bluuebunny/crossref_metadata_2025 huggingface dataset:
Nonholonomic Constraints and Gauss's Principle of Least Constraint
Authors: Ray John R.
Published: August 2005

The form of the equations of motion for a mechanical system subjected to nonholonomic constraints is discussed. A modified form of Gauss's principle of least constraint is used to derive the equations of motion for systems with nonlinear, nonholonomic constraints. Other derivations of these same equations of motion are discussed.
More about Variable Mass Systems
Authors: Siegel Stan
Published: August 2005

Through the use of an example, it is indicated how the subject of variable mass systems may be introduced to even beginning students.
Measurement of the Magnetic Properties of Superconductors
Authors: Hendricks J. B. , Bloom R. W. , King C. A.
Published: August 2005

An advanced undergraduate laboratory experiment is described that employs a variation of the superconducting flux pump and commercially available magnetometer to measure the critical temperature, transition width, and the Meissner effect in type I superconductors in small external magnetic fields. The experiment is intended as an introduction to low-temperature techniques and to the magnetic properties and uses of superconductors.
Computer Augmented Physics Lab
Authors: Geller Kenneth N. , Newstein Herman
Published: August 2005

A computer augmented physics lab has been developed for the third-quarter introductory physics course in wave motion, sound, and light. New experiments are designed with application to interesting phenomena of the real world. The speed of sound and its temperature dependence are measured using time-of-flight techniques. Phenomena of reflection, refraction, diffraction, and anomalous propagation (mirage) are studied using the He-Ne laser. The computer is used to process and analyze experimental data and to extend experimental observations through simulation.
Relativity in an Undergraduate Laboratory—Measuring the Relativistic Mass Increase
Authors: Parker Sherwood
Published: August 2005

A method is described for measuring the relativistic mass increase using simple, inexpensive equipment. The effect is large and easily seen.
The Hall Effect in a Flowing Electrolyte
Authors: Wright John J. , Van Der Beken Stephen
Published: August 2005

This experiment demonstrates that a charged particle moving through a magnetic field experiences a force qv × B. When a saltwater solution flows through a magnetic field, the positive and negative ions are separated by the Lorentz force and establish an electric field. This field is measurable by means of the potential, or Hall voltage, developed across the flow tube.
An Undergraduate Experiment in Fourier-Transform Spectrometry
Authors: Berkey Donald Keith , King Allen L.
Published: August 2005

The construction, theory, and application of a simple Fourier-transform spectrometer for an undergraduate student laboratory experiment are described and illustrated. The instrument is a modified, commercially available, inexpensive Michelson interferometer, and the Fourier transform is produced by a time-shared computer, using a program in basic based on the Cooley-Tukey fast-Fourier-transform algorithm.
Cumulative Experiments in the Advanced Laboratory
Authors: Graetzer Hans G.
Published: August 2005

An advanced laboratory course for physics seniors is described that uses open-ended projects organized in such a way that all of the students work on each project in turn. The students change every two or three weeks from one project to another, each time being confronted with an ongoing experiment to which they are asked to make their contribution. The laboratory notebooks contain the cumulative total of a group effort. Individual experiments can be carried to considerable depth, but at the same time the individual students are not confined to the limitations of working on just one project.
A Simple Procedure for Computing Density of States Spectra in Solid State Physics
Authors: Buchheit M. , Loly P. D.
Published: August 2005

The histogram method for computing density of states spectra is simplified considerably for the cubic lattices. As an example we treat the fcc lattice by randomly sampling a cube in k space (composed of octants from two adjacent Wigner-Seitz cells of the reciprocal lattice). Graphical results for the magnitude of the group velocity are used to locate the critical points that cause the singularities in the density of states. Illustrations are given that show how this can be used to improve the resolution of singularities that are not clearly resolved by the histogram method. A utility dispersion relation has been used for the examples, and it can be applied to spin waves as well as to electrons in the tight-binding approximation. Students can gain much insight into solid state research from this method since it helps to bridge the gap between the standard textbook treatments and the highly technical discussions of the research literature. The authors have used this method in a detailed study of the spectra of fcc lattices that will be presented elsewhere.
The Isochronous Problem inside the Spherically Uniform Earth
Authors: Lee S. M.
Published: August 2005

The isochronous problem is worked out assuming that a particle oscillates along a constraining curve inside the spherically uniform Earth. This modification of the usual isochronous problem becomes complicated due to (1) the force acting on the particle is not unidirectional; (2) the curve of constraint must have its endpoints on the Earth's surface. A set of parametric equations satisfying the condition of isochronous motion are obtained. Then the values of these equations that are permitted by the second condition mentioned above are calculated and presented in a graph. The calculation shows that, in addition to the familiar straight line along which the particle oscillates isochronously inside the Earth, there are many curves that satisfy the conditions. The frequencies of the isochronous oscillation along these curves are simply related to the frequency along the straight line. Thus the problem treated here also has application to the Brachistochrone problem that is similarly modified.
Spectral Analysis Using a Camera
Authors: Greenberg L. H. , Balez T.
Published: August 2005

A grating in front of a camera can be used as a spectrograph in an introductory physics laboratory. The student obtains a permanent record of the spectra of various elements, and using a grating equation and also a calibration curve, wavelengths can be found with sufficient precision to identify unknown sources. The precision of the methods described allows the student to obtain much greater accuracy than usually obtained with a grating spectrograph at the introductory level.
A Magnetic Curl Meter
Authors: Phillips Melba , French A. P. , Rosenfeld Jon
Published: August 2005

As first shown by Faraday, a magnet suspended in a conducting fluid in a region of distributed current density will rotate continuously. The measured torque on such a magnet is substantially in accord with that predicted theoretically.
Classical Limit and the WKB Approximation
Authors: Brown Lowell S.
Published: August 2005

We prove that a wave-packet solution in the WKB approximation to the Schrödinger equation follows the classical trajectory, and we discuss the nature of this solution.
Computer Aided Physics Laboratory Instruction: Project caplin
Authors: Bron W. E.
Published: August 2005

A project on computer assisted physics laboratory instruction (Project caplin) has led to the development of material used in a first semester introductory physics laboratory for nonscience majors. In the laboratory the student first obtains data from traditional laboratory experiments. The student then has the option to use parts (or all) of preprogrammed computer material designed to: (1) accept the experimental data and scan it for inconsistencies; (2) carry out an error analysis on the data; (3) perform calculations of physical parameters based on the experimental data; (4) yield tabular displays of calculated results; and (5) yield graphical displays of results. In some cases, computer programs allow simulation of experiments with the possibility of altering values of parameters or experimental details. It has been observed that the computer aided laboratories have considerably improved comprehension of data error analysis, of graphic representation of physical concepts, and have aided in carrying out calculational phases of the experiment left to the student. Furthermore, laboratory time saved through the use of the computer system has enabled expansion of the scope of individual laboratories.
On Lagrangians with Higher Order Derivatives
Authors: Riahi F.
Published: August 2005

Classical mechanics based on Lagrangians with higher order derivatives is investigated. It is found that this generalization does not lead to any new feature of the theory, apart from an increase of the dimensionality of phase space. Conserved quantities are also derived that reduce to the usual ones in the absence of higher derivatives.
The Gravitational Red Shift: A Three-Body Effect
Authors: Peres Asher
Published: August 2005

The nonlinearity of Einstein's gravitational equations produces three-body forces in the equations of motion. One of their consequences is that the motion of an electron around a nucleus (or a satellite around a planet) is slowed down by the existence of a distant massive body. This is the familiar gravitational red shift, which can thus be derived without invoking the equivalence principle.
Electron Optics: A Topic of a Computer Applications Course
Authors: Romagnoli R. J.
Published: August 2005

Electron optics is especially suited as a topic for independent study as part of a computer applications course. The principles are elementary, and the student gains greater understanding of the classical similarities between particles and waves. A method of solution is illustrated, and the results appear more reliable than those existing in prior literature.
Mass Distribution and Frequencies of a Vertical Spring
Authors: Edwards T. W. , Hultsch R. A.
Published: August 2005

A vertical spring in a gravitational field has a density increase from top to bottom. The density variation, which is often not noticeable, depends on the ratio of the spring weight to the quantity kz0, the spring constant k times the unstretched length z0. Two springs prepared by prestretch-ing 78 and 23 turn portions of a “Slinky” showed density increases by factors of about 10 and 4, respectively. The detailed density distribution of the smaller spring agrees very well with the results of an analysis based on Hooke's law behavior. The heavier spring shows non-Hookean effects. The lowest few frequencies can be measured by driving the spring in resonance by hand, and for the lighter spring these also agree well with calculated values. The predicted nonuniform distribution of nodes is observable. This simple apparatus may provide stimulating experiments for intermediate laboratories.
The Context of Inquiry in Physics
Authors: Diederich Mary E.
Published: August 2005

College physics textbooks emphasize the conclusions of research at the expense of the context of inquiry in physics. In order to overcome this deficiency, at least one of the physics courses within a student's program should include specific consideration of the context of inquiry in physics. An excellent focus for this consideration would be the process of theory evaluation in physics whose character is indicated in this paper.
Comparison of the Magnetic Dipole and Electric Quadrupole Spin Precessions
Authors: Ley-Koo E.
Published: August 2005

In this paper we compare the spin precessions of a magnetic dipole in a uniform magnetic field and of an electric quadrupole in an axially symmetric electric field gradient. We derive in general the classical equations of motion, energies, and precession frequencies for both cases, pointing out the similarities and differences. By using the vector model we also obtain the quantum expressions for the energies and transition frequencies. Some results, which are relevant for the interpretation of magnetic resonance, quadrupole resonance, and perturbed angular correlation phenomena, are briefly discussed.
Necessary and Sufficient Conditions for a Canonical Transformation
Authors: Hurley James
Published: August 2005

Necessary and sufficient conditions are given for a transformation to be canonical. It is shown that if the transformation is to be canonical for all Hamiltonians, the condition is equivalent to the usual fundamental Poisson bracket conditions.
A Physicist's Introduction to Bayesian Statistics
Authors: Raeside D. E.
Published: August 2005

A brief, elementary review of the basic concepts of Bayesian statistics is presented with the focus being on those aspects of the theory which are especially suitable for physics applications. Examples illustrating the usefulness of these concepts are taken from the field of nuclear physics.
The Fresnel Hologram of a Square Aperture
Authors: Matulka R. D. , Sullivan J. G. , Fuhs A. E.
Published: August 2005

A simple analytical method is presented for the complete prediction of the interference pattern of a square aperture as recorded by a hologram in the near field. Graphical means are used to evaluate the resulting Fresnel integrals and to locate the fringe positions and intensities. The resulting exercise is considered a valuable tutorial device for the understanding of the holographical phenomenon.
A Laboratory Experiment for Determining the Partial Half-life of K40 for Beta Emission
Authors: Gopal K. , Sanjeevaiah H. , Sanjeevaiah B.
Published: August 2005

A simple and straightforward laboratory experiment to determine the partial half-life of K40 using Analar (analytical reagent) grade KCl powder is discussed. The experiment is believed to be a good addition to an undergraduate laboratory with limited resources. The partial half-life obtained by this method is (1.14±0.08)×109 yr.
Covariant Equations for the Motion of a Point Body with Variable Rest Mass
Authors: Henry J. , Barrabes C.
Published: August 2005

The general equation for the motion of a point body with variable rest mass can be obtained in a covariant way by using the principle of the conservation of four-momentum. The correct definition of thrust is given, and several particular cases are studied: the emission or absorption of one or several particles and of photons; and the isotropic exchange of energy.
Spin Waves and Generalized Susceptibilities for Classical Models
Authors: Patterson J. D.
Published: August 2005

Lowest order noninteracting spin-wave theory for uniaxial, classical, Heisenberg, antiferromagnets, and ferrimagnets is considered. By use of the transverse generalized wave vector dependent magnetic susceptibility, the magnetization and mean energy are evaluated for low temperatures in the spin-wave approximation. Both two- and three-dimensional lattices are considered.
Standing Waves by Oblique Incidence on a Mirror
Authors: Taylor Billy M. , Wallace Eddie R.
Published: August 2005

We have employed the convenient wavelengths of microwaves to develop an introductory experiment with standing waves produced by oblique incidence upon a mirror. This experiment in physical optics was performed in two parts: (1) with polarization of the electric field perpendicular to the plane of incidence as an empirical introduction to the lower limit of the distance between maxima or minima in an interference pattern and (2) with polarization of the electric field parallel to the plane of incidence as an introduction to elliptical polarization. We have indicated the sources of error, illustrated graphically the sizes of errors to be expected, and suggested optimum dimensions of equipment.
On the Quantum Theory of the Symmetric Top
Authors: Zaharia M.
Published: August 2005

The rotation operator of an ad hoc introduced particle is used to study the free symmetric top. A comprehensive and remarkable simple treatment is obtained.
Quantum Theory of a Damped Two-Level Atom
Authors: von Foerster T.
Published: August 2005

The interaction of a two-level atom with the radiation field in a cavity is discussed in quantum mechanical terms that are closely analogous to those used in discussing the classical Langevin equation; the quantum Langevin equation for this case, however, is nonlinear. A technique is developed for finding the measurable properties of the solution of the equations exactly; the properties of the solution are compared with those for the harmonic oscillator.
Poincaré's Rendiconti Paper On Relativity. Part II
Authors: Schwartz H. M.
Published: August 2005

This is a continuation of the modernized presentation of Poincaré's Rendiconti paper (begun in the November 1971 issue of this Journal). It covers Secs. 5–8 of that paper, dealing with its central theme, as indicated by its title, “On the dynamics of the electron,” the subject being of interest to both the historian of the classical theory of the electron and the historian of relativity.
Green's Function Treatment of Short Linear Heisenberg Chains
Authors: Unruh Henry
Published: August 2005

The Callen and Tyablikov decoupling schemes used in the Green's function method are tested numerically for short Heisenberg linear chains which are first subjected to a constraint. The constraint is imposed to insure that internal excitations alone contribute to the calculated thermal averages so that in this sense these averages correspond to thermodynamic quantities. It is found that improved agreement with the exact results occurs if the Tyablikov decoupling is corrected by a term linear in the temperature.
Research Project for Undergraduates: Ionic Thermoconductivity in Dielectrics
Authors: Fuller Richard M. , Fuller Robert G.
Published: August 2005

Research projects for undergraduates should satisfy several conditions with regards to the physical insight, experimental manipulation, data analyses, and time for the experimental run that are required of the students. These conditions are satisfied by the study of dipole relaxations in dielectric materials using the method of ionic thermocurrents (ITC). ITC can be used to determine the concentration, activation energy, and relaxation time of dipoles in a dielectric. The necessary equipment and some possible research projects are discussed.
Measurement of the Speed of Light
Authors: Domkowski A. J. , Richardson C. B. , Rowbotham Noel
Published: August 2005

Measurement of the speed of light by the rotating mirror method of Foucault using a laser source and photodiode detector is described. With a path length of 38 m and rotation rates up to 500 Hz, the result c =  3.00±0.02×108 m/sec is obtained.
Versatile Electromechanical Fourier Synthesizer for Laboratory or Lecture Demonstration
Authors: Clark T. A.
Published: August 2005

A demonstration unit has been devised that provides Fourier series synthesis of regular waveforms by the use of mechanically geared sine/cosine potentiometers and a simple summing amplifier. Considerable flexibility in the design allows immediate demonstration of any common waveform via preprogrammed plug-in circuit cards for lecture use while an alternative operating mode incorporates a fully variable control panel for student use in the laboratory. Mounting of the mechanical gearing in a transparent frame provides immediate evidence of frequency ratios in the laboratory or in a lecture class by overhead projection.
The Period of Damped Simple Harmonic Motion
Authors: Allen Mildred , Saxl Erwin J.
Published: August 2005

Both by theory and by experiment with an oscillating torsion pendulum it is shown that to determine the period of a damped simple harmonic motion accurately the measured intervals must be taken between the times that the oscillator passes through its equilibrium position or, less satisfactorily, between the times of maximum displacement.
Hydrogenic Wave Functions for an Extended, Uniformly Charged Nucleus
Authors: Yano A. F. , Yano F. B.
Published: August 2005

An exact, closed solution for the hydrogenic wave functions of an extended, uniformly-charged nucleus is presented.
The Martini Perpetual Motion Machine: A Semiprogrammed Problem
Authors: Brigman George H.
Published: August 2005

The reader is challenged to show, using only Newtonian mechanics, why a device with unbalanced buoyancy forces cannot be a perpetual motion machine. Then, in case they are needed, three sets of clues are given to assist in simplifying and solving the problem. Finally the reader is given a solution that he may compare with his own.
Single-Photon Double-Slit Interference—A Demonstration
Authors: Parker Sherwood
Published: August 2005

Apparatus is described which produces an interference pattern using only one photon at a time. It can be used in a lighted room—no significant dark adaption is needed to see the pattern, even at the one-photon level. The number of photons per second producing the pattern is measured in the same apparatus with a photomultiplier.
The Role of the Constraining Force in a Foucault Pendulum
Authors: Curott David R.
Published: August 2005

The Foucault precession is calculated from the Coriolis force plus central harmonic restoring force; the latter contribution to the precession rate is shown to be comparable to the first. The derivation has been chosen to be easily understood by underclassmen. A related paradox develops that can be used to provoke considerable classroom discussion.
Describing Reactions with Analogous Processes
Authors: Finkel Robert Warren
Published: August 2005

A generalized extrapolation relation is developed for probability amplitudes of unknown analytic form having parametric differences only. This expression enables a reaction to be described empirically using data from related processes. As an instrument for phenomenology, this comparative approach requires little theoretical knowledge of the related systems and relegates complexities due to structure to the input data. A linear approximation to the basic equation is obtained when the related systems are similar. Simple illustrations are provided by elastic scattering applications.
The Twin-Rod Thought Experiment
Authors: Winnie John A.
Published: August 2005

Einstein's 1911 twin-rod thought experiment is analyzed, and some of its implications for the physical status of length-contraction within the special theory of relativity are examined. Contrary to a widespread view, it is shown that the twin-rod thought experiment does not require that the two rods be travelling at equal speeds (with respect to a given inertial frame K) in order that the experiment serve its intended purpose. Since the equality or inequality of the speeds of the rods will depend upon the criterion of simultaneity adopted within the inertial frames of the special theory, the irrelevance of the speeds of the rods here indicates the synchrony-independence of this length-contraction effect within special relativity.
A Momentum Representation Treatment of the Hydrogen Atom Problem
Authors: Ivash Eugene V.
Published: August 2005

Energy levels and wave functions are obtained for the quantum mechanical, nonrelativistic, hydrogen atom problem for the l = 0 case, using the momentum representation. The result for the energy levels is extended to the general case of arbitraryl, using the factorization method.
An Evaluation of a Nonlecture Technique in the Teaching of Physics
Authors: Munsee J. H.
Published: August 2005

A nonlecture group technique for teaching physics is described and examination results are compared with classes using the lecture technique. It is concluded that there is no panacea for teaching physics but that a smorgasbord of methods will probably give the students the best educational opportunity to achieve.
Experiment to Measure the Increase in Electron Mass with Velocity
Authors: Geller Kenneth N. , Kollarits Richard
Published: August 2005

An experiment is described for measuring the mass increase with velocity of relativistic electrons. A beta-ray spectrometer is used to momentum-analyze electrons emitted from a Tl204 source, and a semiconductor detector is used to measure the energy of the electrons. The energy calibration of the semiconductor detector is established absolutely. The experimental results serve to verify the predictions of special relativity, and provide precise values for the electron rest mass and the speed of light.
A “Medical Physics” Course Based Upon Hospital Field Experience
Authors: Onn David G.
Published: August 2005

A new course in “medical physics” with a basic element of direct hospital field experience is described. Noncalculus, the course is designed to follow an introductory general physics or chemistry course. Intended primarily for premedical students, the course may be taken by nonscience majors interested in health studies. Eighteen hours of in-hospital time are included for each student, supplemented by laboratory work in the physics department, including radiation dosimetry studies with a 2.5 meV van de Graaff accelerator using thermoluminescent dosimetry techniques that allow students to develop their interests into research projects.
Velocity, Momentum, and Energy Transmissions in Chain Collisions
Authors: Kerwin James D.
Published: August 2005

A theoretical analysis is presented for a chain-collision process occurring in a one-dimensional arrangement of objects having, in general, different masses, when independent collisions are assumed. Expressions for the velocity and momentum gains and the energy transfer are derived and applied to configurations with various mass ratios between neighboring objects. Intriguing transformation properties are displayed by these quantities under the permutation operation. These effects are shown to be due to the invariance of the forces between colliding objects under this operation.
Non-Dispersive Mirror Wavepackets
Authors: Greenman J. V.
Published: August 2005

We argue for greater use of the no-dispersion approximation in introductory courses on quantum mechanics for the following two basic reasons: (i) the approximation yields in many situations a simple serniclassical picture of the time development of localized wavepackets; (ii) it makes explicit the fundamental importance of phase relations in the quantum model.
Electromagnetic Induction: A Computer-Assisted Experiment
Authors: Fredrickson J. E. , Moreland L.
Published: August 2005

Minimal equipment is used in a sophomore laboratory experiment demonstrating Faraday's Law. A complicated mathematical expression for the induced EMF is solved with an electronic desk calculator or computer for comparison with experimental results. Data are given for a typical experiment.
Satyendranath Bose: Co-Founder of Quantum Statistics
Authors: Blanpied William A.
Published: August 2005

Satyendranath Bose's recognition of the fact that the photons in a cavity radiator are indistinguishable led him to a derivation of the Planck law free from any assumptions of classical electrodynamics. His result, published in 1924, was a significant vindication of the photon concept that Einstein had championed since 1905. It also laid the foundations of quantum statistics, as was freely acknowledged by Einstein and Dirac, among others. Various aspects of Bose's career, including his apparent failure to understand the full implications of his work, may be of interest both to physicists and historians of science.
The Product-Integral Calculus Formulation in Quantum Mechanics
Authors: Kramer Ivan
Published: August 2005

In this paper we investigate the advantages of using the product-integral calculus rather than the usual successive approximation perturbative expansion in three branches of quantum physics. The mathematics of the calculus is fully developed, and its superiority over the perturbative expansion is explored in specific examples from physics. All of time-dependent perturbation theory in quantum mechanics can be written in terms of the calculus, as well as the most general solution for the density operator in quantum statistical mechanics.
A Different Proof of the Maxwell-Boltzmann Distribution
Authors: Mello P. A. , Brody T. A.
Published: August 2005

The Maxwell-Boltzmann Distribution (MBD) for a classical ideal gas is obtained as the mean over phase space of the number of momentum components less than some value p, without making any assumptions beyond those implicit in the microcanonical ensemble. The variance of the fluctuations of actual distributions of the momentum around the average given by the MBD is shown to go to zero as N−1, where N is the number of particles. This proof of the MBD has the advantage over the usual type of proof in that it does not employ a subdivision of phase space into cells, a trick which gives rise to certain difficulties discussed in the introduction. Moreover, it is more complete in that the problem of the fluctuations is treated at an elementary level.
Neutron Diffusion as a Random Walk Problem
Authors: Karmeshu  , Kothari L. S.
Published: August 2005

The one-dimensional random walk problem has been generalized to allow for absorption at lattice sites, and then this technique has been used to study one velocity neutron diffusion. We show that most of the results that are normally obtained by solving the diffusion equation under appropriate boundary conditions, can be obtained directly. Various special cases have been considered, including leakage from a finite lattice and neutron-wave propagation in an infinite lattice.
A New Emphasis in Diffraction Theory and Experiments
Authors: Peterson Steven D. , Kasper Joseph E.
Published: August 2005

Scalar diffraction theory is usually presented as a closed subject in current textbooks. Actually, the theory is extremely unsettled and open to original investigation, and the authors feel that student understanding and motivation could be significantly enhanced if the problematic nature of the theory were stressed. With this in mind, the Kirchhoff, Huygens and Rayleigh theories are reviewed, emphasizing the fundamental inconsistencies and contradictions which are often ignored. Instructive and provocative experiments are then described which confirm the unwarranted success of the theoretical solutions under extreme conditions. The investigations are based on the diffraction of microwaves by a circular aperture, and are on a level suitable for undergraduate work.
An Illustrative Example for the Undergraduate Thermodynamics Curriculum
Authors: Sevenich R. A.
Published: August 2005

Intrinsic disorder of a simple type is discussed and recommended for inclusion in the undergraduate thermodynamics curriculum as a practical example. The concentration of intrinsic defects is calculated as a function of temperature. The dc conductivity and diffusion coefficient are also examined.
Keller vs Lecture Method in General Physics Instruction
Authors: Philippas Michael A. , Sommerfeldt R. W.
Published: August 2005

A description of the use of the Keller method of instruction in a general physics class of 100 students is presented. This teaching technique is critically evaluated by comparing the performance of the students in the program with that of 100 students in a concurrent control group run by the traditional lecture method. It is found that performances are not significantly different and the cost of running the program is not excessive. Furthermore, student reaction to the program is found to be quite favorable.
A Statistical Experiment Using Resistors
Authors: Worrell Francis T.
Published: August 2005

In undergraduate laboratories we frequently ask the student to use error theory to evaluate his results without giving him the opportunity to measure and analyze a large statistical sample to see how well it follows theoretical models. In the experiment described here, the student investigates the statistics of a set of resistors. In the process he gets some practice in the use and interpretation of histograms, and gains some insight into the relation of the Gaussian error curve and a real statistical distribution as well as the significance of standard deviation and standard error..
Application of the Similarity Transformation to Some Simple Problems
Authors: Wong Cho-Fai
Published: August 2005

The similarity transformation is discussed with the aid of some simple problems in elementary physics. These examples are intended to provide an introduction for physics students who have just commenced the study of this mathematical technique.
A New Look at the Quantum Mechanical Problem of Measurement
Authors: Maxwell Nicholas
Published: August 2005

According to orthodox quantum mechanics, state vectors change in two incompatible ways: “deterministically” in accordance with Schr0̈dinger's time-dependent equation, and probabilistically if and only if a measurement is made. It is argued here that the problem of measurement arises because the precise, mutually exclusive conditions for these two types of transitions to occur are not specified within orthodox quantum mechanics. Fundamentally, this is due to an inevitable ambiguity in the notion of “measurement” itself. Hence, if the problem of measurement is to be resolved, a new, fully objective version of quantum mechanics needs to be developed which does not incorporate the notion of measurement in its basic postulates at all.
Individualized Instruction in Introductory Physics
Authors: Swartz Clifford E. , Zipfel Christie
Published: August 2005

For the third year, an introductory physics course at Stony Brook has been presented in an individualized mode without class meetings of any kind. There are about 400 students in the course representing a wide range of ability, experience, and professional intentions. The course is strongly laboratory centered and can be taken at various levels including calculus and noncalculus. When a student finishes a subtopic, on the average of once a week, he reports to his faculty examiner to take a proficiency exam. The exam is partly written and partly oral. This type of course mechanism has been used in various places in all subjects, especially at lower school levels, since 1912. For successful operation of the method it is necessary to have appropriate special curricular material. Preparation requires a great deal of advance work, although prototype material is now becoming available. Students prefer this mechanism over the standard lecture method, but there is no easy way to demonstrate that they learn more.
Order and Correlation in Finite Antiferromagnetic Ising Chains
Authors: Falk H.
Published: August 2005

Several quantities associated with order and correlation in finite, antiferromagnetic Ising chains (free ends) in the presence of a uniform magnetic field have been computed. The results show that although for 1≤i<j≤N the sign of the two-spin cumulant 〈SiSj〉 −  〈Si〉〈Sj〉, is unaffected by the external field, the quantities 〈SiSj〉 and 〈Si〉 may change sign for sufficiently large magnetic fields, and the latter quantities thereby provide a more intuitive measure of the effect of the field on the spin order.
On the Quantum Theory of Electrical Transport in a Uniform Magnetic Field
Authors: Weisenthal L. , de Graaf A. M.
Published: August 2005

The Boltzmann equation of electrical transport in a uniform magnetic field has been very successful in describing a variety of transport phenomena in metals and semiconductors and has yielded important information concerning the electronic structure of these materials. However, textbooks usually do not derive the Boltzmann equation, whereas the quantum mechanical derivations which have appeared in the literature are either very complex or are based on a particular gauge describing the magnetic field. It is the purpose of this note to describe a very simple quantum mechanical derivation of the field terms of the Boltzmann equation. This derivation does not depend on the initial choice of gauge, since use is made of a gauge-independent density matrix formalism. The effect of scattering is taken into account phenomenologically. The derivation is carried out for free electrons as well as for Bloch electrons.
A New Derivation of the Virial Expansion
Authors: Mullin William J.
Published: August 2005

To overcome the mathematical complexity on the one hand or the lack of rigor on the other in usual treatments of the virial expansion, a new derivation is presented. This derivation, while simple and mathematically valid, clearly illustrates the most important features of the cluster expansion derivation of the second and third virial coefficients. Thus it is expected to be of use in statistical mechanics courses.
Analytic Independent Particle Model for Molecules
Authors: Whalen J. E. , Green A. E. S.
Published: August 2005

Solutions to the Schrödinger equation for an electron in an analytic spheroidal potential are considered. The analysis is carried out in the prolate spheroidal coordinate system resulting in a simple second-order differential equation, which is solved numerically by the Cowell-Numerov method. Computations are presented for models of nitrogen and oxygen molecules. The energy levels can be brought into reasonable accord with experimental Rydberg levels by the adjustment of the two parameters of the spheroidal potential. The results of this study represent an interesting tutorial example of a realistic quantum mechanical problem.
Undergraduate Experiment on Low-Temperature Dependence of the Conductivity of Copper Wire
Authors: Dasheiff R. M. , Risk W. S.
Published: August 2005

A simple experiment is described that permits advanced undergraduates to investigate the temperature dependence of electrical conductivity in copper wire down to liquid helium temperatures. At temperatures below 40° K the experimental results approach the T5 behavior expected from quantum mechanical calculations. At temperatures below 8° K a constant, nonvanishing resistance is found. The apparatus uses a nested Dewar system in conjunction with a helium gas thermometer.
Eigenvalues in Quantum Mechanics: A Computer-Generated Film
Authors: Davis Craig R. , Schey Harry M.
Published: August 2005

A computer-generated film illustrating eigenvalues in quantum mechanics is described. Dealing with the reduced radial wave equation in the s-wave case and a short-range central potential which supports three bound states, the film illustrates the behavior of solutions of the equation as the energy is allowed to vary continuously. The conditions which must be satisfied by physically acceptable solutions are presented and the film shows that such solutions arise only for certain discrete values of the energy. Stills from the film are presented and discussed, and details of the numerical methods involved in solving the wave equation are given.
The Falling Body Problem in General Relativity
Authors: Lapidus I. Richard
Published: August 2005

The one-dimensional general relativistic motion of a falling body in a uniform gravitational field is obtained. The inertial mass of the particle is a function of its velocity and position. The results are compared with the special relativity and Newtonian motions.
The Richtmyer Memorial Lecture: A Physicist Looks at Mars
Authors: Leighton Robert B.
Published: August 2005

Response of the Richtmyer Memorial Lecturer to the American Association of Physics Teachers, 1 February 1972.
A Topical Approach to Astronomy for Nonspecialists
Authors: Liming F. Glenn
Published: August 2005

The goals of a science course for nonscience students can be adequately met with an astronomy course which is also suitable for science majors. The replacement of the survey approach by the topical approach in the course provides greater coherence and meaning for the information presented. A specific set of topics is presented and evaluated in relation to the goals of an astronomy course for nonspecialists.
Teaching Cultural Physics to Texas Aggies
Authors: McGuire J. H.
Published: August 2005

At Texas A&M University we have developed a course designed to relate to people with interests in fields not closely associated with physics. We hope that the content and technique described in this article may provide some helpful guidelines for teachers who are now developing or who are considering developing similar courses.
A Model for Improving “Advanced” Courses in Physics
Authors: Friedman Charles P.
Published: August 2005

An alternative to the lecture format for teaching junior and senior level material is outlined. The basis of this alternative is the widely used Keller plan which features self-pacing, personal attention for each student, and emphasis on mastery of specific learning objectives. To meet needs particular to upperclass students and to create a learning atmosphere more appropriate for “pre-professionals,” we have added the following features: (1) student freedom in selecting his own procedure (textbook readings, exercises, etc.) for mastering the course material, and (2) some variety in topics studied by each individual student. Two successful trials of this adapted Keller plan in an atomic physics course at MIT are described, with emphasis on student performance and the administrative structure of the new format.
The Use of Compton Scattering for the Study of Electron Velocities
Authors: Nha S. K. , McIntyre J. A.
Published: August 2005

A demonstration of the motion of electrons in atoms is described. The demonstration is provided by measuring the Doppler shift of gamma rays scattered by the moving electrons. Scattering materials of CH2, aluminum, brass, and lead were used; the scattered gamma ray spectra clearly show the differences in the electron velocities in these materials.
Construction and Possible Uses of an Electron Linear Accelerator
Authors: Bammann D. , Lesniak E. , Pratt T. A. E. C.
Published: August 2005

A cheap electron accelerator is constructed, and possible experiments that could be investigated are suggested. The limitations of the system are also discussed.
Geometric Nature of Lagrange's Equations
Authors: Beers Brian Lee
Published: August 2005

It is shown that Lagrange's equations may be obtained by projecting Newton's second law onto the moving tangent vectors associated with a change in the generalized coordinates qi. This exposes the Lagrange equation for qi as the component of the force equation in the indicated direction.
Complex Numbers and the Lagrangian
Authors: Gelfman Samuel
Published: August 2005

A method to determine the Lagrangian with the use of complex numbers is described. The kinetic energy is found from the magnitude of the complex velocity, and the potential energy is found from the real part of the complex displacement. Finally this method may be used to determine generalized forces with Lagrange's method of undetermined multipliers.
On Obtaining the Exact Green's Function Solution for the Two-Spin-1/2 Heisenberg Ferromagnet
Authors: Lawson J. O. , Brient S. J.
Published: August 2005

A method is outlined for obtaining the exact Green's function solutions for the two-spin-1/2 Heisenberg ferromagnet utilizing commutator and anticommutator Green's functions. It is observed that the exact solutions can be obtained much more easily and readily when utilizing anticommutator Green's functions than when utilizing commutator Green's functions.
Eigenvalues of One-Dimensional Systems by a Matrix Method
Authors: Nicola Michel
Published: August 2005

A matrix method for finding the energy eigenvalues of one-dimensional systems is given. The method utilizes the correspondence principle to find the separation of every two successive eigenvalues and the uncertainty principle to find the lowest energy. The harmonic oscillator and the infinite square well are solved exactly, and the WKB approximation for bound state energies is deduced.
Environmental Topics in an Undergraduate Physics Curriculum
Authors: Cowan David J.
Published: August 2005

The number of bachelor's degrees in physics conferred annually is predicted to decline. This decline may be abated by emphasizing the versatility of an undergraduate physics degree. The introduction of environmental topics throughout the undergraduate curriculum is one method of illustrating this flexibility, and this approach is presented. Examples of the applications of physical principles to several areas of environmental change are given. These areas are air pollution, energy conversion and resources, environmental radiation, noise, thermal pollution, transportation, and water pollution. Representative bibliographies are presented in each area to facilitate the introduction of these topics into the curriculum. For the most part, items in the bibliography refer to environmental problems that are amenable to the laws of physics. No major changes are proposed for the standard undergraduate physics curriculum, although a course in fluid mechanics or transport phenomena would provide a valuable background for students of all interests.
Down With Calculus!
Authors: Silvert William
Published: August 2005

The importance of calculus is over emphasized in elementary physics courses. More stress should be placed on the application of other types of mathematical reasoning, especially modern algebra and numerical methods. This paper presents approaches to several problems in physics teaching that either use a time-sharing computer terminal or symmetry arguments to solve sophisticated and physically significant problems at a level appropriate for liberal art students.
Experimental Verification of the Fresnel and Airy Equations for an Air-Glass-Air System
Authors: Shaw D. E. , Wunderlich Francis J.
Published: August 2005

We describe two experiments using simple equipment suitable for an undergraduate laboratory course in physical optics or advanced electromagnetism. The monochromatic optical transmission characteristics of a glass flat with and without multiple reflections are measured as a function of the angle of incidence and the results compared with the theoretical predictions based on the Fresnel and Airy equations.
On the Validity of Kirchhoff's Law in a Nonequilibrium Environment
Authors: Burkhard Donald G. , Lochhead John V. S. , Penchina Claude M.
Published: August 2005

In the heat radiation literature, the words absorptivity and emissivity have both been used in different senses. This can lead to confusion, and in one case it was argued that Kirchhoffs law of equality between emissivity and absorptivity does not apply to the radiation from a material for which the stimulated emission depends on the temperature of the environment. We clarify the proper thermodynamic definition of absorptivity (and emissivity) and show that Kirchhoff's law stated in terms of those definitions correctly predicts the results of experiments. This follows even when there are large deviations from equilibrium, or when there is nonlinear absorption or emission.
Exact and Impulse Scattering of Weakly Coupled Probes by an Harmonic Oscillator
Authors: Gersch H. A.
Published: August 2005

Comparison is made between the exact and impulse approximation expressions for scattering of weakly coupled probes by a one-dimensional harmonic oscillator. These results are utilized to estimate the applicability of the impulse approximation to several experimental situations. A first correction term to the impulse approximation is evaluated.
Dimensional Analysis and the Buckingham Pi Theorem
Authors: Evans John H.
Published: August 2005

Working from a simple example of a dimensional transformation, the essential elements are identified, and an abstract prototype transformation is defined. With the aid of careful definitions and a geometric interpretation of what happens in a dimensional transformation the Buckingham pi theorem is written down but not proved. The application of this theorem to the heat equation in spherical coordinates and one dimensional gas motion without boundary conditions serve to illustrate the usefulness of the theorem in physics.
Physics Courses—Some Suggested Case Studies
Authors: Swetman T. P.
Published: August 2005

This paper briefly suggests some possible case study topics, all involving elements of controversy and speculation, for inclusion in physics courses.
E = mc
2
and the Repulsion between Plane Aerials
Authors: Ericson T. J.
Published: August 2005

By analyzing the interaction between the electromagnetic radiation -produced by one plane aerial and the current induced in another plane aerial, it can be shown by simple mathematics that the energy in an electromagnetic field is equal to its mass times c2.