bluuebunny/crossref_metadata_2025 huggingface dataset:
Elementary treatment of some difficulties in the construction of irreducible representations of the rotation group in terms of products of the spin-1/2 representation
Authors: Daniels J. M.
Published: March 2005

In order to understand in detail how the representations of the rotation group are constructed from products of the spin-1/2 representation, a clear distinction must be maintained between three related but conceptually different quantities: a vector in an abstract vector space, its components in some chosen basis, and its representatives. The rotation group provides an example that these are indeed different concepts, and that paradoxes result if they are confused.
Demonstration of reduced gas pressure in a centrifugal field
Authors: Fischer Fred , Wild R. L.
Published: March 2005

A simple effective demonstration of the reduced pressure in a gas trapped in a centrifugal field is shown by the force necessary to separate two plates (radius R, angular velocity ω) rotating in loose mutual contact. Agreement with the calculated value, F=πρR4ω2/4, is good, where it is assumed that the air trapped between the plates approximates an ideal gas of density, ρ, which obeys Boltzmann’s distribution law in the centrifugal field.
Analytical and numerical solution of the Schrödinger equation for a surface potential barrier including spin-orbit interaction
Authors: Moya M. M. , Helman J. S.
Published: March 2005

We consider the problem of an electron interacting with a surface potential barrier which includes the spin-orbit interaction. An exact solution of the Schrödinger equation is given for the case of a step potential. For smooth barrier profiles, the time- dependent Schrödinger equation is numerically solved, and the time evolution of the spin-up and spin-down components of a wave packet is displayed in a series of pictures.
Magnetic multipole expansions using the scalar potential
Authors: Gray C. G.
Published: March 2005

Using the magnetic scalar potential, the multipole expansion is derived for the magnetostatic field outside a localized current distribution.
Advanced geometric optics on a programmable pocket calculator
Authors: Nussbaum Allen
Published: March 2005

An exact ray-tracing method has been developed by combining some ideas of Herzberger with the matrix approach to geometrical optics. This method, which can be implemented on a programmable pocket calculator, applies to any conic surface, including paraboloids, spheres, and planes (both refracting and reflecting) as examples. For the aspheric elements, in particular, this method is exact; iterative procedures are unnecessary.
Light scattering by surface tension waves
Authors: Weisbuch G. , Garbay F.
Published: March 2005

This simple and inexpensive experiment is an illustration of the physical concepts of interaction between light and surface tension waves and provide a new method of measuring surface tension.
Information theory density matrix for a simple quantum system
Authors: Titus William J.
Published: March 2005

The density matrix is derived that best describes, according to information theory, a one-dimensional single particle quantum system, when the only information available is the values for the linear and quadratic position-momentum moments. In addition, moment generating functions and the time development of the system under a simple interaction are considered.
Ground-state pressure of an ideal Fermi gas
Authors: Delsante A. E. , Frankel N. E.
Published: March 2005

A simple relationship between the pressure, internal energy, and Fermi energy of an ideal ultradegenerate Fermi gas is derived in two ways. The conditions for its validity and its use in simplifying calculations are discussed.
A new model of the Foucault pendulum
Authors: Weltner Klaus
Published: March 2005

Foucault showed the rotation of the earth by his fundamental pendulum experiment. In the classroom the experiment is usually simulated by a gravitational pendulum on a rotating turntable. By this the situation on the poles of the earth may be simulated, but it is impossible to investigate the dependency on geographical latitude. If we simulate the Foucault pendulum by an elastic steel wire pendulum we get the opportunity to show the entire effect, inclusive of the dependency on geographical latitude.
Green’s functions in space and time
Authors: Peter Rowe E. G.
Published: March 2005

A sketch of some topics in distribution theory is given which does no serious injustice to the theory, yet provides techniques for handling the partial differential equations that the most important Green’s functions in physics satisfy; these techniques are usable by students with relatively little mathematical sophistication.
What is the American Journal of Physics?
Authors: Taylor Edwin F.
Published: March 2005

A classified tabulation of the regular articles of the American Journal of Physics for 1977 shows that the journal is properly described as a scholarly archival journal, a description which fits 80% of the regular articles published in that year. At most five regular articles, or 2%, would reasonably fit the category of educaton research.
Physical theory in biology: An interdisciplinary course
Authors: Lumsden Charles J. , Trainor L. E. H. , Silverman Melvin
Published: March 2005

We describe a new interdisciplinary course which explores the relations between physics and biology in terms of their conceptual structures and mathematical frameworks. The course is designed for senior undergraduate physics students who have little or no background in the life sciences. In this paper we highlight the course content, its system of cross-disciplinary literature resources, and several innovative aspects of the method used for evaluating students.
In search of the ’’starbow’’: The appearance of the starfield from a relativistic spaceship
Authors: McKinley John M. , Doherty Paul
Published: March 2005

One prediction for the appearance of the starfield from a moving reference frame has been circulated widely despite physically objectionable features. We reexamine the physical basis for this effect. To the well-known aberation and Doppler effects we add the transformation of intensity of light upon a change of reference frame. We integrate the transformed spectrum of a star, represented as a blackbody, over the response function of the human eye. We present a one-parameter function to represent the dependence of the apparent visual magnitude of different stars upon Doppler factor. We conclude with a sequence of computer-generated figures to show the appearance of Earth’s starfield at various velocities. A ’’starbow’’ does not appear.
Twin paradox: A complete treatment from the point of view of each twin
Authors: Perrin Robert
Published: March 2005

A specific round trip situation is set up, and is worked through from the point of view of each twin. The gravitational field equations, and geodesic equations of motion, are solved in the traveling twin’s reference frame, in order to determine the time elapsed on the Earth during the periods of acceleration. The equality of the results obtained by each twin is explicitly exhibited.
Entropy state of a multiple choice examination and the evaluation of understanding
Authors: Vawter Richard
Published: March 2005

Considering a student’s examination as one state of a system which consists of the set of all possible examinations, a new method for evaluating multiple choice examinations is developed by measuring the entropy state of a student’s exam above the ’’thermal background level’’ (the most probable state). The entropy grade is shown to contain standard scoring as a special case when both the number of questions given and the number of possible selections become large. The entropy grade is also shown to be related to the information it takes a student to go from one state of understanding to another state of understanding. The student’s state of understanding is characterized either by his personal probability that his selections will be correct or by experimentally measured probability that the students’s selections were correct.
From snowballs to ICBM’s
Authors: Scherr Charles W.
Published: March 2005

The elliptic range RE of a ballistic missile is the length of arc between the two intercepts of the circle of the earth with the elliptic orbit of the projectile. When expanded in powers of the projection velocity v, RE is given by RE=2v2 sinϑ cosϑ/e+O (v6), where e is the eccentricity of the orbit. Units are such that GM=1 and the radius of the Earth is one. The lead term is thus the correct form for the solution to the elementary ballistic problem. It is shown that this lead term not only describes the flight of a snowball, but can also give a good account of the range of an ICBM. Thus, for a projection velocity of v=√2/2 (half the escape velocity) the lead term gives the range for any angle of projection with less than a 2% error.
Should the premed requirements in physics be changed?
Authors: Liboff Abraham R. , Chopp Michael
Published: March 2005

Factors influencing the premedical requirement in physics are examined. A review is given of the various reasons why physics is important in medical education. The new Medical College Admissions Test is discussed. In looking at the rapid advances in technology in medicine, it is argued that the medical student is presently disadvantaged in physics, simply not having taken enough physics as an undergraduate. It is urged that an additional (applied) course, requiring introductory physics and calculus as prerequisites, be included among medical school entrance requirements.
Reynolds on the internal cohesion of liquids
Authors: Trevena David H.
Published: March 2005

During the past three decades there has been considerable interest in the tensile strength of liquids. However, it is not generally realized that some pioneer experiments on the subjection of liquids to tension were carried out during the last century. Reynolds was one of the workers in this field and he was able to illustrate and measure the tension that a column of liquid could sustain. In the present paper this work of Reynolds is described and assessed and is compared with some of the other related work published in French journals in the last century.
Definition of virtual levels
Authors: Shore Bruce W.
Published: March 2005

Examination of graphical displays of solutions to the time-dependent Schrödinger equation modeling a laser-excited three-level atom suggests that an energy level may be regarded as virtual when it is detuned from resonance by more than two Rabi frequencies.
Nonspreading wave packets
Authors: Berry M. V. , Balazs N. L.
Published: March 2005

We show that for a wave ψ in the form of an Airy function the probability density ‖ψ‖2 propagates in free space without distortion and with constant acceleration. This ’’Airy packet’’ corresponds classically to a family of orbits represented by a parabola in phase space; under the classical motion this parabola translates rigidly, and the fact that no other curve has this property shows that the Airy packet is unique in propagating without change of form. The acceleration of the packet (which does not violate Ehrenfest’s theorem) is related to the curvature of the caustic (envelope) of the family of world lines in spacetime. When a spatially uniform force F (t) acts the Airy packet continues to preserve its integrity. We exhibit the solution of Schrödinger’s equation for general F (t) and discuss the motion for some special forms of F (t).
Improved field-effect transistor equations for computer simulation
Authors: Kidd Richard , Ardini James
Published: March 2005

A lab experiment to acquaint students with field-effect transistor characteristics and circuits was developed. The characteristic curves and forward transfer curve were to be plotted and checked against computer generated curves. These curves could not be produced on the computer by available equations and a new continuous expression was developed, giving rise to a π/2 power law for the forward transfer curve. This expression can be used to simulate amplifier characteristics, including distortion.
Vector operators and spherical harmonics in quantum mechanics
Authors: Andrews M.
Published: March 2005

The usual explicit expressions for spherical harmonics are derived by a method which does not involve the solution of differential equations or the use of angular momentum operators in spherical polar form. Instead a raising operator constructed from an arbitrary vector is used together with the usual angular momentum raising and lowering operators. The method is first presented as simply as possible in Schrödinger representation using position as the vector. Then it is generalized to an arbitrary vector and arbitrary integral angular momentum without using a particular representation. Finally it is shown how a conserved vector (other than angular momentum) of a central system can be used to reveal properties of the energy eigenstates. As an example, eigenstates of the hydrogen atom are found using the Runge-Lenz vector.
Electronic device of didactic and electrometric interest for the study of R
L
C circuits
Authors: Pérez Rodríguez Angel L. , Peña Bernal Juan José , Mahedero Balsera Benito
Published: March 2005

This paper presents a method of studying RLC circuits with the help of the oscilloscope in the XYZ mode, complemented by an electronic device which generates a marker-trace on the screen and which is used to measure frequencies without needing any reference point on the screen. Although the electronic device can be used in a fairly quantitative manner, the authors have proved its special utility in the teaching of electric resonance, since it shows the phenomena associated with electric resonance in a very intuitive way.
Wigner distribution for angle coordinates in quantum mechanics
Authors: Mukunda N.
Published: March 2005

The method of Wigner distribution functions, and the Weyl correspondence between quantum and classical variables, are extended from the usual kind of canonically conjugate position and momentum operators to the case of an angle and angular momentum operator pair. The sense in which one has a description of quantum mechanics using classical phase-space language is much clarified by this extension.
Quantum state determination: Quorum for a particle in one dimension
Authors: Band William , Park James L.
Published: March 2005

In this paper we wish to illuminate the axiom that the quantal state describes a statistical ensemble of similar systems identically prepared, and is not to be identified with any single system. The mathematical representative of the general quantum state is the density matrix or statistical operator in Hilbert space. We demonstrate how this operator may be determined empirically by calculations involving only the measured mean values of a set of observables we call a ’’quorum.’’ As an example of this approach a state determination procedure is described for a spinless particle moving in one dimension; the corresponding quorum turns out to involve only position data associated with various instants subsequent to the act of preparation.
Electrostatic potential energy leading to a gravitational mass change for a system of two point charges
Authors: Boyer Timothy H.
Published: March 2005

A system consisting of two point charges has an energy contribution from the system electrostatic potential energy and accordingly a contribution to the system mass given by this energy divided by c2. Here we investigate the change in weight associated with the electrostatic potential energy for a system of two point charges supported side by side against a weak gravitational field. The gravitational distortion of the Coulomb field of a point charge is calculated using the equivalence principle, and it is then shown that the change in the two-particle system weight can be understood precisely as the change in supporting force necessary to balance the electric force of each charge upon the other. The example provides a clear illustration and detailed mechanism for understanding the mass-energy connection for weak gravitational fields.
Kinetic theory simulator for laboratory use
Authors: Eaton Bruce G. , Finstad Richard G. , Lane Paul D.
Published: March 2005

An apparatus is described which allows one to study the speed distribution, the gravitational distribution, and the mean free path of steel balls agitated into two-dimensional motion through collisions with the moving walls of their enclosure.
A physics teacher looks at the new (1977) Medical College Admission Test
Authors: Iona Mario
Published: March 2005

It appears, from the recently published ’’illustrative test’’ and the sample questions which were published previously and from the list of topics, that the new Medical College Admission Test contains a large number of physics related questions in the chemistry section in addition to those in the physics section. Also, many of the questions in the reading and quantitative analysis skill section are of concern to physics teachers who hope their students learn to read carefully and to analyze data. Although most questions are straightforward at a reasonable first year level, there are a disturbing number of questions that seem ambiguous. Physics teachers should be concerned about such shortcomings of a test that plays a major role in the career of many of their students.
Fraunhofer diffraction patterns from apertures illuminated with nonparallel light
Authors: Klingsporn Paul E.
Published: March 2005

The size of the Fraunhofer diffraction pattern produced when a circular aperture is illuminated with a diverging beam of light, in contrast with a parallel beam, is derived on the basis of simple lens theory by introducing the concept of a virtual diffraction pattern. The results of the simple analysis agree with the diffraction pattern size determined by a formal analysis of the light wave amplitude. The formal analysis reveals a general scale factor relating the Fraunhofer diffraction pattern size for an aperture illuminated with parallel light to the size for nonparallel illumination. The diffraction pattern intensity is independent of the position of the aperture in its plane, based on a property of the Fourier transform. The invariance in intensity for nonparallel illumination of the aperture is also shown by a simple argument based on the Abbe theory of image formation by diffraction. Finally, some experimental results are given.
Quantization of inequivalent classical Hamiltonians
Authors: Edwards Ian K.
Published: March 2005

It is well known that to quantize any dynamical system it is necessary for a generator of the classical motion to exist in the form of a Hamiltonian function. It is shown, by using the example of a damped harmonic oscillator, that a particular class of inequivalent classical Hamiltonians exist which make quantization of the system ambiguous. Hence it is conclued that it is not sufficient for the Hamiltonian to merely generate the motion, but it must also be necessarily related via a canonical transformation to the total energy of the system.
Catastrophe of the molecular field
Authors: Williams D. E. G.
Published: March 2005

The molecular field theory of ferromagnetism is used as an example to illustrate the use of elementary catastrophe theory. It is shown that the molecular-field approach gives rise to a cusp catastrophe set. A brief examination is made of the reasons why the elementary catastrophe theory does not produce critical exponents which are in agreement with experimental values. It is suggested that the assumption of an equal areas rule denies the transversality upon which the generality of catastrophe theory is based. It is proposed that an approach to the problem of critical exponents through the much more sophisticated generalized catastrophes might prove fruitful.
Linear collisions with harmonic oscillator forces: The inverse scattering problem
Authors: Newby Jr. Neal D.
Published: March 2005

A particular kind of elastic scattering is studied between three bodies of equal mass. Two of the bodies are at rest and in contact with each other. The third body impinges on these two. The motion of the bodies is confined to a straight line as in a linear air track. The scattering is mediated by nearest-neighbor Hooke’s law forces having force constants k1 and k2. The final velocities of all three bodies are studied as a function of β (=k2/k1). It is shown that the possible final scattering states may be divided into two classes. In one class it is possible to determine β from a knowledge of the final velocities of the three bodies. In the other class no such determination is possible. A formula is derived that yields an infinite set of values of β, all of which produce the same velocities in the final state. Other measurements are proposed which allow a determination of β and the individual spring constants k1 and k2 as well as the size of the springs. These further measurements involve time correlations between incident and scattered particles. No measurements are permitted during the time of interaction. The correspondence principle indicates that the same ambiguity will be present in the analogous one-dimensional quantum- mechanical problem necessitating time correlation measurements to solve the inverse scattering problem.
Geometry of the Kepler initial value problem explored with two circles
Authors: Dumais Jean-François
Published: March 2005

It is shown, by a judicious exploitation of the Runge-Lenz vector, that the Kepler initial value problem is endowed with a nice geometric structure which enables one to figure out, even mentally, after a single trivial arithmetic calculation, the orbit associated with any given set of initial data.
Use of ‖Ψ‖2 and flux to simplify analysis of transmission past rectangular barriers or wells
Authors: Draper James E.
Published: March 2005

The transmission coefficient for a completely general one-dimensional rectangular potential barrier or well, or series of steps, is analyzed simply by concentrating on ‖Ψ‖2 rather than Ψ. Graphs of ‖Ψ‖2 for all cases are given, whereas only two textbooks graph anything related to Ψ, and those plots of Re(Ψ) can be misinterpreted.
Fluorescence spectrum of NaI(Tl) crystal: A laboratory experiment
Authors: Chikkur G. C. , Lagare M. T. , Umakantha N.
Published: March 2005

A laboratory experiment, using the single-photon counting technique, to determine the fluorescence spectrum of NaI(Tl) crystal under gamma excitation, is discussed.
Radial flux distribution of low-energy neutrons
Authors: Higinbotham J.
Published: March 2005

Using a 100 mCi 241Am-Be neutron source, the radial flux distribution of low-energy (epithermal) neutrons in distilled water was measured by students in our Advanced Physics Laboratory and the main features of the distribution accounted for on the basis of a simple model.
Doppler shift for a radar echo
Authors: Gleiser R. J.
Published: March 2005

The Doppler shift formula for a radar echo is derived without the use of transformation equations by considering the superposition of the incident and reflected waves. The results are then used as a basis for a discussion of the concepts of proper length and time as regards the transformation properties of wavelength and period in special relativity.
Perception of perspective
Authors: Haywood T. W.
Published: March 2005

It is shown that perspective distortion in photography can be explained analytically if the eye operates as a simple lens and the brain remembers the hyperbolic relationship between image size and distance.
Valid approximations of the dispersion equation
Authors: Cayton Thomas E.
Published: March 2005

The problem of deriving accurate long-wavelength approximations of a particular dispersion equation for electromagnetic waves in a magnetized plasma is examined. Because the dispersion equation includes dependence upon external parameters, the approximation obtained by straightforward expansion is invalid in certain cases. An accurate approximation is derived in these cases by a modified expansion technique. Although only one specific practical problem is studied here, this example involves and exhibits general techniques that have broad application in related problems. Some features of long-wavelength low-frequency waves in a magnetized high-temperature plasma are illustrated.
Spreading of wave packets in the coordinate representation
Authors: Lai C. S.
Published: March 2005

By dealing with the Schrödinger equation for a free particle in the coordinate representation alone, the expression for ψ (r,t) at time t is derived in terms of ψ (r,t0) at an initial instant t0 with the use of the ’’method of self-similar solution of partial differential equations.’’ The use of Green’s function is necessary due to the complex nature of the Schrödinger equation. The same technique can also be applied to the case of spreading of wave packets in a dissipative medium.
Simple soliton solutions
Authors: Hansen P. J. , Nicholson D. R.
Published: March 2005

Solutions to linear wave equations can always be expressed as a superposition of special solutions called plane waves. Some solutions to an important class of nonlinear wave equations can be thought of as a superposition of special solutions called solitons. In this paper, we present a simple method for generating these special soliton solutions.
The physics of electrochromism: An advanced laboratory experiment
Authors: Peterson C. W. , Parlett J. , Crandall R. S.
Published: March 2005

Amorphous tungsten trioxide films offer an interesting electrochromic system whose properties are readily amenable to study in a senior undergraduate laboratory. Basic optical color center properties, and electron and proton diffusion processes are characterized for the HxWO3 produced; additional experiments including the variation of the chemical potential of the hydrogen component and low-temperature exploration of the metal-insulator transition are proposed for the advanced student. The samples are easily prepared and measured by elementary means. The broad solid-state concepts involved enrich standard advanced laboratory repertoires of more conventional nuclear and NMR experiments.
Teaching T
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Authors: Harrison David
Published: March 2005

A course in modern physics and Eastern mystical philosophy is described.
Excited levels 1s
n, n−1 of the two-electron atom
Authors: Vidal-Quadras A. , Casas M. , Ortega M.
Published: March 2005

Closed formulas for the Coulomb and exchange integrals in the excited states 1snl, l=n−1, of the two-electron atom are applied to the computation of the ionization energy of the singlet and tripet 1s2p states from He i up to O vii and to singlet and triplet 1s3d and 1s4f states of He i and Li ii. Two methods are compared: (a) the use of first-order perturbation theory considering the mutual electrrostatic repulsion e2/r12 as a small perturbation and (b) imposing as solution of the Schrödinger equation a symmetrized product of a Z and a screened Z−1 hydrogenic wave functions. Computed and experimental values of the ionization energy and of the singlet-triplet interval are compared and the evolution of agreement with increasing Z and n is discussed.
Application of Hamilton’s principle to the study of the anharmonic oscillator in classical mechanics
Authors: Gilmartin Harvey , Klein Abraham , Li Ching-teh
Published: March 2005

A form of Hamilton’s principle for classical mechanics, appropriate to the study of arbitrary self-sustained vibrations in one dimension is presented. It is applied as an approximate computational tool to the study of several examples of anharmonic oscillation. The trial function is a finite Fourier series chosen to approach the exact solution as the number of terms increases without limit. Analytic approximations can be obtained for the limits of weak and strong anharmonicity. Numerical results for the amplitude-dependent frequencies compare favorably with the exact solutions.
Small amplitude oscillations of a quasi-ideal pendulum
Authors: Gleiser R. J.
Published: March 2005

A variational principle, resembling that used in quantum mechanics, is formulated and applied to study the first-order correction to the period of a simple pendulum. The relevant small parameter is the ratio of the mass of the suspension cord to that of the pendulum bob. The suspension cord is assumed inextensible but otherwise both its elastic properties and mass distribution are arbitrary. Results previously derived independently for a rigid rod or flexible cord suspension are thus obtained within a single formalism. The discussion of the connection between these cases and of related results is thereby simplified.
The Schrödinger-Einstein correspondence and the sources of wave mechanics
Authors: Hanle Paul A.
Published: March 2005

Unpublished letters of late 1925 between Einstein and Schrödinger and the doctoral thesis of de Broglie reveal sources of Schrödinger’s inspiration to invent wave mechanics. Schrödinger saw a congenial similarity of de Broglie’s work on the stability of the atom with his own earlier speculation in relativity, which he noted to Einstein. But the last chapter of de Broglie’s thesis, on quantum statistics of gases, which is unfamiliar to many modern readers, provided Schrödinger with the method of treatment of a gas of material particles considered as a system of modes of vibration, of ’’matter waves.’’ This method especially, and other successes of de Broglie’s ’’ingenious thesis,’’ convinced Schrödinger to take seriously the first part, on the conditions of stability of the atom in a wave picture. Thus he sought and found an equation to describe the states of the electron from the matter-wave viewpoint.
Concise derivation of the rotational partition function
Authors: Hynne F. , Andersen Knud
Published: March 2005

The classical partition function for the rotation of a rigid asymmetric molecule is derived by a transformation of variables in the phase integral circumventing the cumbersome manipulations of the canonical prescription.
The Two Cultures gap revisited
Authors: Green Martin
Published: March 2005

I read C. P. Snow’s The Two Cultures in 1960, when I was teaching English at Wellesley, and it made such an impression on me that I spent the next two years trying to redress the imbalance of mind deriving from a purely literary education, by taking a year of undergraduate science and then teaching for a year at a technical college. I wrote a book on the subject, called Science and the Shabby Curate of Poetry, published in 1964. But in the fifteen years since then I have given only sporadic attention to the issue, though I have never forgotten it. I’ve been defeated by the problem of getting past the pious platitudes—’’it’s a crying shame that the two cultures are so divided’’—to arguments that are intellectually or any other way substantial. But now it seems to me that certain external circumstances have change enough that that problem can be resolved; not the problem of the very different experience of men in the humanities from men in the sciences, but the problem of communication between them. What follows are the 1979 reflections on the split, various in character but partly joyful, of a long-term desponder.
A look at the 1979 AAPT Winter Meeting
Authors: St. John Mark , Cid-Campos Raul
Published: March 2005

From January 29 to February 1, 1979, the American Association of Physics Teachers held its annual Winter Meeting in New York City. In this report we describe the results of an illuminative study which investigated the activities and perceptions of those who participated in that meeting. Through interviews, observations, and an assortment of questionnaires, we gathered information about many different aspects of the meeting and from many different points of view. We describe in the report who the participants were and what they wanted from this meeting. We then evaluate the various activities of the meeting in term of their effectiveness in meeting the participants’ wants. Finally, we point out and discuss a few major issues that emerged in the course of our study and were sources of conflict for many of those attending.
Dante and the 3-sphere
Authors: Peterson Mark A.
Published: March 2005

We describe three different methods of visualizing the ’’closed universe’’ S3, and point out language in Dante’s Divine Comedy which suggests that he visualized his universe in the same ways, making his universe topologically S3.
Another look through the Heisenberg microscope
Authors: Corben H. C.
Published: March 2005

Conditions are examined for measurement of the position and momentum of a particle by Compton scattering from various directions. In addition to the usual uncertainty relation that emerges from this analysis, it is shown that, for a given initial frequency, there is generally a critical angular aperture at which the error in position is a minimum.
Single beam holography
Authors: Chen Hsuan , Ruterbusch Paul H.
Published: March 2005

A simple technique of holography, using only one source beam is introduced. Impressive curved holograms and rainbow holograms can be fabricated on an unisolated laboratory table with this technique.
Additivity, rapidity, relativity
Authors: Lévy-Leblond Jean-Marc , Provost Jean-Pierre
Published: March 2005

A simple and deep standard mathematical theorem asserts the existence, for any one-parameter differentiable group, of an additive parameter, such as the angle for rotations and the rapidity parameter for Lorentz transformations. The importance of this theorem for the applications of group theory in physics is stressed, and an elementary proof is given. The theorem then is applied to the construction from first principles of possible relativity groups.
Detonation in miniature
Authors: Fickett Wildon
Published: March 2005

A mathematical analog for one-dimensional compressible flow in a chemically reacting fluid is constructed and used as a vehicle for a simplified introduction to such flows, with particular application to detonations. The presentation includes a concise self-contained introduction to the elements of nonreactive compressible flow.
Time variation of a vector attached to a moving frame
Authors: Weinstock Robert
Published: March 2005

It is well known that for any moving rigid frame of reference there exists at each instant an angular-velocity vector ω such that the time variation of any vector q constant relative to the frame is given by (dq/dt) =ω×q. With the use of elementary vector algebra and calculus, a rather simple proof is presented of the unique existence of ω and of the validity of the above equation in fullest generality.
Hydrogen atom and relativistic pi-mesic atom in N-space dimensions
Authors: Nieto Michael Martin
Published: March 2005

We derive in simple analytic closed form the eigenfunctions and eigenenergies for the hydrogen atom in N dimensions. A section is devoted to the specialization to one dimension. Comments are made on the relation to the harmonic oscillator, the ground-state energy per degree of freedom, the raising and lowering operators, and the radial momentum operators. By particular changes of variables, the relativistic pi-mesic atom is solved in the same functional form.
Symmetry and invariance of the Coulomb problem
Authors: Chen Augustine C.
Published: March 2005

New canonical transformations for the Coulomb problem are introduced, and their geometrical and physical significance discussed. The existence of two invariant momemtum components are shown to be related to the two constants of the motion in a Coulomb field.
Influence of the mass of the spring on its static and dynamic effects
Authors: Galloni Ernesto E. , Kohen Mario
Published: March 2005

The influence of the mass of a spring on its static elongations or on the oscillation period, when a mass is suspended at its end, is discussed. It is also demonstrated by theory and experiment that the coefficients 2 or 3 commonly used in the literature are not always correct.
Different views of accelerated reference frames
Authors: Tuttle E. R.
Published: March 2005

Several uses of the theory of accelerated reference frames are presented. It is shown that, when successive rotational motions occur, the identification of the various terms in the expression for the acceleration observed in an inertial frame is not unique, but rather depends on the interpretation of the observer. A simple derivation of the rigid-body equations of motion in terms of the Eulerian angles is presented and discussed, and some simple examples presented. The approach given is suitable for presentation to undergraduate students taking a first course in mechanics and does not require a knowledge of variational or energy methods.
Determination of the speed of light by measurement of the beat frequency of internal laser modes
Authors: Brickner R. G. , Kappers L. A. , Lipschultz F. P.
Published: March 2005

Detection of the beats between the internal modes of a commercially available laser is used to determine the speed of light. A fast response photodiode attached to the uhf terminals of a television set permits the beats to be detected and displayed.
Intrinsic nonlinear effects in vibrating strings
Authors: Elliott John A.
Published: March 2005

The two perpendicular polarizations of transverse oscillation in stretched strings are shown to be parametrically coupled so that energy is spontaneously exchanged between the perpendicular modes. The approximate solution of the equations of motion shows that the trajectory is an ellipse with a reverse precession. The effect is commonly observed in the teaching laboratory, and may be important in the performance of musical instruments.
Einstein and Lorentz: The structure of a scientific revolution
Authors: Brouwer W.
Published: March 2005

In a course entitled ’’Revolutions in Physics’’ a number of episodes in the history of physics are examined, in order to test the theories of Kuhn, Popper, Lakatos, and others, with regard to any common structure exhibited by the various revolutions that physics has undergone. The conflict between Lorentz’s Electron Theory and Einstein’s Special Relativity becomes a major focal point in the second half of the course for the models of scientific revolutions that are studied.
Classical inverse scattering in one dimension
Authors: Lazenby John C. , Griffiths David J.
Published: March 2005

A particle constrained to move in one dimension encounters a potential V(x) on the interval 0?x?L. Question: can V(x) be deduced from a knowledge of the transit time as a function of energy? The answer is no, although a unique ’’canonical’’ potential is determined, and we show how to find it.
Self-consistent-field calculation on lithium hydride for undergraduates
Authors: Rioux Frank , Harriss Donald K.
Published: March 2005

Students generally acquire an understanding of theoretical concepts only after they have attempted actual calculations based on those concepts. Consequently there is a need for realistic calculations in quantum theory which can be used with undergraduates to illustrate its important concepts. In this paper we describe a self-consistent-field–linear combination of atomic ortibals–molecular orbital calculation on the valence electrons of LiH using the method of Roothaan. The calculation is modest in scope, mathematically simple, and easy to program. These factors enhance its usefullness with undergraduates.
Solutions to the equation of continuity
Authors: Tempelman Wayne
Published: March 2005

Solutions to the one-dimensional continuity equation are discussed for nonsteady flows.
Elementary derivation of the Saha equation
Authors: Nickel G. H.
Published: March 2005

The condition of equilibrium molecular dissociation is investigated without using thermodynamic reasoning explicitly. The approach of ’’phase-space maximization’’ illuminates the basic principles of statistical mechanics while providing an understanding of an equation which is useful in many applications.
Kater pendulum modification
Authors: Jesse Kenneth E.
Published: March 2005

A more precise measurement of the acceleration due to gravity is made possible by modifying a Welch, Kater pendulum. (AIP)
Reflection and transmission in terms of polarization
Authors: Hill Nora E.
Published: March 2005

The reflection and transmission of an electromagnetic wave at an air-dielectric interface is considered in terms of the polarization in the simple case when a plane electromagnetic wave is incident normally on a plane interface. The Ewald–Oseen extinction theorem is obtained and the implications of the calculation for time domain reflectometry is discussed.
Steady magnetic field from charges in arbitrary motion
Authors: Benoit Henri
Published: March 2005

The vector potential A and its time integral for an electric charge in a given motion are calculated at some observation point O. It is shown that the time integral of A depends only on the geometrical path followed by the charge during the retarded time interval. Then the time integral of the magnetic field B is calculated. We discuss some cases where this time integral depends only on the geometrical path, B can then be calculated in a slow motion approximation, that is with the Biot and Savart law.
Electrostatic potential on a laboratory measurement experiment
Authors: Murata Hiroshi , Sakuraoka Mitsuru
Published: March 2005

The theoretical potential is derived by taking into account the boundary of the actual experimental setup as faithfully as possible. The theoretical potential is in good agreement with the experimental results.
The sufficient condition for an extremum in the classical action integral as an eigenvalue problem
Authors: Hussein M. S. , Pereira J. G. , Stojanoff V. , Takai H.
Published: March 2005

The sufficient condition for an extremum in the classical action integral is studied using Morse’s theory. Applications to the classical harmonic and anharmonic oscillators are made. The analogy of the calculations to the quantum-mechanical problems in one dimension is stressed.
Experimental simulation in the modern physics laboratory
Authors: Wilson Jack M.
Published: March 2005

Graphic computer simulations of laboratory experiments in modern physics have been developed for student use prior to each laboratory. The graphic simulations partially replace the traditional pre-lab briefing in an open laboratory setting. Experimental simulation is intended to familiarize the students with the experiment, to allow the students to try a larger number of ’’experimental’’ combinations of variables, to encourage student participation in the design of the experiment, and to build the students confidence in their laboratory ability. Each simulation is designed to be as realistic as posible to provide the student with the same choices of experimental procedure and the same type of data output as would be provided in the laboratory.
Discovery of the Earth’s core
Authors: Brush Stephen G.
Published: March 2005

In 1896 when Emil Wiechert proposed his model of the Earth with an iron core and stony shell, scientists generally believed that the entire earth was a solid as rigid as steel. R. D. Oldham’s identification of P and S waves in seismological records allowed him to detect a discontinuity corresponding to a boundary between core and shell (mantle) in 1906, and Beno Gutenberg established the depth of this boundary as 2900 km. But failure to detect propagation of S waves through the core was not sufficient evidence to persuade seismologists that it is fluid (contrary to modern textbook statements). Not until 1926 did Harold Jeffreys refute the arguments for solidity and establish that the core is liquid. In 1936 Inge Lehmann discovered the small inner core. K. E. Bullen argued, on the basis of plausible assumptions about compressibility and density, that the inner core is solid. Attempts to find seismic signals that have passed through the inner core as S waves have so far failed (with one possible exception), but analysis of free oscillations provided fairly convincing evidence for its solidity.
Miniature magnet assembly for NMR–ESR spectroscopy
Authors: Shanks J. G. , Tsay Fun-Dow , Rhim W. K.
Published: March 2005

A compact and inexpensive permanent magnet assembly, well suited for educational NMR–ESR demonstrations, field use, and possibly space flight applications is described. For NMR a field of 3.2 kG, homogeneous over a 4-mm sample to within 4 ppm, has been achieved (at 0.44-in. air gap). The assembly, mounted with a different set of polecaps designed for X-band ESR, provides a 3.4-kG field (at 0.6-in. air gap), uniform to within 40 ppm. A simple, mechanical means of sweeping the field through 70 G without significantly affecting the homogeneity is also described.
Microprocessor multichannel analyzer laboratory project
Authors: Munger Burton L. , Zammit Ronald E.
Published: March 2005

An undergraduate laboratory project that combines microprocessor programming, interfacing, and system design to produce a multichannel analyzer with requires only a small investment in time and money.
Solar eclipse predictions
Authors: Mottmann J.
Published: March 2005

A method suitable for intermediate level astronomy courses is presented for the calculations of solar eclipses. The results are surprisingly good considering the simplifications used and the avoidance of spherical trigonometry.
Using paradoxes
Authors: Welch Daniel W.
Published: March 2005

Far from being simply amusing (or frustrating), paradoxes are uniquely effective in addressing specific deficiencies in understanding. Three examples from physics, and one from astronomy, are given to show how paradoxes may be constructed and used to concentrate attention on a desired point.
Relativistic motion in a plane
Authors: Coulter Byron L.
Published: March 2005

One observer with a light clock is assumed to be moving in the x–y plane of a second observer. Formulas are derived for the length and orientation of the clock, the path of the light ray, and the time kept by the clock as measured by the second observer. Effects of the relative rotations of the coordinate frames and of the clocks are investigated.
Demonstration of shear waves, Lamb waves, and Rayleigh waves by mode conversion
Authors: Leung W. P.
Published: March 2005

When a plane elastic wave strikes an interface between two different media, mode conversion occurs. The reflected and refracted waves may consist of both longitudinal waves and shear waves. Under some circumstances, Rayleigh surface waves and Lamb waves can also be excited. A simple experiment which can be demonstrated in the classroom is introduced here to show that shear waves, Rayleigh waves, and Lamb waves can be easily generated and observed by means of mode conversion.
Elementary introduction to the properties of angular momentum operators through three-dimensional rotations
Authors: Leubner C.
Published: March 2005

For pedagogical purposes it is demonstrated that with little effort the customary discussion of rotations in introductory courses can be extended to naturally produce a number of angular momentum operator properties, if coordinate-free rotation operators are used in their exponential form. This form gives rise to a particularly useful coordinate-free representation of the generators of rotations in three-space, from which the student can derive the usual angular momentum formalism for the case j=1 by elementary vector algebra alone. Since in this approach the j=1 formalism appears as a set of relations among simple geometric objects in ordinary space, it admits of a geometric interpretation and will leave the student better prepared for a more profound appreciation of the abstract concepts of the full theory.
Regarding magnetic flux quantization
Authors: Firth L. D.
Published: March 2005

It is pointed out that the magnetic flux quantum is more readily derived using single electrons rather than Cooper pairs.(AIP)