtain-discharge” chamber for observation of β rays from a radioactive source, with curved trajectories in a magnetic field. Attention has been given to minimizing the cost of the components and the difficulties of fabrication and assembly.
Introduction to Resolution Distortion
Authors: Grissom J. T. , Koehler D. R.
Published: August 2005

The distortion of a distribution function due to the resolution of the experimental apparatus used to measure it is discussed, and the mathematical formalism connecting an “ideal” distribution with the corresponding measured distribution is presented. The approach is based on the use of a resolution function, which can be measured experimentally, to describe the distortion effects of the apparatus. The formalism is examined in general, and examples are used to illustrate some typical characteristics of distortion. The treatment given here can be usefully exploited in introducing this subject to the student.
Homogeneity of Time
Authors: Augustynek Zdzislaw
Published: August 2005

The contemporary theory of space-time contains a number of assumptions called invariance or symmetry principles. One of them is the principle of time-translation invariance, which expresses a symmetry property of time which is called its homogeneity. The principle of time homogeneity plays a fundamental role in physics and also has many philosophical connections. In spite of that it has not become, until now, the subject of a sufficiently broad and exact philosophical analysis. The present paper is an attempt to remove this gap. We consider here only central philosophical problems concerning the principle of time homogeneity: its physical meaning, its epistemological status, and its scope of applicability.
Second-Sound Experiment for Advanced Laboratories
Authors: Merrill John R.
Published: August 2005

This paper describes an advanced laboratory experiment concerning the propagation of second sound in liquid helium II. Both pulse propagation and standing-wave mode experiments are performed. Typical student data are presented. Both velocity and attenuation as functions of frequency and temperature are measured. Students' results agree well with published data. The student also learns how to handle liquid helium and its associated hardware.
Elementary Explanation of Lorentz-Fitzgerald Contraction
Authors: Parker E. N.
Published: August 2005

The electromagnetic fields of a charge q moving with velocity v through a medium of dielectric coefficient ε can be obtained in an elementary way, by analogy with the electrostatic field of a point charge, if v < c/ε12. Comparison of the two cases ε >> 1 and ε = 1 provides a simple physical explanation for Lorentz-Fitzgerald contraction of the field of a relativistic particle and hence for the contraction of any structure produced by electromagnetic interaction of such particles.
High-Vacuum System for Teaching and Research
Authors: Kendall B. R. F. , David D. R.
Published: August 2005

A simple, compact, and inexpensive high-vacuum system is described. It consists of a detachable vacuum chamber connected through a specially machined aluminum block to a conventional mechanical pump. The block contains all of the vacuum valves and ducts required for initial evacuation of the system, its maintenance at low pressures, and admission of sample gases. Residual vapors are pumped by zeolite-coated copper surfaces, which are housed in a detachable container connected to the block. The vacuum chamber can be pumped from atmospheric pressure down to pressures suitable for electron-beam experiments in approximately 90 sec. Ultimate pressures of 2 × 10−5 Torr can be achieved without cooling the zeolite. Pressures below 4 × 10−6 Torr are possible if the zeolite is cooled by liquid nitrogen. Applications of the system in lecture demonstrations, undergraduate projects, and graduate-level research are discussed.
Transmission Characteristics of Filters
Authors: Arlotto J. J. , Fox J. N.
Published: August 2005

A study is made of the light transmission of several optical filters, used individually and in combination. Measurements are made over a wavelength range of 0.36–0.75 μ. A strip-chart recorder is used to plot the output of a Barnes ES-100 educational spectrometer.
Evolution of a Gaussian Wavepacket
Authors: Blinder S. M.
Published: August 2005

An alternative derivation is given for the evolution in time of a Gaussian wavepacket representing a free particle. This is based on explicit evaluation of the action of the evolution operator on the initial wavefunction, rather than on expansions in free-particle eigenstates. Both the cases of a free particle initially at rest and in uniform linear motion are considered.
Student Laboratory Demonstration of Flux Quantization and the Josephson Effect in Superconductors
Authors: Richards P. L. , Shapiro Sidney , Grimes C. C.
Published: August 2005

A simple apparatus is described which permits observation of magnetic flux quantization and the alternating current Josephson effect in superconductors. The apparatus, which has been used successfully by students in the Advanced Undergraduate Physics Laboratory at Berkeley, consists of point contacts between two niobium wires which are attached to a probe so that the contact pressure can be adjusted while the contacts are in a storage Dewar of liquid helium. The current-voltage characteristic of the point contact junction is displayed on an oscilloscope. Flux quantization causes the zero-voltage current carried by the junction to oscillate as a magnetic field is applied by moving a permanent magnet close to the storage vessel. The ac Josephson effect causes constant voltage steps to appear on the current-voltage characteristic when a small amount of power from a K-band (∼24-GHz) klystron is coupled to the points.
The Low-Pressure Arc Positive Column in a Longitudinal Magnetic Field
Authors: Hoyaux Max F.
Published: August 2005

This is a review of the literature relevant to low-pressure arc positive columns in a longitudinal magnetic field. At low magnetic fields, and provided that the column is sufficiently long with respect to its radius, normal ambipolar diffusion prevails; however, above a certain critical magnetic field, plasma turbulence progressively sets in and leads to an abnormal loss of particles and an increase in voltage drop. The final discussion is relevant to the possible ultimate limit of applying Steenbeck's minimum principle to this type of column.
Matrix Methods in Quantum Mechanics
Authors: Merzbacher Eugen
Published: August 2005

Some standard results of matrix theory are derived in a manner designed to appeal to physicists and are illustrated by examples from quantum mechanics. Sylvester's formulas, expressing a function of any n-dimensional square matrix as a linear combination of the first n−1 powers of A, are applied to the evaluation of the rotation matrices D(i)(R) for low values of j. The neutral K meson is used as an example of the usefulness of matrix techniques for systems with two basis states.
Momentum of Longitudinal Elastic Vibrations
Authors: Gilbert I. H. , Mollow B. R.
Published: August 2005

The field-theoretic momentum of longitudinal vibrations in an elastic medium is not the same as the total momentum of the particles which constitute the medium. In this article, we discuss the connection between these two quantities in terms of a new conservation law which follows from an underlying symmetry of the system. The surprising feature of this conservation law is that it is expressed in terms of variables which refer to the medium only, and yet remains valid under a very wide class of couplings of the medium to external systems. The analysis is carried out within the context of a simple one-dimensional model which is easily generalized to three dimensions.
Formulation of Special Relativity by Means of Galilean Transformations
Authors: Gomberoff L. , Krause J. , López C. A.
Published: August 2005

Special relativity is formulated in terms of Galilean transformations. This is possible by using the principle of general covariance in the framework of special relativity. In particular the relativistic contraction of lengths and time dilation are discussed. It is further shown that classical electrodynamics also can be formulated consistently when using Galilean transformations. Finally, this result is illustrated by evaluating the field of a uniformly moving charge.
Einstein and the “Crucial” Experiment
Authors: Holton Gerald
Published: August 2005

This paper was presented on 5 February 1969 at a joint symposium of the AAPT and APS on the history and philosophy of physics, held during the AAPT-APS annual meeting.
One-Dimensional Hydrogen Atom
Authors: Haines Larry K. , Roberts David H.
Published: August 2005

The time-independent Schrödinger equation is solved for the bound state solutions of the one-dimensional Coulomb potential, −e2/|x|. The wave functions obtained are normalizable and continuous. The energy spectrum consists of a set of discrete levels with energies equal to the Bohr energies of hydrogen, and a set of continuum levels with energies lying strictly between the discrete levels. The odd wave functions associated with the discrete levels are differentiable everywhere, but the even wave functions associated with the continuum levels have a cusp with infinite slope at the origin. The energy levels are not degenerate. Following the method of Loudon, the bound state solutions of a truncated Coulomb potential −e2/(|x|+a), a>0, are also obtained. For small a, the discrete spectrum of this potential contains: (1) energy levels which approach arbitrarily close to the discrete levels of the true Coulomb potential as a→0, with odd wave functions identical to the odd wave functions of the true Coulomb potential at a = 0; (2) energy levels which approach arbitrarily close to the discrete levels of the true Coulomb potential as a→0, with, even wave functions which are not the even wave functions of the true Coulomb potential at a = 0; and (3) a ground state level belonging to an even wave function with an arbitrarily large binding energy as a→0. The ground state energy is quite sensitive to the actual value of a chosen. It is concluded that the solution to the one-dimensional hydrogen atom shows a critical dependence on the detailed behavior of the Coulomb potential at small distances.
Electrostatic Field and Force on a Dielectric Sphere near a Conducting Plane—A Note on the Application of Electrostatic Theory to Water Droplets
Authors: Davis M. H.
Published: August 2005

Because of the short charge relaxation time for water, an electrostatic solution for conductors usually applies. But to extend the analysis to very short interaction times, a solution is derived for the electrostatic field strength and force acting on a nonconducting dielectric sphere near a grounded conducting plane. This solution has more general interest, since it is one of the relatively few that are exact and apply to a physically realizable geometry.
A Nonlinear Klein-Gordon Equation
Authors: Scott A. C.
Published: August 2005

A simple nonlinear partial differential equation suitable for study by an undergraduate in applied science is discussed. Several physical realizations are outlined and the construction of an analog model is described. The equation is analyzed to determine nonlinear pulse and periodic waveforms, and the stability of these waveforms is investigated using a recently developed “averaged Lagrangian” technique.
On the Connections between Thermodynamics and Statistical Mechanics
Authors: Leff Harvey S.
Published: August 2005

The canonical, grand-canonical, and constant-pressure ensembles of statistical mechanics are related to thermodynamic functions by simple canonical forms. The basic such form is S̃ = klnQ, where S̃ represents a Legendre transformation of the entropy and Q is an appropriate partition function. This expression is of the Boltzmann form, which arises naturally in the microcanonical ensemble. The canonical structure, which is demonstrated, is pedagogically useful as (1) a memorization device, (2) an example of the utility of Legendre transformations in statistical mechanics, and (3) an aid in understanding the relationships of the various ensembles to one another.
A New Approach to the Measurement of Complex Impedance in the Undergraduate Laboratory
Authors: Everett Glen E. , Bruner L. J.
Published: August 2005

The use of the Hewlett-Packard Model 4800A vector impedance meter for complex impedance measurements in our undergraduate teaching laboratory has been very effective. The ease of operation of this direct reading instrument permits the student to obtain more significant results. Curves of impedance magnitude and phase angle for an inductor and capacitor, separately as well as for their series and parallel combinations, are shown as illustrations of the instrument's use. The directness of comparison between experiment and theory is shown by impedance magnitude log-log plots versus frequency, and polar plots versus phase angle.
Counterexample to the Tangherlini Argument
Authors: Rindler W.
Published: August 2005

Tangherlini has stated a set of postulates which lead to Schwarzschild's metric without the use of field equations. These postulates are shown to be inconsistent when applied to the parallel vacuum field.
Properties of the Discrete and Continuous Spectrum of a Central Potential under Scaling
Authors: Ronveaux André
Published: August 2005

Transformation properties of the phase shift and the scattering length corresponding to a change in the scale of length for the central potential V(r) are established. They are compared with the equivalent relations for the discrete spectrum of V(r). Corresponding variational relations emphasize the strong correlation between the strength and the range of the potential. Using dimensional analysis, one can predict the dependence on the scattering coefficients of the strength or the cutoff parameters in the potential.
James Clerk Maxwell and Thermodynamics
Authors: Garber Elizabeth
Published: August 2005

Although Maxwell was directly involved in teaching and writing a textbook on heat theory he did not actively engage in research in this area until after he had read Gibbs' papers on thermodynamics. The stimulus of Gibbs's first two papers on the thermodynamics of homogeneous substances was such that Maxwell went beyond Gibbs and developed his own ideas on heterogeneous substances. These concepts remained unpublished, probably because they were included in Gibbs's thermodynamics later. Maxwell developed the concept that Gibbs subsequently called the potential. He also realized the importance of Gibbs's work for chemistry as well as for physics and proceeded, privately and in public to make Gibbs's work better known. Not only did he work in thermodynamics but he also stimulated colleagues at Cambridge to start research in this area, several years before Gibbs was “discovered” by Ostwald.
Diffraction of Electrons by Standing Electromagnetic Waves: The Kapitza-Dirac Effect
Authors: Nieto Michael Martin
Published: August 2005

The Bragg diffraction of electrons off of a standing electromagnetic wave, first predicted by Kapitza and Dirac, is discussed. The original derivation of Kapitza and Dirac is reviewed. This is followed by a more general derivation, which uses quantum mechanical, Born approximation, scattering theory. A review of the recent experiment results is given. Because the Kapitza-Dirac effect reverses the usual roles of “particles” and “waves” in Bragg diffraction, the discussion emphasizes the physical insight that this phenomenon gives into light and the particle-wave duality of quantum mechanics.
Geometrization of the Relativistic Velocity Addition Formula
Authors: Brehme Robert W.
Published: August 2005

If we define the proper-time component, vτ, of the coordinate velocity to be vτ = cdτ/dt, the expression for the invariant interval between two infinitesimally close events on the world line of a particle leads to an equation vx2+vy2+vz2+vτ2 = c2. Allowing only motion in the x, y plane, we see that this equation is that of a sphere of radius c in velocity space. Each possible velocity in the x, y plane is represented by a different point on the surface of a sphere. If an object is observed from a set of inertial frames, all in relative motion with respect to one another in a given fixed direction, the locus of representative points on the sphere forms a great circle. A method is given for relating the relative velocity between two Lorentz frames to the angle between two points on the surface of the sphere for the special case in which all motion lies in the x direction.
On the Conservation Laws in Classical Mechanics
Authors: Chamorro Alberto
Published: August 2005

It is pointed out that any classical system having n degrees of freedom has 2n − 1 constants of motion which can be found from the dynamical equations. A subsequent analysis is made of the dynamical content of the conservation laws. In this connection, transformation theory is applied by using a complete set of dynamical variables that, in general, are not required to form a canonical conjugate set.
Gravitation and Two-Dimensional Curved Surfaces
Authors: Brehme Robert W. , Moore Wayne E.
Published: August 2005

A general method is shown for embedding Riemannian spaces in Euclidean or Minkowskian spaces. This method differs from those of others in that emphasis is placed on the pedagogical value of regarding Minkowskian spaces as Euclidean. The technique is applied to two-dimensional Riemannian surfaces. When the metric of the Riemannian surface depends on only one of the coordinates, the intrinsic geometry of the surface is the same as that of a surface of revolution curved in a Euclidean or Minkowskian three-space. The Schwarzschild radius-time plane and the radius-azimuth plane are given as illustrations of the technique.
New Aspects of the Teaching of Special Relativity
Authors: Rekveld J.
Published: August 2005

A brief survey is given of four new approaches to the teaching of special relativity, namely the so-called k calculus, methods based on the invariance of the space-time interval, the dynamical approach, and the introduction by means of thought experiments. Each approach has been illustrated with a few examples.
Rest Mass in Special Relativity
Authors: Leibovitz C.
Published: August 2005

Specialized literature deals occasionally with potentials for which the rest mass of a particle is variable. Proper attention should be given in the teaching of special relativity to the relation between the rest mass and the potential field in all cases. The case of a scalar potential is considered.
Exact Normal-Mode Analysis for a Linear Lattice with “Periodic Impurities”
Authors: Lee S. M.
Published: August 2005

The normal-mode analysis for a diatomic linear lattice of alternating point-masses of mass M and m is carried out by setting M = (1+ε)m, where εm is regarded as an “impurity” added to the basic mass m. A uniform chain containing particles of mass m is taken as the basic system which is modified by the addition of the impurities to alternating particles. Lagrange's equations of motion for the basic system are then modified by the inclusion of extra forces due to such impurities. A process of intermediate coordinate transformation, in which the modified equations of motion are written in terms of the normal coordinates of the basic uniform lattice rather than the original displacement coordinates, simplifies the analysis. The correctness of the analysis is verified by applying it to the systems containing several particles and comparing the results with those obtained by direct calculations.
Partial Differential Equation for the Time-Dependent Probability Densities of Quantum Mechanics
Authors: Kostin M. D.
Published: August 2005

The Schrödinger equation for the wave functions is used to derive a linear partial differential equation for the time-dependent probability densities, ħ24m δ3P(x, t)δx3 = 2V(x) δPδx + V′P(x, t) − 2δε(x, t)δx − mδj(x, t)δt, where P(x, t), ε(x, t), j(x, t) are the time-dependent position, energy, and current densities, respectively. In the limiting case where the system is in the nth quantum state, it is shown that this partial differential equation reduces to the previously derived third-order ordinary differential equation for the probability position density.
Dynamical Rotations of Spinors and Other Quantum Systems
Authors: Moore Gerald T.
Published: August 2005

The adiabatic theorem of quantum mechanics is used to investigate the dynamical rotations of quantum systems which are coupled to an external rotating field. The use of such rotations in combination with interference experiments in principle renders the sign change of spinors under 2π rotations observable. Some practical difficulties of such experiments are mentioned.
Harmonic Vibrations of Spherical Nuclei
Authors: Meyer Eugene
Published: August 2005

The simplest type of vibration, that in which the nucleus makes surface oscillations about an equilibrium spherical shape, is reviewed in light of current nuclear literature. Such a model, based on purely harmonic vibrations, shares some success with other models in describing the origin of nuclear level schemes. However, a detailed examination of known nuclear spectra and recent measurements of quadrupole moments and transition probabilities suggest that this approach is only semivalid, emphasizing the need to include anharmonicity in the vibrational Hamiltonian.
Conducting Spiral as an Acyclic or Unipolar Machine
Authors: Serra-Valls A. , Gago-Bousquet C.
Published: August 2005

This paper shows that a conducting spiral behaves as a unipolar machine. As a first approximation, the current in the spiral can be viewed as a superposition of a system of circular currents, which provide a magnetic field perpendicular to the plane of the spiral, and a radial current on which the Ampere forces produce a self-torque. An essential feature of unipolar machines is stressed, i.e., the relevant electromagnetic interactions take place between perpendicular currents and not between parallel ones, as happens in the other machines. A simplified series unipolar machine for laboratory and classroom instruction has been built and is discussed.
Absolutely Stable and Metastable Thermodynamic States of a Magnetic Model Exhibiting a First-Order Phase Transition
Authors: Kaplan J. I. , Stenschke H.
Published: August 2005

The thermodynamic states of a particular magnetic model are obtained in terms of the temperature, external magnetic field, and magnetic moment. The magnetic moment plays the role of the order parameter in the usual Landau theory of phase transitions. Absolute and local minima of the free energy as a function of the order parameter (the magnetization) are obtained which correspond, respectively, to absolutely stable and metastable states of the system.
Who Named the -ON's?
Authors: Walker Charles T. , Slack Glen A.
Published: August 2005

Many entities in physics have both particlelike and wavelike properties. In representing the particlelike properties physicists usually use words ending in -ON. The originators of the concept underlying the particle nature, and the coiners of the name are discussed for the following “particles”: boson, electron, exciton, fermion, magnon, neutron, phonon, photon, plasmon, polariton, polaron, proton, and roton.
Radar Cross Section of a Half-Wave Dipole
Authors: Mott David L.
Published: August 2005

The radar cross section of a half-wave dipole target is obtained by assuming that there are no losses in the scattering process and that the induced current has a simple waveform. The derivation serves to introduce the scattering matrix of a radar target.
Bremsstrahlung Radiation in Plasmas
Authors: Papadopoulos Konstantinos
Published: August 2005

A new, short derivation of the radiation formulas from a homogeneous, field free, nonrelativistic plasma is presented. The nonrelativistic assumptions are emphasized.
Absorption and Emission of Energy at Electron Cyclotron Resonance
Authors: Bloch S. C. , Brooker H. R. , KeKelis G. J.
Published: August 2005

Experiments are described in which the absorption and emission of energy at and near electron cyclotron resonance may be studied with simplified equipment. The magnetic field is measured by electron spin resonance, thus bringing out aspects of spin as well as orbital angular momentum; the magnetic field may also be measured by the radius of the electron orbit, rendered visible by low-pressure hydrogen. It is observed that, in a gas-focused electron beam tube, the frequencies of maximum electron cyclotron resonance absorption and emission (as determined by the zero crossing of the derivative of the line shape) are generally different from the frequency of electron spin resonance, and the frequency shifts are functions of electron beam current. The line shapes are asymmetric and are also functions of beam current. These effects are tentatively identified with plasma effects in the gas-focused beam.
One-Dimensional Atom
Authors: Klein James J.
Published: August 2005

A one-dimensional model of an atom is proposed that simulates some of the wavelike characteristics of the hydrogen atom. The model consists of an elastic string under tension in which the transverse waves simulate the ψ wave of the electron in an atom, and the waves of varying tension simulate the electromagnetic waves interacting with the atom. Because of its simplicity, the model may be useful, for teaching purposes, in introductory quantum mechanics courses.
Electromagnetic Momentum of Charged Particles
Authors: Cohn Jack
Published: August 2005

The current definition of the comomentum associated with a moving charge is discussed, and it is shown to be unsuitable for a charge undergoing nonuniform motion. An alternative definition is then proposed for a charged particle of vanishingly small size, and it is demonstrated that this definition is satisfactory for a charge in arbitrary motion.
When Does a Point on a Thermodynamic Diagram Represent a Unique State?
Authors: Thomsen John S.
Published: August 2005

The paramagnetic system discussed by Curry and Henry presents an example of isentropic curves appearing to intersect when viewed in the H-M plane. A similar example is given by liquid water near its density maximum when represented in the p-V plane. These apparent paradoxes arise because a point in a particular coordinate plane may correspond to two or more different thermodynamic states of the system. By a slight generalization of Trevor's earlier analysis, a sufficient condition is derived for choosing the (n + 1) variables describing an (n + 1)-degree-of-freedom system so that each point represents a unique thermodynamic state. For a simple fluid the (T, p), (T, V), (S, p), and (S, V) representations satisfy the uniqueness condition; the widely used (p, V) and (T, S) ones do not.
Legendre's Equation for Undergraduates
Authors: Bragg Lincoln E.
Published: August 2005

Expansion of solutions in powers of sineθ has been recently suggested as a means of avoiding strain on students when discussing Legendre's differential equation. Suggestions are made for easing the strain further during the determination of the solutions, the part of the analysis which is made naturally easy by this mode of expansion. The problems that are not made as easy are discussed, such as the problem of deciding which solutions are physically acceptable.
A Simple Alternative to Double Groups
Authors: Brown E.
Published: August 2005

The representations of point groups appropriate to spin-12 particles is usually determined by consideration of a group of double the order of the point group under consideration, known as the double group. An alternative approach is described which makes use of ray representations. The character tables for the 32 crystallographic point groups are derived simply by means of this approach.
Laser Roulette and Other Diversions
Authors: Browne M. E. , Ingerson T. E.
Published: August 2005

The use of games for teaching introductory physics is discussed. The elements of game design are reviewed, and seven examples are described that illustrate different varieties of teaching games suitable for use by beginning physics students.
The Linearized Boltzmann Equation. Navier-Stokes and Burnett Transport Coefficients
Authors: Ernst M. H.
Published: August 2005

The Boltzmann equation is linearized around total equilibrium and solved by means of a projection operator, which projects the single particle distribution function on the slowly varying local density, temperature, and stream velocity. For small spatial variations the exact solution approaches asymptotically to the Chapman-Enskog normal solution with a relaxation time of the order of the mean free time. The heat current and pressure tensor obtained from this solution are connected with the gradients of the local temperature and stream velocity in a nonlocal and noninstantaneous manner by means of time correlation kernels. For large times and small gradients, the transport currents are expanded in gradients of the local densities, yielding expressions for the Navier-Stokes and linear Burnett coefficients as matrix elements of the linearized Boltzmann collision operator. An Onsager relation between two linear Burnett coefficients is demonstrated.
Similarity Transformation and the Eigenvibration Problem of Certain Far-Coupled Systems
Authors: Chen Fan Y.
Published: August 2005

Similarity transformation can be used advantageously to compute the eigenvalues and the corresponding eigenvectors of multi-degree-of-freedom far-coupled, vibration systems with equal masses and equal spring stiffnesses.
How to Sum a Finite Series
Authors: Albright J. R.
Published: August 2005

The summation of series is considered as a problem analogous to that of evaluating a definite integral. Each series that can be handled in this way gives rise to an “indefinite sum.” A table of summands and their corresponding indefinite sums is provided, along with suggestions for testing the correctness of table entries and for extending the table. The methods of summing are applied to several examples taken from standard physics courses.
Underspecification of the Quantum State
Authors: Reisler Donald L.
Published: August 2005

The state representative for a composite system cannot be uniquely reconstituted solely from knowledge of the state of the constituents. Spin and angular momentum examples are used to illustrate this behavior. The need and motivation for holistic principles to allow the determination of a single state is discussed.
An Introductory Scattering Experiment by Simulation
Authors: Merrill John R. , Morrow Richard A.
Published: August 2005

An introductory physics laboratory concerned with scattering particles off various force centers is reported. The experiment uses simulation techniques and a computer. The scattering is classical, and the student examines plots of computed particle trajectories. The results illustrate the concepts of differential cross section, total cross section, and effective potential. Introductory students understand the calculational method geared to the computer. The response of both students and faculty has been very positive.
Expulsion of Free Electronic Charge from the Interior of a Metal
Authors: Saslow W. M. , Wilkinson G.
Published: August 2005

Using the frequency dependent conductivity, we show that electronic charge is expelled from the interior of a metal by setting up an oscillation driven by the Coulomb repulsion at the plasma frequency. This oscillation damps out in a time on the order of an electronic collision time. The usual textbook derivation does not obtain this result because it discusses this high-frequency phenomenon in terms of the zero-frequency conductivity. In the case of poorer conductors which do not support plasma oscillations the usual treatment is valid.
Data Smoothing
Authors: Grissom J. T. , Koehler D. R.
Published: August 2005

A class of methods is derived for data smoothing based on minimizing an error function consisting of two terms. The first term is the weighted sum of the squares of the deviations between the smoothed values and the original data, and the second term is the weighted sum of the squares of the (k+1)st order finite differences of the smoothed values. The method embodies two arbitrary parameters. Specifying the value of k chooses one member of the class of methods. The other parameter is a weighting factor that determines the degree of smoothing achieved at each point. Limits on the value of the weighting factor can be imposed based on the statistical properties of the data.
A Ramiform View of Unpredictable Events
Authors: Hart Roger G.
Published: August 2005

This is an attempt to reconcile the formalisms of quantum mechanics with ordinary macroscopic experience. Thus the formal superposition of alternative physical states is interpreted as an actual superposition of differing “copies” of the same object or objects. Chance events usually regarded as mutually exclusive are here assumed to have simultaneous effects on different copies of the same system, including its human observers. In this way, initially superposed copies become separated and undergo differential changes. Reconvergence of differentiated copies gives rise to familiar diffraction phenomena. Specific physical examples and human experiences are treated, and the Schrödinger equation is derived.