bluuebunny/crossref_metadata_2025 huggingface dataset:
The information-theoretic statistical mechanics of a system in contact with a heat reservoir
Authors: Bowers R. G. , McKerrell A.
Published: March 2005

The subject of this paper is the information-theoretic statistical mechanics of a system in contact with a heat reservoir. The fundamental extremum principle of Jaynes is introduced, and a new essentially thermodynamic characterization of a heat reservoir is established. This allows a new extremum principle—involving a generalization of the Helmholtz free energy of thermodynamics—to be derived. This new extremum principle is used to find that probability distribution which, roughly speaking, best represents a system at fixed temperature. Not unexpectedly, the canonical distribution of Gibbs results. Some consequences of the analysis are discussed. An example of other applications of the new extremum principle is given.
The problem of several delta-shell potentials in the Lippmann–Schwinger formulation
Authors: Jain A. K. , Deb S. K. , Shastry C. S.
Published: March 2005

The quantum-mechanical problem of the bound states corresponding to a sum of several delta-shell potentials is solved exactly as an illustration of the applications of the Lippmann-Schwinger formulation. We obtain the bound-state energies and illustrate their relation to the poles of the corresponding S matrix. In addition, the several-delta-shell-potentials problem also gives a good example for the study of localization of states in an elementary level, and we do this in some detail. It is found that for two well-separated delta-shell potentials, the ground state is localized in the stronger well whereas the excited state is localized in the weaker well. This result is generalized for n delta-shell potentials. A simple proof that n attractive delta-shell potentials cannot have more than n S-wave bound states is also given. Like other classical problems of quantum mechanics, namely the harmonic oscillator and the hydrogen atom, this problem of several delta-shell potentials serves as a good illustration of various physical and mathematical aspects of quantum mechanics.
Quantum measurements on a computer: An interactive teaching program
Authors: Krass Allan S.
Published: March 2005

An interactive computer program is presented which allows a student to perform simulated quantum measurements on a one-dimensional simple harmonic oscillator. The program is designed to illustrate the consequences of the basic axioms of quantum theory and illustrates such features as the random statistical nature of measurements, time dependence of superpositions of eigenstates, collapse of the wave function in measurement and the uncertainty principle, among others.
An individualized apparatus course for high school teachers
Authors: Reynolds James M.
Published: March 2005

The paper briefly describes an individualized apparatus course for high school teachers. In addition to the usual purposes of such a course, this one endeavored to teach the design of high school experiments. This course included self-pacing, contract grading, and student determination of projects.
Examination of Eulerian and Lagrangian coordinate systems
Authors: Remillard Wilfred J.
Published: March 2005

The relationship between Eulerian and Lagrangian coordinate systems is studied with the help of computer plots. A universal curve relating the spatial derivatives of particle displacement in the two systems acts as a basis for identifying such phenomena as shock and cavitation. Examples are given which illustrate the differences in the shape of a traveling wave as seen by observers in the two systems.
A simple discrete model of scattering in a fluctuating inhomogeneous medium
Authors: West Bruce J.
Published: March 2005

The intractibility of most scattering problems in continuous media is discussed and a simple discrete model for scalar wave scattering from inhomogeneities on a lattice is presented. The ’’exact’’ scattered wave solution is given in terms of the ratio of determinants. The amplitude of the average field scattered from a point reflector is related to the characteristic function of the fluctuations in the scatterer’s motion.
String-coupled pendulum oscillators: Theory and experiment
Authors: Moloney Michael J.
Published: March 2005

A coupled-oscillator system is given which is readily set up using only household materials. The normal-mode analysis of this system is worked out, and an experiment or demonstration is recommended in which one verifies the theory by measuring two times and four lengths.
Real variable inversion of Laplace transforms: An application in plasma physics
Authors: Bohn C. L. , Flynn R. W.
Published: March 2005

Laplace transform techniques are applicable to a wide variety of problems. The Bromwich inversion employing contour integration on the complex s plane is commonly used to invert untabulated transforms. Most physicists believe Laplace inversion must necessarily involve operations on the complex plane. This is not so. An alternative, the Widder inversion, uses real variables exclusively. We have applied Widder’s method to the problem of Landau damping, a notoriously difficult inversion, to illustrate the power of the techique.
Aharonov-Bohm effect in perturbation theory
Authors: Purcell Kay M. , Henneberger Walter C.
Published: March 2005

The Aharonov-Bohm effect is obtained in first-order perturbation theory. It is shown that the effect occurs only when the initial state is a superposition of eigenstates of Lz corresponding to eigenvalues having opposite sign. This corresponds to the two paths separated by the magnetic flux that are considered in usual discussions of the effect.
Velocity of energy flow
Authors: Newman E. T.
Published: March 2005

We point out and discuss a frequently misunderstood, overlooked, or disregarded relationship between the energy-momentum tensor and the velocity of energy flow.
An experiment to measure range, range straggling, stopping power, and energy straggling of alpha particles in air
Authors: Ouseph P. J. , Mostovych Andrew
Published: March 2005

Experiments to measure range, range straggling, stopping power, and energy straggling of alpha particles are discussed in this article. Commercially available equipment with simple modifications is used for these measurements.
Unperformed experiments have no results
Authors: Peres Asher
Published: March 2005

This paper discusses correlations between the results of measurements performed on physical systems which are widely separated, but have interacted in the past. It is shown that quantum correlations are stronger than classical correlations. This property leads to the following paradox, known as Bell’s theorem: Let us assume that the outcome of an experiment performed on one of the systems is independent of the choice of the experiment performed on the other. Now, let us try to imagine the results of alternative measurements, which could have been performed on the same systems instead of the actual measurements. Then there is no way of contriving these hypothetical results so that they will satisfy all the quantum correlations with the results of the actual measurements. However, the weaker classical correlations can be satisfied.
Piagetian-styled and process-based physics lecture course for liberal arts majors
Authors: Prigo Robert B.
Published: March 2005

The recent surge of evidence that a good percentage of incoming college students have not fully reached the Piagetian stage of intellectual development necessary for scientific abstraction has prompted the reorganization of a ten-week introductory physics course for liberal arts majors at the University of California, Santa Barbara. Without a formal laboratory, this course now attempts, through a specific scheme of lecture demonstrations and homework problems, to involve the students with the material of the discipline in a manner consistent with Piagetian developmental psychology. The developmental scheme is maintained within an instructional framework that emphasizes the historical processes involved in concept formation as well as the humanistic side of the physics discipline. The initial results, obtained through a student questionnaire and departmental survey, suggest physics understanding and appreciation.
Simple technique for determining the mean lifetime of the cosmic ray μ meson
Authors: Owens A. , Macgregor A. E.
Published: March 2005

A single scintillation counter is used for determining the lifetime of cosmic ray μ mesons. The experimental arrangement has a greater detection rate and a higher detection efficiency than the conventional multidetector delayed coincidence technique.
A low-cost electronic solar energy control
Authors: Blade Richard A. , Small Charles T.
Published: March 2005

A simple, inexpensive differential thermostat circuit, for use with a solar heating system, is described.
K harmonics in one dimension
Authors: Amado R. D. , Coelho H. T.
Published: March 2005

In one dimension, N particles have N-1 internal coordinates. Therefore the K-harmonic method is easier to conceptualize in this case than for three dimensions. For three particles in one dimension the hyperspace is a plane. We examine this case formally, geometrically and numerically in order to shed light on the method, its strengths and its weaknesses. We demonstrate the geometrical basis for its utility for identical particles as well as the basis for its difficulty in dealing with more asymmetrical problems. We also touch on the problem for four and for N particles.
On the Bethe-Peierls-Weiss method of ferromagnetism: An illustrative calculation of a phase transition
Authors: Cabrera G. G.
Published: March 2005

The cluster method of ferromagnetism of Bethe, Peierls, and Weiss is studied for the case of spin S=1/2 and simple cubic structure. A pedagogical calculation is made using the exact eigenfunctions and eigenvalues to compute the transition temperature (Tc), the short-range parameter, the energy per atom, the temperature dependence of the internal field, and the discontinuity in the specific heat at Tc. As it is well known from the original work of Weiss, short-range order effects are included in this theory yielding results above the Curie point which are not predicted by the molecular field theory but are present in most physical materials. On the other hand, the finite size of the cluster produces the instability of the ferromagnetic state at very low temperatures since the low-energy spin-wave states of long wavelength are not allowed. This appears to be the main limitation of the model which must be used cautiously in the ferromagnetic phase.
An advanced undergraduate nuclear lifetime experiment
Authors: Rollefson A. A. , Prior R. M.
Published: March 2005

An experiment is described for measuring the lifetime of the 60-keV state in 237Np which is populated in the α decay of 241Am. The technique used is the delayed coincidence method using a time-to-pulse-height converter. Advantages of this experiment for use in an advanced undergraduate laboratory course are discussed.
Summary of the Kronig-Penney electron
Authors: Wolfe J. C.
Published: March 2005

A package containing a simple solution and numerical analysis of a Kronig-Penney electron is presented.
A model of a discrete transformation using stored water
Authors: Patterson B. D. , Ramm-Arnet A. J.
Published: March 2005

A discrete linear transformation may be represented by a vector-matrix multiplication. A device in which the content of a vector component is given by the height of a column of stored water performs such a transformation by filtering the water through a matrix plate.
Alternative formula for the classical deflection function in a central field
Authors: Klein Abraham
Published: March 2005

Approximation to a continuous and piecewise differentiable central potential by a sequence of step potentials permits the integration in the conventional formula for the deflection function to be done explicitly. Return to the continuous limit after integration yields a new formula which involves an integral only over the region of nonvanishing force. The physical significance of the result is made evident by a more direct derivation combining elementary kinematics and Newton’s law. The utility of the form for carrying through perturbation theory is illustrated.
Cognitive level and college physics achievement
Authors: Cohen H. Daniel , Hillman Donald F. , Agne Russell M.
Published: March 2005

195 students randomly chosen from the four courses that constitute the introductory hierarchy of physics courses at the University of Vermont were tested with selected Piagetian tasks. The results obtained from these tasks as well as SAT verbal and mathematics scores were correlated with level of course as well as with final course grade, used as a measure of achievement. Though 58% of the sample were rated at the level of concrete operations, the Piagetian level was found to be only weakly correlated with both level of course and with final course grade. SAT scores were used as controls with the mathematics score correlating highly, in general, with both course level and final grade, and the verbal score not correlating with either. Implications relative to recently proposed changes in curriculum are discussed.
Symmetry and conservation
Authors: Rosen Joe , Freundlich Yehudah
Published: March 2005

Nature exhibits symmetries and conservations; we associate symmetry and conservation in our theories. Assuming that this association is one of the most fundamental aspects of the laws of nature, it is proposed to find and investigate minimal general theoretical structures that link symmetries and conservations. Two structures are presented and examined, and an example is given of each. These sets of assumptions are subsets of the basic assumptions of quantum and/or classical theories. In one of the examples classical Lagrangian theory is developed from a unique point of view, and a generalization of the Hamiltonian equations of motion is obtained.
Teaching the approach to thermodynamic equilibrium: Some pictures that help
Authors: Baierlein Ralph
Published: March 2005

Although the approach to thermodynamic equilibrium is a subtle issue, one can capture the essence even in an introductory physics course. Here I share a method of pictorial, intuitive presentation that has evolved during a dozen years of teaching the topic.
Teaching relativity with a different philosophy
Authors: Angotti J. A. P. , Caldas I. L. , Neto D. Delizoicov , Rüdinger E. , Pernambuco M. M. C. A.
Published: March 2005

A teaching module on special relativity is described in which priority is given to attitudinal objectives as opposed to objectives of content. The implications of this for the methodology and the structure of the course are described. The functioning of the course material in practice is discussed together with some conclusions drawn from evaluations of the module.
Calculation of the displacement current using the integral form of Ampere’s law
Authors: Dahm A. J.
Published: March 2005

The magnetic field as a function of position between two capacitor plates during discharge is derived with the use of the integral form of Ampere’s law and real currents only. The displacement current must be included to obtain the same result for arbitrary choices of contours.
An air-table experiment on rigid body dynamics
Authors: Hinrichsen P. F.
Published: March 2005

An experiment which studies the motion of an irregular Lucite glider on an air table and demonstrates the dynamic properties of the center of mass is described. By measuring the ratio of the angular velocity to the linear velocity, the radius of gyration is determined and compared with that found from the period of oscillation and by graphical calculation.
A demonstration of radiation-pressure effects by double-exposure holographic interferometry
Authors: Lee Steven W. , Sachse Wolfgang
Published: March 2005

We describe in this brief note an easily performed experiment which utilizes the technique of double-exposure holographic interferometry to demonstrate electromagnetic wave radiation-pressure effects on an illuminated object.
Effect of a magnetic field on the polarizability of a particle bound to a Coulomb potential
Authors: Lambin P. , Van Hay J. C. , Kartheuser E.
Published: March 2005

We present a calculation of the Stark effect experienced by a hydrogen atom placed in a uniform magnetic field. It is suggested that this example may serve as a further application in quantum mechanics courses which demonstrates the simplification of Rayleigh-Schrödinger perturbation theory by introducing the ’’F-operator’’ technique.
A recursive method for calculating certain partition functions
Authors: Woodrum Luther , Tavel Morton , Tavel Judith
Published: March 2005

This paper sets forth a simple recursive method for calculating the partition function and average energy of a system consisting of N electrons and L energy levels. A particularly simple and efficient apl computer program for performing the calculation is also presented. The use of a recursive method makes it unnecessary to enumerate the possible states of the system, and no combinatorics whatsoever are involved.
Mathematical theory of the waterbed
Authors: Press William H.
Published: March 2005

The support of a loading body by a waterbed involves a rather complicated interplay between tension (in an inextensible membrane) and buoyancy forces (in a fluid). In the idealization of a slab symmetry, the equilibrium equations for the shape of the membrane can be solved to give a two-parameter family of solutions. Mathematically, these parameters are (i) a dimensionless measure of the degree to which tension T is important, and (ii) a dimensional length (T/gρ)1/2 which sets the scale of the problem. The two parameters can be shown to be physically equivalent to (i) the weight of the loading body and (ii) the fullness of the waterbed. The problem of N bodies is also considered.
The American science educator in a developing country: A review of the literature
Authors: Watson John G.
Published: March 2005

This article is an attempt to begin a systematic review of the literature concerning the role of the American science educator in developing countries. Three major areas are focused on: limited availability of science teaching facilities and materials, lack of experience on the part of both native teachers and the American science educator operating in a culturally different setting, and the general problems posed by language and cultural differences.
The pressure curve for a rubber balloon
Authors: Merritt D. R. , Weinhaus F.
Published: March 2005

An equation is derived relating the internal pressure of a rubber balloon to its radius. The theoretical pressure curve is shown to be experimentally verifiable in the case of low to moderate extensions, as long as the effects of hysteresis are ignored. The problem of the equilibrium configuration of two interconnected balloons is also discussed.
On the equilibrium states of interconnected bubbles or balloons
Authors: Weinhaus F. , Barker W.
Published: March 2005

A description is given of the equilibrium states of a system composed of two spherical membranes made of either soap film or rubber. The membranes are filled separately with air to unequal radii and then connected by a hollow tube, allowing the air to pass freely from one to the other. The equilibrium configurations are determined by the method of minimization of the availability of the system at constant temperature.
Quantization and independent coordinates
Authors: Essén Hanno
Published: March 2005

This paper reviews canonical and other quantization methods, gives a quantization rule that gives results that agree with those obtained by direct transformation of the Laplacian, and thus expresses the correct Hamiltonian operator in terms of proper conjugate momentum operators. It gives applications to a number of curvilinear coordinates, introduces the class of independent coordinates, presents generalized Jacobi coordinates, and discusses the molecular vibration-rotation Hamiltonian.
How do you know when you’ve got critical damping?
Authors: Heald Mark A.
Published: March 2005

Simple algorithms are presented for determining damping in the vicinity of critical damping from empirical data for a damped simple-harmonic-motion system. In particular, the algorithms allow one to recognize the condition of critical damping with considerable precision.
Steps toward new ways of teaching astronomy
Authors: Celnikier L. M.
Published: March 2005

In this paper, I submit that astronomy-astrophysics courses should be restructured, particularly since the subject is being increasingly opened to nonastronomers. Astronomy provides numerous examples in which one and the same concept is used in many different contexts (experimental techniques as well as theory): this pedagogically invaluable feature is generally lost in traditional courses and books which concentrate on modeling a particular object or class of objects using many different ideas simultaneously. Response from students to experimental courses of this nature has been most encouraging.
Stability at potential maxima: The L4 and L5 points of the restricted three-body problem
Authors: Greenberg Richard , Davis Donald R.
Published: March 2005

The restricted three-body problem, which treats the motion of an infinitesimal particle due to the gravitational attraction of two massive primaries moving on circular orbits about one another, provides an example of motion which is stable at potential maxima. In a reference frame rotating with the two primaries’ orbital angular velocity, the potential felt by a test particle in the plane of the primaries’ orbit has maxima at the two points which form equilateral triangles with the primaries. This potential is the sum of the gravitational potential and a term representing the position-dependent centrifugal force. The maxima, called L4 and L5, are stable locations for the test particle thanks to the velocity-dependent Coriolis force, which is not incorporated in the potential function. Any energy-dissipating process would tend to drive the test particle away from one of these stable points. These phenomena may run counter to common experience and physical intuition.
Photoelectric effect: Back to basics
Authors: Powell R. A.
Published: March 2005

The measurement of Planck’s constant by use of the photoelectric effect has long been a cornerstone experiment of the introductory modern physics laboratory. In this paper, the classic experiment is revisited in order to place more emphasis on the physics of the photoemission process. Toward this end, a measurement and theoretical analysis of the quantum yield of a commercial photocell are presented. Near the photoemission threshold, the quantum yield Y is shown to go as (hν−φc)2, where φc is the work function of the metal photocathode. Hence, φc can be determined from an experimental plot of Y1/2 vs hν. In addition, justification is given for a procedure used for many years to determine the stopping potential from a plot of (photocurrent)1/2 versus applied bias voltage.
Comparison of wave propagation in related continuous and discrete systems—An example
Authors: Schwartz Manuel , Wu Shi-yu
Published: March 2005

An example is given to show that analogous equations result for wave propagation in continuous and discrete systems with corresponding properties, particularly for relatively long wavelengths.
Geometry of the Thomas precession
Authors: Goedecke G. H.
Published: March 2005

The geometrical-kinematical origin of the Thomas precession is emphasized by a derivation which makes use of base vector tetrads.
An electronic analog of the diffraction grating
Authors: MacLeod A. M.
Published: March 2005

An outline description is given of electronic circuitry which is analogous to the optical diffraction grating or to crystals used in the Bragg reflection of x rays or electron waves. The circuitry has 16 slits, each of which may be open or closed, and 2 wavelengths, each of which may be on or off. The set of experiments described shows how the apparatus may be used to demonstrate the simple well-known effects in principal and secondary maxima, and to show additional effects which are difficult to unravel in the true physical situations with gratings or crystals.
Engineering electronics: An alternative degree program for departments of physics
Authors: Jirgal G. H. , Ross J. B.
Published: March 2005

This article describes a terminal degree program in the area of physics which has been developed and taught by the Department of Physics and Astronomy at Park College. This degree program in engineering electronics prepares electronics technicians for employment in industry as senior technicians or junior engineers. Courses from this alternative degree program added to a traditional physics curriculum provide a major curriculum in engineering physics which prepares physics majors for employment in industry.
Time delays in reactions with intermediate and compound nuclear structure
Authors: Rosengaus E. , Mello P.A. , Bauer M.
Published: March 2005

We present a simple model, analytically solvable, of the time evolution of the scattering of a wave packet, which exhibits and clarifies the compound nucleus process, and can be easily extended to the study of the time delays involved when intermediate structure is present.
Point charge in a three-dielectric medium with planar interfaces
Authors: Barrera R. G. , Guzmán O. , Balaguer B.
Published: March 2005

A simple method of obtaining integral representations of the electrostatic potential, the induced surface charge density, and the image potential for a point charge in a three-dielectric medium with infinite planar interfaces is presented. The total induced charge at the interfaces is readily evaluated. Numerical results for the image potential in several illustrative cases are also shown. The case of a point charge between two grounded conducting plates becomes a special limiting case of the present problem.
Modern thermocouple experiment
Authors: Chang K. N. , Cook M. S. , Hamlyn K. M. , Chaplin R. L.
Published: March 2005

A special thermocouple circuit has been used to measure the Joule heating as well as the Peltier heating and cooling for a copper-Constantan metallic junction. It is shown how the Seebeck effect from a thermocouple can successfully monitor the temperature condition of a junction with regard to input power and Peltier effect. By comparison of theoretical and experimental results, it is found that the experimental evaluation of the thermocouple response is 18% of the actual value of the Peltier coefficient.
Jerk: The time rate of change of acceleration
Authors: Schot Steven H.
Published: March 2005

The time rate of change of acceleration has been called the jerk and is important in certain applications of mechanics and acoustics. For planar motion, the jerk vector is resolved here into tangential-normal and radial-transverse components, and the normal component is expressed in terms of an affine differential invariant known as the aberrancy. Using known aberrancy properties of curves, several geometrical properties of the jerk vector are established for plane motion.
The development of a personalized-system-of-instruction introductory physics course for life-science students
Authors: McFarland E. L. , Hallett F. R. , Hunt J. L.
Published: March 2005

The development and operation of an introductory biophysics course for university life-science students is described. The course combines the features of a standard lecture format with the possibility for the student to elect a self-paced, self-study method of instruction. The educational materials of lecture, modularized study guides, and laboratory are described, as well as the use of diagnostic quizzes and individual instruction. The performance of 1800 students in three semesters is analyzed in terms of their weekly effort and their overall achievement. Finally, the economics of such a flexible system is discussed and speculations are made on possible future improvements.
An experience with an individualized system of instruction in a developing country
Authors: Mathur Rajeshwar N.
Published: March 2005

The personalized system of instruction, comprising self-paced, self-study, student-tutored, and mastery systems of instruction, has become very popular in the developed countries. A similar system of instruction has been tried in India. The students welcomed the change from the rigid traditional system. The fast learner helped other students in understanding the course material. Students enjoyed the freedom from attending lectures (no lectures were given) and demonstrated mastery of the material. The students’ responses to this type of instructional system, given in this paper, indicate a demand for more courses using this system. This plan could be successfully used in large classes.
The many uses of disposable plastic hypodermic syringes−A shot in the arm for small equipment budgets
Authors: Ferguson Joe L.
Published: March 2005

The disposable hypodermic syringe can be the primary piece of equipment for many physics experiments and demonstrations. Its low cost makes available to poorly funded programs, and to individuals, a wide range of phenomena which are usually observed only by those with vacuum systems and other relatively expensive equipment. Sometimes-hard-to-see lecture demonstrations can now become desk-top or take-home experiments which students do for themselves. This paper reviews several previously published uses of disposable syringes and presents ten new uses in several different areas of physical science.
On optimizing an Archibald rubber-band heat engine
Authors: Mullen J. G. , Wasserstein Ronald , Burmeister Louis
Published: March 2005

We show that the torque of an Archibald rubber-band heat engine is maximized by an appropriate choice of dimensions. Workable engines must have very low friction. We develop a criterion for determining maximum allowable friction, which indicates how to minimize frictional torque. We give an explicit criterion and discuss procedures for obtaining a sufficiently matched set of rubber bands to avoid engine stalling.
A simplified quantum mechanical model of diatomic molecules
Authors: Nielsen Lars Drud
Published: March 2005

A one-dimensional molecule model with Coulomb potentials replaced by δ functions is introduced. The mathematical simplicity of the model facilitates the quantum mechanical treatment and offers a straightforward demonstration of the essentials of two-particle problems. In spite of the crudeness of the model, quantitative results are obtained in fair agreement with those of a true hydrogen molecule.
Concept of the exponential law prior to 1900
Authors: Curtis Lorenzo J.
Published: March 2005

The historical development of a quantitative perception of the processes of exponential growth and decay is traced from its ancient origins through pre-20th century mathematical formulations and physical applications. Evidence indicates that the concepts of the mean life and the half life and their relationships to linear differential rate equations and to multiple simultaneous and sequential processes, as well as the nonlinear conditions which bring about the breakdown of the exponential law, were all understood and presented in written records long before their now nearly synonymous application to nuclear radioactivity. Exponential processes were among the earliest quantitative concepts to be mathematically formulated, and our modern understanding of them can be enhanced by historical perspective.
Elementary quantum mechanics in a high-energy process
Authors: Delville A. , Jasselette P. , Vandermeulen J.
Published: March 2005

Two approaches to strong absorption in the framework of elementary quantum mechanics are compared: the black sphere and a model based on the continuum theory of nuclear reactions; both contain a sole parameter. The application to proton-antiproton interactions at low momenta is examined; the black sphere model is not appropriate but the second model is surprisingly rewarding in spite of its simplicity.
Completeness of the Coulomb wave functions in quantum mechanics
Authors: Mukunda N.
Published: March 2005

We give an explicit, direct, and fairly elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses only some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory; therefore it would form useful supplementary reading for a graduate course on quantum mechanics.
Construction and use of an astronomy test item file
Authors: Turner Lawrence E.
Published: March 2005

A test item file for Introductory Astronomy questions has been constructed. The characteristics of the file include: construction from readily available and inexpensive materials, an efficient organization by a content categorization scheme to allow quick retrieval, classification of questions according to behavioral objectives to aid in construction of a balanced exam, a format that permits a direct generation of exams without further typing, and a record of use including ease and discrimination information so that the effectiveness of the questions can be enhanced.
Experiment in scientific investigation
Authors: Epp Chirold D.
Published: March 2005

An experiment designed to give students a feel for the way in which theoretical models evolve is discussed. Students are given a system about which they have no a priori knowledge and asked to develop a consistent model which fully explains all their observations on the system.
Newtonian limit for a geodesic in a Schwarzschild field
Authors: Harvey Alex
Published: March 2005

In the 19th century there were many attempts to explain the advance of the perihelion of Mercury by modifying the Newtonian potential by the addition of velocity-dependent terms. That such potentials did not give better results was due to the wrong choice of sign of the velocity term. This is demonstrated by showing that in a simple Newtonian limit for near-circular orbits the geodesic of a mass point in a Schwarzschild field may be expressed as motion in a velocity-dependent central potential. The sign of the velocity term is opposite to that arbitrarily assigned in the past.
Relativistic negative acceleration components
Authors: González-Díaz P. F.
Published: March 2005

The most general case of a body acted upon by a force with x, y, and z components is investigated. Combining several Fx/Fy and Fz/Fy ratios, the behavior of ax/ay and az/ay versus velocity is studied in the situation where vx=vy=vz. When the three force components are different from zero, it is shown that, at a given sufficiently high velocity, a negative acceleration component along the axis of the smallest force component always results. In addition, at another higher velocity, the acceleration component along the axis of the intermediate force component also becomes negative. A special case is considered in which one of the three force components is zero. Here, the acceleration component along the axis with zero force component is negative at any velocity; a negative acceleration component, along the axis with intermediate force component, also appears (at sufficiently relativistic velocities), provided that the third (nonzero) force component is larger than twice the intermediate force component. Explanations are given for the behavior of these relativistic accelerations.
Some useful identities in normal ordering
Authors: Bose S. K.
Published: March 2005

I state and prove some useful identities in normal ordering. The identities can be very useful in ordinary quantum-mechanical and many-body problems.
Induced angular momentum
Authors: Parker G. W.
Published: March 2005

The angular momentum induced in the bound motion of an electron by an external magnetic field B is evaluated classically and quantum mechanically. The quantum-mechanical model used is one in which the angular momentum is quenched when B=0 so that it is representative of a molecule rather than an atom. The current density and its associated magnetic moment are calculated and discussed. Two different methods are used to solve the first-order perturbation theory equation for the required eigenfunction.
Inverse-square orbits: A geometric approach
Authors: Rainwater James C. , Weinstock Robert
Published: March 2005

Kepler’s first law of planetary motion is derived from Newtonian principles in a way that directly reveals the orbit as a locus of points for which the sum of distances from two fixed points is constant. The elementary differential calculus of vectors is the most advanced mathematical tool used. Also presented are derivations of the same character showing that a nonreturning comet’s orbit is either a set of points for which the difference of distances from two fixed points is constant or a locus all of whose points are equidistant from a fixed point and a fixed line. The hyperbolic orbit for inverse-square repulsion is derived as a by product.
Teaching about the colonization of space
Authors: Huebner Jay S.
Published: March 2005

The topic of space industrialization and colonization affords science teachers the opportunity of having students study topics in contemporary science and technology which illustrate the role science has in shaping human destiny.
Observing simulated Cepheid variable stars in an introductory astronomy lab
Authors: Flesch Terry R.
Published: March 2005

An astronomy laboratory exercise has been developed which allows students to discover for themselves the relationship between the temperature and luminosity changes in Cepheid variable stars. The equipment used is either easily constructed or readily available from among instruments commonly found in physics departments. A sinusoidally varying light source is monitored using a telescope-photomultiplier tube combination. Filters are employed allowing color index information to be obtained. The light curves are recorded on a strip-chart recorder, allowing each student to make his own observations and use his own chart recording in the data reductions.
Physics requirements in undergraduate engineering education: Report of a private survey
Authors: Kaup D. J. , Czanderna A. W.
Published: March 2005

A questionnaire addressed to the physics department chairmen at 92 colleges and universities with accredited engineering programs in the U. S. generated 77 responses. These responses have provided hard data concerning the physics lecture and laboratory requirements at engineering schools. Most schools offer from eight to 12 credit hours of physics, which includes one or two credit hours of laboratory work. In the last four years, there has been no significant decrease or increase in these requirements.
Equilibrium and stability of a pendulum in an orbiting spaceship
Authors: Blitzer Leon
Published: March 2005

A simple pendulum attached to a fixed point inside a spaceship moving in a circular orbit about a planet can be in equilibrium in either 2, 3, 4, or 6 positions, of which 1, 1, 2, and 2, respectively, are stable. The number, orientation, and stability of the equilibria depend on the length of the pendulum and the location of the point of attachment relative to the center of gravity of the spacecraft.
Application of the nonlinear vector product to Lorentz transformations
Authors: Farach Horacio A. , Aharonov Yakir , Poole Charles P. , Zanette Susana I.
Published: March 2005

The nonlinear vector product used in a previous publication to treat successive space rotations has been extended to the case of Lorentz transformations by employing an imaginary angle in place of the real angle used for the space rotation case. Expressions were derived for operations of pure Lorentz transformations and for the form of a general Lorentz transformation. The utility of the method was demonstrated by applying it to the derivations of the addition law of velocities and the Thomas precession.
Available energy via nonequilibrium thermodynamics
Authors: Woollett E. L.
Published: March 2005

Basic macroscopic relations involving the concept of available energy are derived from the local equations of nonequilibrium thermodynamics. The available energy is that part of a system’s energy which can be converted into useful work. The model used describes a mixture of heat conducting compressible inviscid chemically reacting fluids in a gravitational field. Integration of the local equations yields instructive derivations of basic available energy relations for closed systems, continuous flow arrangements, and for diffusive mixing or separation processes.
Behavior of a real top
Authors: Stefanini Ledo
Published: March 2005

This article is concerned with the behavior of a top (the extreme end of which is made round) spinning on surfaces provided with friction.
Heat diffusion in a solid sphere and Fourier theory: An elementary practical example
Authors: Unsworth J. , Duarte F. J.
Published: March 2005

A method to determine the thermal diffusivity of a polymer, which is suitable for the undergraduate laboratory, is described. It serves as a practical demonstration of classical Fourier theory. In particular, techniques of realizing near-to-perfect boundary conditions are described.
Stable circular orbits of freely moving balls on rotating discs
Authors: Weltner Klaus
Published: March 2005

If balls are set on rotating discs these balls do not leave the rotating plane but move on circles. The frequency of this circular movement depends on neither radius nor mass of the balls, nor on the radius of the circle. It depends only on the frequency of the rotating disc. It can be shown that this surprising phenomenon, which can easily be observed, is due to friction between ball and disc. A theoretical solution is given.
T
2 in coherent optics: Collision, dephasing time, or reciprocal linewidth
Authors: Nettel Stephen J. , Lempicki Alexander
Published: March 2005

When relating measurements in the frequency domain (linewidths) to those in the time domain (coherent optical transients), one is faced by the question of the exact meaning of T2, the transverse relaxation time introduced by Bloch for NMR. We give a simple quantum-mechanical derivation of T2 as a collision time, and then discuss dephasing in coherent optical decay to bring out the role of both T2 and linewidth in this process.
Motion of electrons in electric and magnetic fields; introductory laboratory and computer studies
Authors: Huggins Elisha R. , Lelek Jeffrey J.
Published: March 2005

We describe a series of laboratory experiments and computer simulations of the motion of electrons in electric and magnetic fields. The experiments, which involve an inexpensive student-built electron gun, study the electron mean free path, magnetic focusing, ratio of electron charge to mass (e/m), and the motion of electrons in crossed electric and magnetic fields (velocity selector). A small search coil is used to map the magnetic field of the Helmholtz coils used in the electron gun experiments. Students have used the computer to simulate the e/m and velocity selector experiments and magnetic mirroring in a dipole magnetic field. This led to a technique for mapping the Van Allen Radiation belt patterns.
Basic physics of the semidiurnal lunar tide
Authors: Arons A. B.
Published: March 2005

Effects producing the semidiurnal tidal bulges are described, using elementary methods, without reference to fictitious forces and without recourse to a potential. One analysis presents a rough but simple analog to the tidal effects in terms of gedanken experiments in a very large, freely falling space laboratory. Another analysis explicitly contrasts the effects that would be observed on the earth in a ’’one-body’’ system (i.e., earth held fixed in an inertial frame; the moon revolving around it) with effects in a ’’two-body’’ system (i.e., earth free; earth-moon system revolving in the inertial frame).
Ground-state energy of one-dimensional many-boson systems with attractive delta interactions
Authors: Moszkowski S. A. , Strobel G.
Published: March 2005

We have calculated the ground-state energy of a system of bosons in one dimension interacting via attractive δ-function interactions. In this example, the K harmonic method in its simplest form gives slightly larger binding than the independent particle method and slightly less than the exact result.
Teaching physicists’ thinking skills in the laboratory
Authors: Reif F. , St. John Mark
Published: March 2005

We describe a prototype introductory physics laboratory designed to teach students some general intellectual skills widely useful in scientific work. These skills include both basic skills (such as estimating quantities, determining errors, or applying useful measuring techniques) and higher-level skills (such as effectively describing experiments and flexibly adapting the resulting knowledge to different conditions). The teaching methods emphasize the utility of organizing information in hierarchical and goal-directed fashion. Furthermore, they strive to use an optimum combination of instructional means (’’minilabs,’’ more major ’’group labs,’’ and integrated assessment devices) to achieve the desired ends. A careful evaluation showed (i) that the prototype course is indeed quite successful in teaching the desired general intellectual skills, and (ii) that these skills are ordinarily not acquired by students in traditional courses. Students’ attitudes toward the prototype course are also appreciably more positive.
Virial theorem and scale transformations
Authors: Kleban Peter
Published: March 2005

In this article the virial theorem, which is useful in classical mechanics, quantum mechanics, and statistical mechanics, is considered. Most derivations of this result are of one of two types. Either one starts with the function r⋅p [or operator 1/2 (r⋅p+p⋅r)], or else takes a derivative with respect to the parameter of a scale transformation. It is pointed out that these two methods are closely related, since [r⋅p or 1/2 (r⋅p+p⋅r)] is the generator of scale transformations. This is demonstrated explicitly for classical and quantum-mechanical systems. The pedagogical advantages in pointing out this connection are also examined.
Frictional force on rolling objects
Authors: Shaw Donald E.
Published: March 2005

An experiment investigating the direction of the frictional force exerted by a horizontal surface on a rolling object is discussed. Students generally find the results surprising; however, the observations support the predictions of rotational dynamics. The experiment is suitable for an introductory mechanics laboratory.
Reading through pinholes: A closer look
Authors: Keating Michael P.
Published: March 2005

A previous discussion of placing a pinhole in front of each eye, and reading with ’’relaxed’’ vision is reconsidered in view of the connection between accommodation and convergence. The increased depth of focus due to the pinholes does not force accommodation to relax. Instead accommodation is free to change without blurring the retinal image. Under these conditions, the accommodative response is dictated, through the accommodative-convergence relationship, by the convergence demands of the situation.
A simple method for illustrating the difference between the homogeneous and inhomogeneous Lorentz groups
Authors: Kim Y. S. , Noz Marilyn E. , Oh S. H.
Published: March 2005

A method is proposed for illustrating the difference between the Poincaré (inhomogeneous Lorentz) and homogeneous Lorentz groups. Representations of the Poincaré group are constructed from solutions of the relativistic harmonic oscillator equation whose physical wave functions have been effective in describing basic high-energy hadronic features in the relativistic quark model. It is shown that the Poincaré group can be represented by solutions of the relativistic oscillator equation in a ’’moving cylindrical’’ coordinate system in which the time-separation variable in the hadronic rest frame is treated separately. Representations which are diagonal in the Casimir operators of the homogeneous Lorentz group are also constructed from solutions of the same oscillator differential equation in a hyperbolic coordinate system. It is pointed out that the difference between the Poincaré and homogeneous Lorentz groups mainfests itself in the coordinate systems in which the oscillator differential equation in separable.