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Dec 1969

Volume 37, Issue 12, pp. 1193-1296

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The Robert A. Millikan Lecture Award 1969

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1193

Online Publication Date: Jul 2005

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Content and Process in Physics Teaching

John M. Fowler

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1194

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Optical Resource Letter on Colorimetry

Günter Wyszecki

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1201

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These Optical Resource Letters are patterned after the materials that have been developed by the AAPT Committee on Resource Letters and previously published in the American Journal of Physics. Since they contain information of direct interest to most teachers of physics, we are pleased to have the permission of the Journal of the Optical Society of America to reprint them in AJP. The purpose is to provide, in an important field of optics, briefly annotated references which should be of value to teachers, researchers, engineers, and technicians interested in the subject area. No claim is made for completeness or exhaustiveness of coverage; rather, it is hoped that the references quoted will be helpful in themselves, and will be representative, or at least suggestive, of the broad literature on this subject. The letter E following an item number indicates that the reference is on a more-or-less elementary level; the letter A indicates an advanced level.
The present Optical Resource Letter, OC-1, was prepared under the direction of the OSA Ad Hoc Committee on Resource Letters: K. M. Baird, H. E. Breed, M. A. Jeppesen, J. M. Stone, and S. S. Ballard (Chairman).
Additional copies are available from the Executive Office of the Optical Society of America, 2100 Pennsylvania Avenue, N. W., Washington, D. C. 20037. Request Optical Resource Letter OC-1, and please enclose a stamped, return-addressed envelope.

Some More Simple Laser Experiments for the Undergraduate Laboratory

F. Y. Yap

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1204

Online Publication Date: Jul 2005

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Certain elementary optics experiments can be performed with considerably greater ease using a laser instead of conventional light sources. This paper describes three such experiments which illustrate the Fresnel-Arago law, elliptical polarization, double refraction and polarization in calcite, and interference by a Fresnel biprism. Because of the high intensity of the laser beam, these experiments lend themselves very well to demonstrations in front of large groups.

A Quantitative Transmission Line Experiment

D. C. Johnston and B. G. Silbernagel

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1207

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Modification of a commercially available strip-type transmission line is described, which makes possible reproducible measurements of standing waves on the line. The experimental data yield values for the characteristic impedance, phase velocity and line wavelength of radiation in the transmission line, and the dielectric constant of material in the line. Interpretation at several levels of difficulty is discussed and quantitative agreement between experiment and theory is obtained.

On the Interpretation of Measurement within the Quantum Theory

Leon N. Cooper and Deborah Van Vechten

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1212 | Cited 2 times

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An interpretation of the process of measurement is proposed which can be placed wholly within the quantum theory. The entire system including the apparatus and even the mind of the observer can be considered to develop according to the Schrödinger equation. No separation, in principle, of the observer and the observed is necessary; nor is it necessary to introduce either the type I process of von Neumann or wave function reduction.

Measurement and Interference

L. S. Schulman

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1220

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We use the density matrix formalism to discuss the often encountered question: When do final states due to various initial states add coherently (interfere)?

Why is Space Three-Dimensional? Based on W. Büchel: “Warum hat der Raum drei Dimensionen?,” Physikalische Blätter 19, 12, pp. 547–549 (December 1963)

Ira. M. Freeman

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1222 | Cited 1 time

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Classification of Electromagnetic and Gravitational Fields

Garry Ludwig

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1225

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The connection between the three main methods of obtaining the Petrov classification is examined. Spinor techniques are used extensively. A five-dimensional complex linear space is introduced whose elements are Weyl tensors. It is found that not only Weyl tensors of type N and type III, but also some Weyl tensors of type I are null vectors in this space. In analogy with the electromagnetic case we would expect these null vectors to correspond to “pure” gravitational radiation.

Fermion Operator Ordering and the Quantum c-Number Correspondence

C. L. Mehta and A. K. Jaiswal

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1239

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The linearly ordered and the exponentially ordered forms of an arbitrary spin ½-Fermion operator are defined and evaluated. As an application an expression for exp (αmath) exp (βmath) is evaluated which resembles the usual Baker-Hausdorff identity. It is shown that the trace of the product of two Fermion operators can be expressed as a three-dimensional integral over c-number functions. Further the quantum equations of motion are also expressible as equations involving c-number functions.

Equivalence of the δ′ and the Hard Core Potentials

R. E. Schenter, H. S. Zwibel, and R. L. Cassola

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1242

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The introduction of the hard core potential into the two-body problem forces the system wave function to vanish, if the interacting particles approach each other more closely than the hard core radius. In this paper it is shown that this “hard core effect” can also be obtained in the two-body problem by replacing the hard core potential with a δ′ interaction of suitable strength.

Infinite Square-Well Potential with a Moving Wall

S. W. Doescher and M. H. Rice

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1246 | Cited 7 times

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The problem of a particle in a one-dimensional infinite square-well potential with one wall moving at constant velocity is treated by means of a complete set of functions which are exact solutions of the time-dependent Schrödinger equation. Comparison is made with a first-order perturbation treatment, and numerical results are presented for a particle initially in the ground state.

The Reflection and Transmission of Electromagnetic Waves by a Moving Dielectric Slab. I. Solution in the Moving Frame

William J. Noble and Carl K. Ross

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1249 | Cited 1 time

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The Darwin scattering method is used to calculate the amplitudes, frequencies and propagation directions of the free space electromagnetic waves reflected and transmitted by a plane-parallel, non-dissipative, isotropic, homogeneous, dielectric slab. The laws of reflection and refraction and the conservation of energy flux follow naturally. Explicit formulas are given for perpendicular polarization but the method is equally applicable to polarization parallel to the plane of incidence. The results of Part I for the reference frame of the moving slab are in a form to be transformed in Part II to the reference frame of a “fixed” observer.

The Reflection and Transmission of Electromagnetic Waves by a Moving Dielectric Slab. II. Solution in a Fixed Frame

William J. Noble and Carl K. Ross

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1253

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In Part II, the results obtained in Part I for perpendicularly polarized electromagnetic waves reflected and transmitted by an infinite, plane-parallel, homogeneous, isotropic, nondissipative slab when at rest are transformed via the Lorentz and field transformations to obtain a similar solution when the slab is in uniform motion with respect to a “fixed” observer. The dependence of the frequencies and direction of propagation of the reflected and transmitted waves on the slab velocity is determined, and an expression for energy conservation is derived to account for momentum transfer between the slab and the electromagnetic radiation.

A Proposed Electromagnetic Momentum-Energy 4-Vector for Charged Bodies

J. W. Butler

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1258

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The conventional electromagnetic momentum- and energy-density expressions (E × H∕c) and [½(E2+H2)], respectively (Heaviside-Lorentz units in free space), are known not to lead to a momentum-energy 4-vector for the fields of charged bodies. Yet the rest of classical electrodynamics is a covariant theory. This is a most remarkable anomaly. The reason for this anomaly is shown herein to lie in the procedure used to derive Poynting's theorem, which is shown not to be covariant in the presence of sources. A 4-vector is derived to represent the 4-momentum dGμ contained within a volume element dV of the electromagnetic field of a charged body with a 4-velocity uμ ≡ (γv, iγc):
math
, where γ ≡ (1 − v2c2)−1∕2. This proposed 4-vector is shown to remove several paradoxes associated with the predictions of the conventional momentum and energy density expressions. And the proposed 4-vector is also shown to be in agreement with the results of several experiments.

Heat Capacity of an Ideal Free-Electron Gas: A Rigorous Derivation

Robert Weinstock

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1273 | Cited 1 time

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It is shown that a standard derivation found in the literature for the heat capacity of an ideal free-electron gas is vitiated by the use of divergent series. A plausible argument is offered to indicate that these series are actually asymptotic expansions that provide good approximations through their first few terms—a provable fact acknowledged by a few writers, but the proof of which has nowhere been seen in print by the present author. The invalid standard procedure is modified through replacement of an infinite series by its first two terms plus a remainder whose bounds are easily estimated as being negligible to the accuracy required; a rigorous derivation of the well-known temperature dependence of the electronic heat capacity of a metal results.
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Mechanical Analogy of Hybrid Resonances in a Plasma

M. E. Oakes and Richard Freeman

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1280

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On Tachyon Lorentz Transformation

K. H. Mariwalla

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1281 | Cited 1 time

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Some Operational Characteristics of the Search Rotational Dynamics Apparatus

Willard C. Sperry

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1282

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Effect of Gravitation on the Lorentz Transformation

L. Karlov

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1283

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The Definition of a Canonical Transformation

Eric Drake

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1284

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Erratum: “Force, Momentum Change, and Motion” [Amer. J. Phys. 37, 82 (1969)]

M. Tiersten

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1285

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Erratum: “A Magnetic Field Diffusion Problem” [Amer. J. Phys. 37, 323 (1969)]

L. T. Klauder, Jr.

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1285

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Letter re: “The Postulational Approach”

F. R. Tangherlini

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1286

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Letter re: “Bernoulli Effect and Kinetic Theory”

F. H. Barnes and T. Robertson

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1286

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Reply to Letter of Dr. Barnes and Dr. Robertson

Francisco Glover, S. J.

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1287

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Comments on “Agreement between Classical and Quantum Mechanical Solutions for a Linear Potential inside a One-Dimensional Infinite Potential Well”

Noble M. Johnson and John N. Churchill

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1287

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Lectures in Theoretical High Energy Physics

H. H. Aly, Editor and Peter A. Carruthers, Reviewer

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1288

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William Whewell's Theory of Scientific Method

Robert E. Butts, Editor and Lancelot Law Whyte, Reviewer

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1289

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Mass Motions in Solar Flares and Related Phenomena (Nobel Symposium 9)

Y. Öhman, Editor and Robert F. Howard, Reviewer

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1289

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Particles and Fields

David Lurié, Author and R. H. Good, Jr., Reviewer

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1290

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Structure of Complex Nuclei

N. N. Bogolyubov, Editor and Raymond A. Sorensen, Reviewer

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1290

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Heavily Doped Semiconductors

Viktor I. Fistul, Author and J. S. Blakemore, Reviewer

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1291

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Introduction to the Theory of Kinetic Equations

Richard Liboff, Author and William Nichols, Reviewer

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1292

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Mechanics in Sixteenth-Century Italy: Selections from Tartaglia, Benedetti, Guido Ubaldo, and Galileo

Stillman Drake, Author, I. E. Drabkin, Author, and Alfred Romer, Reviewer

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1293

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Minnesota Section

Richard E. Pontinen

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1295

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American Association of Physics Teachers Treasurer's Report for the Year Ended 31 December 1968

Harold H. Holen

American Journal of Physics -- December 1969 -- Volume 37, Issue 12, pp. 1296

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