bluuebunny/crossref_metadata_2025 huggingface dataset:
Model of the behavior of solid objects during collision
Authors: Bayman B. F.
Published: March 2005

When two hard solid objects collide, acoustic waves are generated at the point of impact. The deformation of the objects and their subsequent separation are associated with the propagation of these acoustic waves through the objects and their reflection from the surfaces. In this paper we follow the time development of these processes in detail for one-dimensional collisions involving Hooke’s law springs. We calculate the degree of inelasticity of the collision from the state of internal excitation of the springs after separation occurs. An attempt is made to generalize the conclusions obtained in this one-dimensional model to the qualitative description of the collision of hard spheres.
Integrating physics and the philosophy of science through guided design
Authors: Goldberg Fred M. , D’Amour Gene
Published: March 2005

The problem of teaching and evaluating decision-making skills in physics is discussed. What is needed is a system which will teach students both (1) how to utilize the techniques of physics to solve open-ended problems in a creative and disciplined way and (2) an understanding of the role these skills play in the ongoing process of physics. The ’’guided design’’ method of instruction is described and suggested as a solution to the first problem. An application of guided design to a multidisciplinary course is then discussed that offers a possible solution to the second problem.
Expansions of spin-1/2 expectation values
Authors: Fernow Richard C.
Published: March 2005

We review some general properties of density and scattering matrices and composite spin spaces of spin-1/2 particles. We give a derivation of a useful expansion of spin expectation values. The expansion is used in a number of simple examples. Spin tensors and pure spin cross sections are introduced.
How good is Hartree–Fock? Calculation of the static electric polarizability in an exactly soluble model
Authors: Krieger J. B. , Kaufman S. E.
Published: March 2005

The exactly soluble model, originally considered by Moshinsky, consisting of two spin-1/2 particles interacting through harmonic-oscillator forces and moving in a common harmonic-oscillator potential is extended to include the effects of an external electric field. We solve for the energy exactly, exactly in the Hartree–Fock approximation, and also compare to the results of Hartree–Fock perturbation theory. We find that the Hartree–Fock method yields the same result for the electric polarizability as the exact solution even though the field-independent part of the energy is not the same. However, when second-order Hartree–Fock perturbation theory is employed, the results for the polarizability can be substantially in error. Similar results obtain for the calculation of the matrix element for optical absorption in the dipole approximation.
Thevenin’s theorem in linear circuits with controlled sources
Authors: Valberg Peter A.
Published: March 2005

In the analysis of electronic circuits, it is often useful to replace a network by its Thevenin equivalent circuit. To do this one needs to calculate the values of the equivalent voltage and series resistance. It is shown that the prescription for finding the equivalent resistance given by most electronic texts is not generally valid when the network contains sources whose strength is controlled by currents within the network. In fact, the source strength coefficients appear in the expression for the equivalent resistance, yet would be eliminated by the usual method of short-circuiting the sources. A correct method of derivation is given and the emitter–follower circuit is shown as an example.
Teaching general learning and problem-solving skills
Authors: Reif F. , Larkin Jill H. , Brackett George C.
Published: March 2005

This article describes the investigation and teaching of two general cognitive skills important in introductory physics. We first analyzed the various abilities needed for understanding a relation (definition or law) well enough to use it appropriately. Then we developed two different instructional methods for teaching students the general learning skill of gaining such an understanding of any new relation. We further taught students a simple strategy for problem solving. Our results indicate that students can indeed be taught such general cognitive skills and that they can transfer these skills to areas outside of physics.
’’Bohr and Einstein’’: A course for nonscience students
Authors: Schlegel Richard
Published: March 2005

A course that has been given at Michigan State University for nonscience upper-class students is described. Its aim is to present the salient ideas of relativity and quantum physics in association with the lives of Albert Einstein and Niels Bohr. Generally qualitative arguments and discussions of key experiments are used to convey the scientific content. The controversy between Bohr and Einstein on quantum theory is included, and serves to point up a basic philosophical innovation in twentieth century physics. Some attention is also given to the attempts of both Einstein and Bohr to influence political events.
Analog computer demonstration of traveling and standing waves
Authors: Russell G. A. , Mankowski R. R. , Fournier D. F.
Published: March 2005

A simple analog computer program is described which, in conjunction with a dual-trace storage oscilloscope, can demonstrate traveling and standing waves, the effect of various reflection coefficients, standing wave ratios, and other wave phenomena. The voltages generated by the analog are viewed on the oscilloscope screen to provide a vivid, easily understood, controllable demonstration, ideally suited for teaching.
Accurate orientation of the polar axis of an equatorial telescope mounting
Authors: Robinson J. R. , Coates D. W.
Published: March 2005

A straightforward method is given for determining the orientation of the polar axis of an equatorially mounted optical telescope. The background theory given illustrates some important properties of the celestial sphere and gives an insight into the usual ’’rule of thumb’’ methods of axis orientation; it also provides a basis for instructors and students to devise their own orientation methods.
Use of Doppler-shifted light beams to measure time during acceleration
Authors: Greenwood Margaret Stautberg
Published: March 2005

In this study of the twin paradox, the periods of acceleration necessary for the astronaut to start the journey, turn around, and return to rest at the starting point are investigated. Each twin sends a light beam of frequency f0 to the other one. The waves received by each twin have a constantly changing Doppler-shifted frequency due to the astronaut’s acceleration. The stay-at-home twin (SAHT) receives K cycles sent by the astronaut and the astronaut receives K′ cycles sent by SAHT, where K≠K′. K and K′ are calculated by integrating the observed instantaneous frequency with respect to time. Then the time for the round trip recorded by the astronaut, TA, and by SAHT, TS, can be compared, where TA=K/f0 and TS=K′/f0. The relationships derived are identical to those obtained by using the concept of proper time. The results are illustrated with numerical examples.
The Richtmyer Memorial Lecture: Progress in x-ray astronomy
Authors: Giacconi Riccardo
Published: March 2005

Response of the Richtmyer Memorial Lecturer to the American Association of Physics Teachers, 30 January 1975, at Anaheim, California.
Critical reading list for teachers of physics-and-society courses
Authors: Spencer Charles , Schroeer Dietrich
Published: March 2005

A critical bibliography of 25 books is presented. It is to aid potential teachers of physics-and-society courses in acquiring competence in this subject area.
On the teaching of introductory quantum mechanics
Authors: Rüdinger Erik
Published: March 2005

Arguments are presented to explain why the usual approach to the teaching of introductory quantum mechanics, as well as some newer ones, in general seems to fail to achieve any profound understanding of the subject. An alternative approach is suggested which, although not new, has hardly been adopted anywhere, for reasons which are analyzed. A course which has been based on this approach is described. The main aim of the article is to contribute to, and hopefully stimulate, a debate on the various approaches used to introduce quantum mechanics and the psychological and didactic premises on which they are based.
Introductory absorption experiment for low-energy β particles
Authors: Murray David G.
Published: March 2005

A student experiment is described in which paper absorbers are used to determine the maximum energy of β particles emitted by 14C. (AIP)
Computer-drawn field lines and potential surfaces for a wide range of field configurations
Authors: Brandt Siegmund , Schneider Hermann
Published: March 2005

An interactive computer program has been written that computes field lines and equipotential surfaces for a wide range of field configurations. The mathematical technique and details of the program, the input data, and different modes of graphical representation are described, and various examples are presented. Possible extensions of the method are discussed.
An inexpensive, reliable, high-power molecular nitrogen laser
Authors: Hilborn Robert C.
Published: March 2005

The design, construction, and performance of a low-cost, transversely excited molecular nitrogen laser are described in detail. Peak powers of over 100 kW at pulse repetition rates of 20 pps have been achieved at a total cost, including vacuum pump and power supply, of under $800. Some simple experiments and demonstrations using this laser are suggested.
On the generalized Bernoulli construction. II. Extension to two and three dimensions
Authors: del Rio Fernando , Trigueros María , Martina Esteban
Published: March 2005

The generalized Bernoulli construction is used to study the equation of state of rigid particles in two and three dimensions. A system of hard squares is considered in detail, and results for hard cubes, disks, and spheres are also presented. The discussion permits the introduction of the mean-free-path problem in the equation of state, and the result of the virial theorem of Clausius is obtained for these systems. This heuristic method can be used to discuss the equation of state at low and high densities without the use of formal theories.
Tsunamis, sealing wax, and string
Authors: Curzon F. L. , Neilson B.
Published: March 2005

A ground glass screen on the side of a wave tank has been used to record the profile left by the peak of a tsunami propagating along a wave tank with a sloping base. Using traditional sealing wax-and-string technology and old-fashioned but cheap data processing, we have carried out a $12 verification of tsunami growth. The features of the experiment are presented in enough detail to enable anyone with the necessary $20 (allowing for inflation) to investigate interesting anomalies which personal circumstances prevented us from pursuing.
Torque on a bar magnet
Authors: Page Chester H.
Published: March 2005

If all magnetic quantities are defined via fields, with no use of poles and with magnetic moment defined as the volume integral of magnetization, energy considerations yield the torque on a magnet immersed in a permeable fluid in an external field. Although the torque on a disk magnet is proportional to B, the torque on a needle magnet is proportional to μ0H, as reported experimentally by Whitworth and Stopes-Roe. The experiment does not prove either A. E. Kennelly [J. Eng. Educ. 27, 290 (1935)] or Sommerfeld to be right or wrong, but demonstrates that magnetic theory based on poles cannot be applied to magnets, and thereby strengthens the philosophy that electromagnetic theory should be based on fields.
Personalized instruction: A summary of comparative research, 1967–1974
Authors: Taveggia Thomas C.
Published: March 2005

This paper summarizes the results of fourteen separate studies comparing the learning outcomes of a new instructional procedure, the ’’Personalized System of Instruction’’ (PSI), with the learning outcomes of conventional approaches to college teaching. The major conclusion suggested by this summary of research is that, when evaluated by average student performance on course content examinations, PSI has proven superior to the conventional methods with which it has experimentally been compared. The author examines features of PSI courses which probably account for this superiority, and he discusses some of the theoretical and practical implications of research on PSI conducted between 1967 and 1974.
Thinking of the photon as a quantum-mechanical particle
Authors: Young Richard A.
Published: March 2005

Using simple arguments we show that a photon, when considered as a quantum-mechanical particle, may be thought of as being attracted to, or repelled from, an atom. A ’’photon Schrödinger equation’’ (PSE) is used to illustrate the common quantum behavior of photons and, e.g., electrons. Using the PSE we relate the attractive or repulsive atom–photon potential to the dielectric constant of a material and show how total internal reflection may be considered as a photon trapped inside a potential well.
Experimental statistics for undergraduates. II
Authors: MacLeod A. M.
Published: March 2005

A detailed description is given of the logic circuitry required for the experiment on undergraduate statistics described in the preceding article. Random events are counted for sampling periods of typically a few milliseconds, and the resulting Poisson distribution is displayed on a multichannel analyzer. The number of sampling intervals, N, and the total count, 𝒥nixi, may be displayed on numerical indicators, which thus permits the easy calculation of the mean of the distribution 𝒥nixi/N. The circuitry also permits the buildup of the distribution of the mean values of a series of runs, each containing a small number of sampling intervals. Input circuitry controlling the dead time is also described.
Principle of equivalence
Authors: Ray John R.
Published: March 2005

The principle of equivalence is discussed in its modern form based oin the theory of general relativity. This is compared to the original formulation of the princple in 1911.
An unusual lunar halo
Authors: Cardon Bartley L.
Published: March 2005

An unusual combination of lunar halos was photographed over Tucson, Arizona on 14 November 1975. Three halos, the 22° refraction halo, the circumscribed halo, and a reflection halo (the paraselenic circle) were present. The origin of these halos is discussed. The form and orientations of the ice crystals responsible for the observed halo features are deduced.
A special topic from nuclear reactor dynamics for the undergraduate physics curriculum
Authors: Sevenich R. A.
Published: March 2005

An example from the dynamics of nuclear reactors is presented for possible inclusion as a special topic in the undergraduate physics curriculum. An intuitive derivation of the point reactor equations is followed by formulation of equations for inverse and direct kinetics which are readily programmed on a digital computer. Several specific computer simulations involving the effect of control rod motion on reactor power are suggested as programming exercises for the student.
Physics of photography course for fine arts students
Authors: Galli Anthony John
Published: March 2005

A physics course for fine arts students majoring in photography and for other non-science students interested in photography has been developed. An outline of the course is given, emphasizing points of particularly great interest to the students.
Spin-weighted spherical harmonics and electromagnetic multipole expansions
Authors: Scanio Joseph J. G.
Published: March 2005

We give the multipole expansion of the electromagnetic fields in terms of spin-weighted spherical harmonics, a set of functions which are both complete and natural for multipole expansion and which are used extensively in general relativity. Examples of the use of this formalism are given. The material discussed could be presented in an advanced course in classical electrodynamics.
On the unambiguity of stationary perturbation theory
Authors: de Muynck Willem M.
Published: March 2005

The relation is obtained between the solution of the stationary perturbation problem for which the unperturbed states ‖ En 〉 and the perturbed states ‖ Wn 〉 obey the relation 〈 Wn ‖ En 〉 = 1, and the solution in case this requirement is not made. This is done in all orders of the perturbation theory. It is shown that the influence of the requirement amounts to a normalization factor which is not merely a phase factor.
Classical and quantum spreading of position probability
Authors: Farina J. E. G.
Published: March 2005

If Δxt is the standard deviation of the position probability distribution at time t of a particle moving freely in one dimension, and Δv is the standard deviation of its velocity distribution, it is shown for a suitable choice of time origin that (Δxt)2 =  (Δx0)2 +  (Δv)2t2 whether the particle is moving classically or quantum mechanically. The quantum-mechanical proof is shown to exactly parallel that in the classical case. In the classical case, the correlation coefficient between the velocity and position distributions is shown to tend to −1 as t → −∞, to increase steadily with time, and to become +1 as t → +∞. A quantum-mechanical analog of this result is also proved.
Satellite motion in the vicinity of the triangular libration points
Authors: Blackburn James A. , Nerenberg M. A. H. , Beaudoin Y.
Published: March 2005

The behavior of natural and artificial satellites in the vicinity of the triangular libration points is examined with the aid of computer simulations. The results of a linearized small-perturbation approximation are compared with the observed orbits. Applications to the Sun–Jupiter and Earth–Moon systems are discussed.
Which mean?
Authors: Squire P. T.
Published: March 2005

The process of averaging in situations involving low random error of measurement is examined critically. The illustrative examples are drawn from physics, but the conclusions apply more generally. In particular, the various averages which can arise in physical situations are discussed. Approximate expressions are given for the differences between them. Finally, the significance of these differences is examined.
Reading with the relaxed eye
Authors: Mathur S. S. , Bahuguna R. D.
Published: March 2005

The relation between the aperture and the depth of focus of a lens is briefly described. A specific application to the eye is discussed in detail.
Physics teaching as a laboratory experiment
Authors: Buckwald R. A.
Published: March 2005

A novel method has been employed at the Technion to expose senior physics students to physics teaching. Students were allowed to substitute for one three-week laboratory experiment, an ’’experiment in teaching physics.’’ The setting for the experiment was the eigth grade class of an unsophisticated Israeli village. The experiment provided a remarkably stimulating experience for the students, the pupils, and the elementary teachers. The experience even changed the career goals of a number of the students involved.
Computer-graded homework in introductory physics
Authors: Hudson H. T.
Published: March 2005

Computer-graded multiple-choice problem sets provide some of the advantages of homework graded in a traditional manner. Solution sheets for each set provide a solution to each problem and hints which will help the student identify his misconceptions.
From the Compton effect to quarks and asymptotic freedom
Authors: Wilson Richard
Published: March 2005

Jesse DuMond’s first major experiments on the broadening of the x-ray line from Compton scattering of x rays showed the electron momenta in atoms and solids. Using electron scattering, momenta of nucleons in nuclei have been measured. Using electron or muon scattering by protons, momenta of quarks in the proton can be determined. These are all related physical processes.
Views of the universe over cosmological time spans
Authors: Lawrence J. K.
Published: March 2005

We consider an Earth observer’s view of the universe as it would appear at various stages of its evolution. This is calculated numerically from the relativistic Friedmann universe models and is presented in the form of Hubble plots of red shift versus distance for distant galaxies. Trajectories of particular galaxies followed through time are also shown. In the case of a closed universe, the results are particularly complex and interesting.
Minimum dipole moment required to bind an electron—molecular theorists rediscover phenomenon mentioned in Fermi-Teller paper twenty years earlier
Authors: Turner J. E.
Published: March 2005

Work leading to the discovery of the minimum dipole moment for electron binding, Dmin=0.639 ea0 (atomic units), by several groups in 1967–1968 is described. It was subsequently learned that this number had been published in 1947 by Fermi and Teller, who did not, however, indicate how they derived it. The author has found a numerical solution in Fermi’s notebooks from 1946–1950 at the University of Chicago Library. Fermi’s work is described and presented here with relevant material from his notebooks.
Illustrative calculations using projection techniques
Authors: Muriel A.
Published: March 2005

Using a pedagogical model introduced by Dresden and Feiock, the quantum mechanical version of the Kac ring model, the following studies are illustrated: (a) solution of the Liouville equation using projection techniques; (b) analysis of the difference between the linear and nonlinear theories; and (c) existence of a kinetic description, with the solution of the Pauli master equation for this example.
Simple geometrical means of visualizing families of Rayleigh hysteresis loops
Authors: Milstein Frederick , Baldwin John A.
Published: March 2005

A simple geometrical means of visualizing and generating families of Rayleigh magnetic hysteresis loops is presented.
Quantitative angular momentum experiment on the rotating chair
Authors: Prigo Robert B. , Reading Melissa
Published: March 2005

The popular rotating chair and hand-held weights demonstration on the conservation of angular momentum has been adapted to the lower division laboratory. The demonstration has been made quantitative by adding radial tracks to the chair along which calibrated masses may be positioned without extension of the occupant’s arms. The conservation of angular momentum can be tested and the moment of inertia of the student in various sitting positions can be determined.
Properties of an infinite linear array of atoms based on a Morse pairwise potential
Authors: Markworth Alan J.
Published: March 2005

Properties of an infinitely long, linear array of atoms are described assuming the atoms interact with each other via a Morse pairwise potential. The equilibrium lattice parameter for a regularly spaced array is calculated, as is the potential function pertinent to vacancy migration. A specific numerical example is considered using the Girifalco and Weizer parameters for the pairwise interatomic potential characterizing body-centered-cubic iron.
Generalized Doppler formula in a nonstatic universe
Authors: Gross Peter G.
Published: March 2005

The general Doppler formula in a nonstatic universe is derived, relating the expansion of the universe and the peculiar velocity of the light-emitting object to the shift of spectral lines measured by a fundamental observer. No reference to the Riemannian metric of general relativity is required; the only assumptions needed are special relativity, homogeneity, and isotropy of the universe. A few examples of applications to physical cosmology are given.
Transformation theory, accelerating frames, and two simple problems
Authors: Schmid G. Bruno
Published: March 2005

An operator which transforms quantum state functions from inertial to certain noninertial reference frames is presented. This operator is applied to solve two well-known problems: (1) the stationary state wave functions for a particle in a uniform gravitational field; (2) the motion and spreading of a Gaussian wave packet in a uniform gravitational field. The salient features of both analyses are discussed.
Projectile motion with air resistance quadratic in the speed
Authors: Parker G. W.
Published: March 2005

We consider two-dimensional motion of a projectile experiencing a constant gravitational force and a fluid drag force which is quadratic in the projectile’s speed. The equations of motions are coupled nonlinear equations. Their solutions have general properties which are easily visualized, although much different from those obtained when a drag force is neglected. Because of these features a study of these equations would provide an interesting counterpoint to the already familiar case of no drag. In this paper we derive simple approximate solutions to the equations of motion for both short and long times. A numerical example is used to compare these approximate solutions with accurate results obtained by numerical integration from an exact but implicit solution. Finally, the origin of the quadratic drag force is discussed.
Two Van de Graaff experiments for the senior laboratory
Authors: Chai J. , McClelland J. B. , Spinka H.
Published: March 2005

Two experiments in nuclear physics for a senior level laboratory course are described. One experiment is a measurement of resonances in a nuclear reaction. Simple electronics, a NaI detector, a system for evaporating thin layers of material onto a metal backing in vacuum, and a method of measuring the magnetic field in the Van de Graaff analyzing magnet are needed. The other experiment is a measurement of the p+p elastic scattering cross section at a laboratory angle of 45° and at bombarding energies near 400 keV. The interference between Coulomb and nuclear scattering is studied. Two surface barrier detectors, standard coincidence electronics, and a windowless gas target are used.
Interactions of a three–two liberal arts–engineering program with a physics department
Authors: Truman J. C. , Fielder D. S.
Published: March 2005

The effects which participation in a three–two liberal arts–engineering program have had on a physics department at a liberal arts college are discussed; they include an increase in the number of physics majors and increased enrollments in physics department courses. Responsibilities which must be accepted by the department are also discussed. We have found that the necessary investment of time and effort is well justified by the benefits which result.
Correlation between mathematical skills and success in physics
Authors: Hudson H. T. , McIntire W. R.
Published: March 2005

A pre-course test of algebraic and trigonometric skills has been correlated with performance in introductory physics without calculus. For 200 students in two sections it was found that mathematical abilities at the beginning of the course weakly correlate with performance in the course. A repeat of the test at the end of the course indicates that mathematical skills alone are not sufficient to guarantee success in physics, but that unless the student has the mathematical skills, the performance in the physics will be poor.
Inside the black hole
Authors: Brehme Robert W.
Published: March 2005

The simplest model of a black hole, the massive point source generating a static spherically symmetric gravitational field, is examined using the Schwarzschild coordinate frame. A brief review is given of this coordinate frame external to the Schwarzschild surface. Greater attention is paid to an interpretation of this frame inside the Schwarzschild surface. Here the roles of space and time are reversed in the sense that the external radial coordinate becomes an internal temporal coordinate, and the external temporal coordinate becomes an internal spatial coordinate. An internal universe is constructed from this frame, and a few simple kinematic phenomena are described in terms of it. The internal and external coordinates are connected graphically by using Kruskal coordinates and physically by considering the world lines of photons and freely moving particles which transit the Schwarzschild surface.
’’Seven Ideas’’ and ’’Entertainment and the Arts’’: Two courses for the non-science major
Authors: Spielberg N. , Christensen S. H.
Published: March 2005

Two one-quarter descriptive physics courses which have been particularly successful are described. Course content and teaching techniques are discussed. Resulting large enrollments and positive reception by students and faculty are reported.
Slowing-down distances and times of 0.1- to 14-MeV neutrons in hydrogenous materials
Authors: Nellis W. J.
Published: March 2005

The slowing-down distances and times of fast neutrons are calculated by extending the early work of Fermi to the case in which the neutron mean free path is energy dependent. This calculation is essentially a one-particle Monte Carlo treatment in which each path length is a mean free path and the neutron is always scattered through a scattering angle ϑ, such that cosϑ=〈cosϑ〉, the average of cosϑ in the laboratory system. The average results derived by this analytic method are shown to be in reasonable agreement with a detailed Monte Carlo computer calculation of the moderation of a 1-MeV neutron down to 40 eV in pure hydrogen. These calculations illustrate the Monte Carlo method and the broad spread in time and energy of the neutron flux resulting from an instantaneous point source in hydrogen. The results also graphically illustrate the greater penetrating distances of 14-MeV neutrons compared to 1-MeV neutrons in hydrogenous materials. Pedagogic, computer-oriented uses of this material are suggested.
Geometrical meaning of the curl operation when A⋅curlA≠0
Authors: Barnes Aaron
Published: March 2005

We examine the geometrical interpretation of the vector operation curl for vector fields A such that A⋅curlA≠0. It is not possible to construct even locally a surface normal to field lines of A at all points; an explicit geometrical demonstration of this fact is given. Such fields do not admit the construction of orthogonal curvilinear coordinates in which one set of coordinate curves lies along field lines of A.
Specific physical consequences of Mach’s principle
Authors: Nightingale J. David
Published: March 2005

Mach’s principle was put onto a solid footing in one particular equation by Einstein in his general theory of relativity. Using classical physics only, we explore, in some simple examples, the major expectations concerning motions due to matter in the rest of the universe.
Versatile optical bench for teaching, development, and testing of electron and ion optical systems
Authors: Bhiday M. R. , Gaud S. W. , Kanitkar P. L.
Published: March 2005

A versatile apparatus for demonstrating the imaging properties of various types of electrostatic lenses, designed and constructed in this department, is described. The chief merits of the apparatus are the simplicity and the facilities provided for externally maneuvering the lens elements in several respects without disturbing the vacuum. The apparatus is used regularly by students in their laboratory experiments to study the focusing properties of different types of electrostatic electron or ion lenses or their combinations, as a part of the laboratory course on electron and ion optics.
Fundamental quantum mechanics—a graphic presentation
Authors: Wise M. N. , Kelley T. G.
Published: March 2005

A presentation of basic quantum mechanics for non-physical science majors is described which, by relying on computer-generated graphic display, circumvents the usual mathematical limitations and allows a detailed treatment of free particle motion in a wave picture. The development is based on a computer-simulated, single-slit, particle diffraction experiment and culminates in a complete description and graphic display of the progress of the diffraction pattern from a square pulse at the slit to the Fraunhofer pattern at infinity.
The free-electron gas in n dimensions
Authors: Cetina E. , Magaña F. , Valladares A. A.
Published: March 2005

An n-dimensional free-electron gas confined in a box is studied and the density of states is calculated explicitly. The energy and specific heat are obtained in the low-temperature limit. Explicit expressions are given for n=1, 2, and 3.
Solar energy—its measurement
Authors: Wieder Sol , Jaoudi Edmond
Published: March 2005

The calibration of bolometric and photoelectric devices for application to the measurement of solar energy is considered. In particular, a bolometric radiometer for measuring this energy is described. Radiometric data is compared to that obtained from a selenium photovoltaic cell.
Environmental noise: An undergraduate research project
Authors: Mahajan Sukhbir , Shea Michael , Robinson D. L. , Mathes Dave
Published: March 2005

We present in this article a description of our undergraduate project in environmental noise measurements. Also included is a brief discussion of the current methodologies used in environmental noise assessment. The usefulness of this kind of project which involves the physics profession with local government agencies and the community is presented.
Protein crystallography in a molecular biophysics course
Authors: Argos Patrick
Published: March 2005

Protein and virus x-ray crystallography is an ideal interdisciplinary topic for a molecular biophysics or physical biochemistry course. X-ray diffraction theory is the domain of physics; chemical techniques are used to isolate proteins and viruses and elucidate mechanisms for active-state geometries; the biological sciences provide the experimental subject, life-sustaining macromolecules. The crystallography lectures are outlined, briefly discussed, and rigorously referenced. Further topics for a molecular biophysics course as well as available texts are given.
Life at low Reynolds number
Authors: Purcell E. M.
Published: March 2005

E d i t o r’s note: This is a reprint (slightly edited) of a paper of the same title that appeared in the book Physics and Our World: A Symposium in Honor of Victor F. Weisskopf, published by the American Institute of Physics (1976). The personal tone of the original talk has been preserved in the paper, which was itself a slightly edited transcript of a tape. The figures reproduce transparencies used in the talk. The demonstration involved a tall rectangular transparent vessel of corn syrup, projected by an overhead projector turned on its side. Some essential hand waving could not be reproduced.
Inexpensive measurements of the elastic constants of steel
Authors: Scott Bernard
Published: March 2005

Novel experiments are described which, using unsophisticated apparatus, permit adequate measurement of the elastic constants of material available in the form of a thin flexible strip. The accuracy attainable is limited, as in standard methods, by the measurement of the thickness of the material. This quantity appears in the calculations raised to the third power in the measurement of both Young’s modulus and the shear modulus.
Method of the perturbation expansion in classical mechanics
Authors: Lai C. S. , Wonnacott E. L.
Published: March 2005

The method of the perturbation expansion illustrated by Landau and Lifshitz in their textbook on mechanics is extended to higher orders. The validity of the method is established by the problem of a particle moving in the central force field f (r) =−k/r2+2C/r3.
Separation of the microscopic and macroscopic domains
Authors: Van Zandt L. L.
Published: March 2005

The possibility of observing interference in ’’quantum magnification’’ experiments such as the celebrated ’’Schroedinger cat’’ is examined. Conditions on the size and complexity of systems for which interference may be reasonably sought are developed. The possibility of observing interference is used as a criterion for separating the realm of microscopic dynamics from the macroscopic. The dividing line is estimated to fall at system sizes of about 100 Daltons.
Do cross sections undergo Lorentz contraction?
Authors: McCarthy Robert L.
Published: March 2005

Cross sections, if defined in accordance with physical intuition, are projected areas, which should be subject to Lorentz contraction. The customary definition of cross sections, however, presumes that they are Lorentz invariant. An alternative, intuitive definition is presented.
Wave functions rotated in phase space
Authors: Snygg John
Published: March 2005

The Fourier transformation which maps wave functions in the momentum representation into wave functions in the coordinate representation may be regarded as a 90° rotation in phase space. Starting from this observation we introduce continuously rotated wave functions. These rotated wave functions make it possible to define the expectation values of products of the form pkxn in an unambiguous way. The result is the same as that of the Wigner–Moyal formulation.
Criteria for bound-state solutions in quantum mechanics
Authors: Kocher Carl A.
Published: March 2005

When does the Schrödinger equation have bound-state solutions? This question is pursued by a variational method with simple trial wave functions. An arbitrary one- or two-dimensional attractive potential is shown to have at least one discrete energy level, and estimates of the binding energy are obtained for shallow potential wells. In other problems, sufficient conditions are established for the existence of bound states.
Improving instruction by measuring teacher discussion skills
Authors: Smith Albert B. , Ward Gray , Rosenshein Joseph S.
Published: March 2005

A college teacher’s verbal behavior can be measured. Types of classroom interaction can be tallied and analyzed, either by an observer in the classroom or by viewing and listening to video tapes. Observational systems such as Flanders’ Interaction Analysis Categories (FIAC) and the Florida Taxonomy of Cognitive Behavior (FTCB) can be used for verbal ratings. Teacher behavior can also be modified. When the teacher selects his own instructional goals or strategy, teaches, and then receives feedback on his performance, that performance can be modified or changed in future sessions. These are our conclusions based upon an experiment with videotaping and classroom verbal rating systems to induce more ’’higher level’’ questioning by instructors in introductory physics laboratories.
Construction of some soluble quantal problems
Authors: Winter Rolf G.
Published: March 2005

Solutions to the Schrödinger equation for two or more simple potentials are used to construct, in closed form, solutions for relatively complicated potentials.
Symmetrical formulation of electron–photon scattering in relativistic quantum mechanics
Authors: Ruei K. H.
Published: March 2005

In this paper, electron–photon scattering in relativistic quantum mechanics is formulated in a symmetrical form by making use of a modified form of the photon wave equation proposed by the author in a previous article, together with the usual form of the Dirac wave equation. By solving the coupled wave equations two S matrices are deduced, one with the photon wave function and the other with the Dirac wave function. For a given scattering process, either one may be used to give the correct result, if it is obtainable from both. Thus, the symmetry of quantum electrodynamics is explicitly revealed in this formulation.
Total reflection of light and water waves
Authors: Gödény I. , Kedves F. J. , Beke D.
Published: March 2005

A simple experimental arrangement is given to demonstrate the frustration of total reflection of visible light. The results obtained are in quantitative agreement with the theory. It is shown that the experiments in a ripple tank are suitable to demonstrate the circumstances on the less dense side of the interface in the case of total reflection.
Hertz vector potentials of electromagnetic theory
Authors: Essex E. A.
Published: March 2005

Recent textbooks on electromagnetic theory rarely do more than mention the Hertz vector potentials, yet many classical problems of radiation and propagation may be elegantly and concisely solved using these potentials. We discuss the definition of the Hertz vector potentials and demonstrate their application to the calculation of electric and magnetic dipole radiation and to the propagation modes of a rectangular waveguide.
On the linear potential hill
Authors: Delbourgo R.
Published: March 2005

By explicitly solving the Schrödinger equation for a particle encountering a linear potential hill (V = 0, x < 0; V = V0x/a, 0 < x < a; V = V0, x ≳ a), we obtain corrections to the quantum (a → 0) and classical (a → ∞) limits for the transmission coefficient, demonstrating the influence of the range a over which the potential rises.
Triple pendulum as an analog to three coupled stationary states
Authors: McKibben Joseph L.
Published: March 2005

The contest entry was a spring-coupled triple pendulum. It was used to demonstrate the character of normal modes and in particular a mode that has high Q even with the center pendulum highly damped. The coupling of one of the springs to a pair of pendulums could be varied while they were swinging and with this adiabaticity in the effect upon a normal mode was observed. In the discussion the mathematical simularity to the equations of three coupled quantum mechanical levels is pointed out. The eigenstate in metastable hydrogen atoms that survives passage through the spin filter of a polarized ion source is compared to the high-Q mode observed in the triple pendulum.
The roller randomizer
Authors: Butler Crispin O.
Published: March 2005

A device that utilizes rollers to generate two-dimensional random motion is described. Quiet, rugged, and versatile, it is suitable for illustrating a wide variety of molecular phenomena. Three specific uses are presented in detail.
Resource Letter WI-1: Weak interactions
Authors: Holstein Barry R.
Published: March 2005

Prepared at the request of the AAPT Editorial Board for Resource Letters. This is one of a series of Resource Letters on different topics intended to guide college physicists, astronomers, and other scientists to some of the literature and other teaching aids that may help improve course contents in specified fields. No Resource Letter is meant to be exhaustive and complete; in time there may be more than one Letter on some of the main subjects of interest. Comments on these materials as well as suggestions for future topics will be welcomed. Please send such communications to Professor Aaron Owens, Editor, Resource Letter Board, Department of Physics, Kenyon College, Gambier, Ohio 432022. Notation: The letter E after an item number indicates elementary level; the letter I indicates intermediate level; and the letter A indicates advanced material. An asterisk (*) indicates those references we feel to be especially helpful.Reprints: When ordering, request Resource Letter WI-1. Enclose $0.75 per copy (not in stamps) together with a stamped, self-addressed envelope and send to Publications Department, American Association of Physics Teachers, Graduate Physics Building, SUNY at Stony Brook, Stony Brook, New York 11794.
Secrecy, simultaneous discovery, and the theory of nuclear reactors
Authors: Weart Spencer
Published: March 2005

The history of nuclear reactors gives us a singular opportunity to study what happens when the world’s leading physicists, faced with the same problem, find solutions in complete isolation from one another. This paper takes as an example an elementary part of reactor theory, the four-factor formula. It was discovered independently at least six times (in France, Germany, the Soviet Union, and the United States). But the groups, separated by wartime secrecy, used the formula in very different ways. Usually it was simply ignored. In only two cases was the formula integrated with experimental work—by the French and, in an entirely different way, by Fermi’s team in Chicago. Thus even though simultaneous discovery occurred, we need not conclude that the physics developed inevitably in a unique pattern.
The transistor and attitude to change
Authors: Macdonald Stuart , Braun Ernest
Published: March 2005

The ability to amplify by means of a semiconductor device can now be clearly seen as the foundation stone of modern electronics, but such clarity of vision was not generally evident in the years immediately following the invention of the transistor. That few should have predicted the future with accuracy is hardly remarkable, but what is of interest is that many seem to have viewed the new transistor only as a possible substitute for the old vacuum tube. Despite radical differences and new possibilities, many chose to see only the similarities between tube and transistor. In the present paper, we explore some of the origins and consequences of this attitude.
Method for determining the radius vector for a planet from two observations of position
Authors: Gainer Michael Kizinski
Published: March 2005

A method is presented for determining the approximate radius vector of a planet or asteroid from two closely separated observations of position. Much of the tedious computation of traditional methods is eliminated, and the mathematical ability required is not beyond freshman or sophomore students.
Dissipative forces and quantum mechanics
Authors: Eck John S. , Thompson W. J.
Published: March 2005

The dissipative forces of classical mechanics can be included in quantum mechanics by the use of non-Hermitian Hamiltonians. The Ehrenfest theorem for such Hamiltonians is derived, and simple examples which show the classical correspondences are given. The viscosity coefficient for a nuclear collision is estimated.
On the strength of the Dirac monopole
Authors: Garwin Laura J. , Garwin Richard L.
Published: March 2005

A magnetic pole of strength g0 is placed initially midway between two electrons of charge e. Consideration of the torque required to move one electron in a semicircular arc into coincidence with the other leads to an evaluation of the angular momentum thus added to the system as 2eg0/c. Since the eigenvalues of the angular momentum operator are spaced by h/, g0 is clearly limited to n (h/c/e2) e/2, the Dirac result.
Black hole physics illustrated in photon orbits
Authors: Cohn Haldan
Published: March 2005

Charts of numerically computed photon orbits near ’’dead’’ and ’’live’’ black holes are presented in order to illustrate some physical properties of the geometry around each of these objects. Especially interesting is the effect of ’’frame dragging’’ around a rotating black hole.
Multisystem temperature equilibration and the second law
Authors: Leff Harvey S.
Published: March 2005

The entropy change during the temperature equilibration of an isolated collection of systems which may exchange heat (but not work) energy is shown to be positive. The proof holds when the constant volume heat capacity of each system is a non-negative function of the temperature. If the collection is allowed to exchange heat ΔQ with its environment during the equilibration, its entropy change ΔS is shown to satisfy the inequality ΔS?ΔQ/Tf, where Tf is the final equilibrium temperature. For infinitesimal equilibration transformations, this inequality reduces to a generalized statement of the second law of thermodynamics, showing that the internal portion of the entropy production during equilibration is non-negative.
Bowling frames: Paths of a bowling ball
Authors: Hopkins D. C. , Patterson J. D.
Published: March 2005

We consider a bowling ball which starts with arbitrary linear and angular velocity and for which the coefficient of kinetic friction is assumed to be constant. We solve the resulting equations in closed form as well as suggest a geometrical construction of the path which may be qualitatively useful. We also numerically evaluate several parameters of the path for typical initial conditions. We find that the description of the problem is greatly simplified by using a coordinate system which is rotated with respect to the bowling alley by an angle which depends on the initial conditions. The ball describes a parabolic path up to a certain characteristic time (which we calculate), and then it rolls without slipping in a straight line. We contrast this solution with some of the folklore of bowling as it relates to ’’hooks.’’