Volume 38, Issue 2, February 1970
 PAPERS


Resource Letter Neu1 History of the Neutrino
View Description Hide DescriptionPrepared at the request of the AAPT Committee on Resource Letters.
This is one of a series of Resource Letters on various topics, intended to guide college physicists to literature and other teaching aids that may help them improve course content in specified fields of physics. No Resource Letter is meant to be exhaustive and complete. In time, there may be more than one letter on some of the main subjects of interest. Comments and suggestions concerning the content and arrangement of letters as well as suggestions for future topics will be welcomed and should be addressed to Professor Joel E. Gordon, Chairman, AAPT Committee on Resource Letters, Department of Physics, Amherst College, Amherst, Mass. 01002.
Notation: An asterisk (*) before an item number indicates items of particular fundamental importance.
Reprints: Individual reprints of this Resource Letter may be obtained by sending 25 cents (in cash) per copy, together with a stamped and selfaddressed envelope, to the Executive Secretary, American Association of Physics Teachers, 335 East 45th Street, New York, N. Y. 10017.

Approach to a General Physics Course for Natural Science Students
View Description Hide DescriptionOn the basis of past experience in the physics department (Facultad de Ciencias Exactas y Naturales, Univ. de Buenos Aires) a general physics course for natural science students was organized by making a careful selection of subject content, organizing lab and discussion periods, and devoting a number of lecture hours to discuss papers selected from current literature.

Theory of a Ball Rolling on a Surface of Revolution
View Description Hide DescriptionThe equations of motion for a ball rolling without slipping on a surface of revolution are derived and applied to the case of the ball scattered by the surface. Our result is a simple integral for the scattering angle. In the limiting case that the ball is small, the integrand is a known function. In the general case it contains several power series.

Supplementary Note on Brownian Motion
View Description Hide DescriptionA modified FokkerPlanck equation is derived to describe Brownian motion for the case of large viscosity. The derivation uses the quasi Huygens relation developed by Chandrasekhar as a starting point. The modified relation is shown to be capable of directly yielding the Smoluchowski equation. Moreover, the momentumconservation equation to which it gives rise is also investigated.

Effective Interactions in Nuclear Structure
View Description Hide DescriptionThe basic notions associated with the idea of an “effective interaction” in nuclear physics are sketched by first recalling isolated twobody scattering analyzed with integral equations and in which the transition operator appears naturally. Brueckner's reaction matrix operator is discussed in the context of both infinite nuclear matter and finite nuclei with doubly closed shells. Finally, openshell nuclei are touched upon by way of a manybody effective interaction operator deduced in simple language and a possible connection between this and the reaction matrix operator is given. It is emphasized throughout that the basic merit of the vantagepoint sketched here is its fundamental origin in the manybody Schrödinger equation.

AharonovBohm Effect—Quantum Effects on Charged Particles in FieldFree Regions
View Description Hide DescriptionThe AharonovBohm effect is relatively little known, but it poses fundamental questions in quantum theory. It concerns physical effects on charged particles in fieldfree regions. The present paper provides an overall critical review and commentary on the literature of the AharonovBohm effect. The two fundamental questions raised by the effect concern the role of the force concept in quantum mechanics, and the localizability of physical effects principle. A recent letter from Professor Bohm concerning his evaluation of the significance of the effect is included in the Appendix.

Foucault Pendulum Experiment by Kamerlingh Onnes and Degenerate Perturbation Theory
View Description Hide DescriptionThe paper pays homage to H. Kamerlingh Onnes by pointing out that he constructed the first properly functioning model of the Foucault pendulum. His success was largely due to an analysis which takes into account the unavoidable mechanical asymmetry of the pendulum. Based on the analysis he was able to eliminate the asymmetry and to obtain the desired performance which earlier workers had realized only to a limited extent. Onnes' analysis is reproduced with more modern tools such as vector notation and, especially, the concept of eigenfunctions. His analysis is probably one of the earliest examples of a particular type of doubly degenerate perturbation theory. Two different effects compete for lifting the degeneracy, one favoring “circular polarization,” the other “linear polarization.” The resulting eigenfunctions represent “elliptical polarization.” The tutorial significance of this perturbation theory is emphasized by mentioning other fields where it is applied if perhaps disguised by a different jargon and analytic technique. Examples include electromagnetictheory(microwavecavities for circular polarization), laser optics (mode analysis of ring lasers for rotation sensing), and quantum theory (quenching of orbital angular momentum by crystalline field).

LowFrequency Bremsstrahlung in Coulomb Scatterings of Nonrelativistic Electrons
View Description Hide DescriptionA simplified derivation of the lowfrequency bremsstrahlung cross section in the classical limit is presented. Also, by expanding Elwert's exact quantummechanical expression for the cross section in powers of and in powers of , corrections are obtained to the Bornlimit and classical formulas, respectively. Averaging over a Maxwellian distribution of incident electrons gives the lowfrequency thermal emission and absorption coefficients; corrections to the Bornlimit and classical formulas are expressed as power series in and , respectively. Significantly, the coefficient of the firstorder correction term for the classical formulas for the cross section, and thermal coefficients turns out to be zero.

Robert Grosseteste on Refraction Phenomena
View Description Hide DescriptionThis translation of the treatise by Robert Grosseteste (1167–1253) On the Rainbow (1235) categorizes the thenknown types of optical phenomena as results of direct, reflected, and refracted light. His discussion of optics as a geometrical science, concerned therefore with explanation rather than description alone, introduces the following subjects: real visual rays, the law of refraction in terms of the law of reflection, the position of an image in refraction in terms of imageposition in reflection, the rainbow, and color theory. Whereas all these discussions show the primitive state of the science, the law of refraction and the attribution of refraction to the rainbow are notable as the first influential attempts along these lines in the history of optics.

Liquid Crystals and Newton's Rings
View Description Hide DescriptionStudies of the birefringence of liquid crystals by means of Newton's rings are described. Some results for 44′dihexoxyazoxybenzene are given. These experiments are suitable for student laboratories.

Energy and Observables in Electromagnetic Theory
View Description Hide DescriptionA comparison is made of two ways of introducing auxiliary variables into Maxwell's equations. The first is the usual introduction of potentials. The second introduces twice the usual number of potentials. Although both formalisms lead to the usual vacuumfield equations when expressed in terms of the original variables (the components of the electromagnetic field tensor), they are found to describe physically distinct theories. It is seen that the second formalism leads to a different stressenergy tensor and to the prediction of new observable quantities, which apparently have no counterpart in nature.

On the Operational Definition of Radiation in WheelerFeynman “ActionataDistance” Electrodynamics
View Description Hide DescriptionThe basic structure of WheelerFeynman “actionatadistance” electrodynamics is reviewed in an attempt to better understand the details of how the process of radiation is described in this theory. In actionatadistance electrodynamics, radiation is not associated with a single current, but instead involves both an “emitter” charge and a “receiver” charge in its definition. We study this process in detail and show the exact manner in which this definition of radiation can be made to agree with the conventional MaxwellLorentz definition of radiation. As a practical example of this definition of radiation, the RayleighJeans blackbody radiation law is derived within the WheelerFeynman electrodynamic framework.

Characteristics of Compressible Fluids and the Effects of Heat Conduction and Viscosity
View Description Hide DescriptionThe behaviors of the characteristics of compressible fluids are known to be singular when the parameters of usual heat conduction and viscosity laws become zero. The understanding of existing resolutions requires a fair amount of sophistication in mathematics. Presented here is an heuristic explanation appealing to simple physical reasoning.

Dimensionality Effects on the Fermi Gas
View Description Hide DescriptionIt is shown how the elementary properties of one, two, and threedimensional free electron gases may be obtained as special cases of a general formulation. The exercise is suitable for a student and furthermore suggests that the concept of nonintegral dimensionality may serve to describe finite geometries as intermediate between the usual integral types.

Special Relativity and Diagonal Transformations
View Description Hide DescriptionWe discuss the form of the special Lorentz transformation, and the corresponding transformation of the electromagnetic field, in which the transformation matrix is diagonal. We derive the diagonal form of the special Lorentz transformation directly, in a simple way, and show that it is sometimes more convenient to apply than the algebraically equivalent conventional form of the transformation. The convenience is especially evident in deriving the linear Doppler effect, and the relativistic addition of more than two parallel velocities. By writing Maxwell's equations in terms of linear combinations of coordinates which have simple transformation properties, we arrive at the transformation equations of the Maxwell fields in a diagonal form, as well as at the plane wave solutions, in a natural manner. The derivations and applications described above should be of use in a course on relativity because of their simplicity and directness.

Graphical Method of Teaching Elementary Collisions
View Description Hide DescriptionA graphical method of teaching elementary collisions is explained. The traditional method consists of an introduction to the conservation laws of linear momentum and energy followed by a treatment of twobody collisions with a few special cases as examples. The new method yields universal solutions to headon collision problems with the target at rest by the use of parameters and graphical analysis at a mathematical level that students can understand. The time required for classroom presentation is little more than that of the traditional method. The author concludes that the graphical method is better than the traditional method because of increased student interest and comprehension. The results suggest an experiment utilizing a linear air track or similar apparatus.

Energy Transients in Harmonic Oscillator Systems
View Description Hide DescriptionThe approach to energy equilibration is discussed for a system of N isolated classical oscillators, coupled or uncoupled. Exact solutions can be given for the kinetic and potential energies vs time, for a simple boundary condition which distributes the potential energy equally between all the normal modes at zero time and which gives zero kinetic energy to all the normalmode oscillators at zero time. Most solutions are ergodic but a special class is nonergodic, i.e., the potential energy vs time shows exact recursions. The halflife for approaching the equilibrium value of potential or kinetic energy is of the order of the reciprocal maximum frequency of the oscillators. The fluctuations from equilibrium are treated by an extension of the method of Rayleigh's problem of random walks. The results are of interest in connection with the ergodic theorem of statistical mechanics.

BoseEinstein Condensation of Noninteracting Particles
View Description Hide DescriptionThe chemical potential is determined for a BoseEinstein gas of noninteracting particles in a closed system. The calculation is done in a manner which shows dependence on an energy gap, limits of application of the results, and behavior through the transition temperature.

Simplified Microwave Frequency Electron Spin Resonance Spectrometer
View Description Hide DescriptionA selfoscillating microwave frequency spectrometer incorporating a solidstate Gunn diode is described. Its simplicity, sensitivity, and relatively low expense make it suitable for instructional laboratory use.

On Statistical Analysis in the General Physics Laboratory
View Description Hide DescriptionMost generalphysics laboratory manuals and textbooks give inadequate and/or erroneous procedures for assessing the validity of experimental data. This paper advocates a procedure both less time consuming and more rewarding than those usually recommended for general physics laboratories. It uses the range of the results of a limited number of repeated measurements to obtain confidence limits about the probable overall average of repeating the same procedure a great many times. This procedure is well established among statisticians, but appears not to be well known to physicists.
