American Journal of Physics 1989 April

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 295 - 295
Guest Comment: Why scientists should popularize science
Carl Sagan

Center for Radiophysics and, Space Research, Cornell University, Ithaca, NY 14853-6801

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 296 - 296
Editorial: AJP Reviewers_Thank You!
Robert H. Romer

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 297 - 298
American Association of Physics Teachers: Citations for Distinguished Service for 1989

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 299 - 308
Molecular beam experiments, the Lamb shift, and the relation between experiments and theory
S. S. Schweber

Department of Physics, Brandeis University, Waltham, Massachusetts 02254
(Received 17 September 1987; accepted for publication 8 April 1988)
The Rabi molecular beam experiments and the Lamb shift experiment are analyzed to elucidate the role the nonrelativistic Schrodinger equation plays in their design, analysis, and interpretation.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 308 - 309
How big is a cyclotron?
Lowell S. Brown

Department of Physics, FM-15, University of Washington, Seattle, Washington 98195
(Received 21 March 1988; accepted for publication 8 May 1988)
The radius of the orbit of a particle of given energy in a laboratory cyclotron is computed in terms of the Bohr radius of the hydrogen atom a[sub 0] and the fine structure constant alpha .

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 309 - 311
Geometrical interpretation of the simultaneous diagonalization of two quadratic forms
P. K. Aravind

Physics Department, Worcester Polytechnic Institute, Worcester, Massachusetts 01609
(Received 13 August 1987; accepted for publication 15 May 1988)
The theory of small oscillations, when cast in matrix form, leads to an eigenvalue problem involving the simultaneous diagonalization of two real symmetric matrices. While a geometrical interpretation of this process exists, its visualization is generally hampered by the multidimensional nature of the coordinate transformations involved. I consider a model problem with just two degrees of freedom for which the coordinate transformations become planar and therefore easily visualizable. A set of plane diagrams is provided showing how the diagonalization is achieved for the model problem considered.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 311 - 311
Problem: Wrapping a string around an object
J. Casey

Department of Mechanical Engineering, University of Houston, Houston, TX 77004

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 312 - 316
Fresnel lenses
B. A. Anicin

Faculty of Mechanical Engineering, University of Belgrade, Belgrade, Yugoslavia
V. M. Babovic
Department of Physics, Faculty of Sciences, University of Kragujevac, Yugoslavia
D. M. Davidovic
Boris Kidric Institute, Belgrade, Yugoslavia
(Received 27 April 1988; accepted for publication 29 June 1988)
This article contains a description of the discovery of the stepped lenses that today bear Fresnel's name, based on a monograph written by Fresnel himself in 1822. Although it stands in the shadow of the rest of his activity, in particular the theory of transverse light waves, including polarization, diffraction, and birefringence, this invention could be regarded as a very interesting and very early result of government-sponsored research activity in science and technology, to be used in lighthouses for at least a century, and to remain important in other fields of modern optics.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 317 - 321
Introducing Schrodinger's cat in the laboratory
T. J. Axon

Department of Physics, Imperial College, London, England
(Received 30 June 1987; accepted for publication 9 May 1988)
A laboratory session that is designed to introduce students to the conceptual foundations of quantum mechanics is described. In this laboratory session, several experiments are used in order to illustrate the important ideas of superposition, interference, and the ``collapse'' of the wavefunction. These experiments form the basis for a discussion of four of the most popular interpretations of quantum mechanics that have been proposed over the years: the instrumentalist interpretation, hidden variable theories, the objective view of the wavefunction, and the many-worlds interpretation. As a finale, students are introduced to the paradox that epitomizes the interpretational problems of quantum mechanics: the paradox of Schrodinger's cat.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 322 - 325
Timely equations of rocket motion and the surprising power of rockets
R. Stephenson

Physics Department, Slippery Rock University, Slippery Rock, Pennsylvania 16057
(Received 15 January 1988; accepted for publication 26 April 1988)
Current general physics textbooks derive equations for rocket acceleration and rocket velocity as functions of mass. Rocket position is ignored in nearly all textbooks. Using time left till total mass consumption as a variable, simple equations for acceleration, velocity, and position can be easily derived. The flight of a rocket subject to constant gravitational acceleration proves quite simple to analyze. Finally, a power analysis shows that in an inertial reference frame, the power of a rocket can exceed the power of its engine.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 325 - 330
A simple method for measurement of the diffusion of vapors
Arnold J. Abraham
Charles P. Bean

Department of Physics, Rensselaer Polytechnic Institute, Troy, New York 12180
(Received 22 December 1986; accepted for publication 8 May 1988)
A simple method for the measurement of the diffusion of vapors is described. Commercially available microcapillary tubes, a ruler, and a watch, allow measurement of the diffusion constant to a precision of better than 1%. This article describes measurements of the diffusion of water, benzene, and various straight chain alcohol molecules in air. The technique is suitable for the undergraduate laboratory or as a home experiment.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 330 - 332
Galilean transformation and the path integral propagator for a crossed electric and magnetic field
Carlos Farina de Souza

Universidade Federal do Rio de Janeiro, Instituto de Fisica, Cidade Universitaria_Ilha do Fundao, Rio de Janeiro, CEP 21945, Brazil
Alvaro de Souza Dutra
Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud, 150, Urca, Rio de Janeiro, CEP 22290, Brazil
(Received 3 August 1987; accepted for publication 10 May 1988)
A Galilean transformation is made in the path integral formalism to obtain the Feynman propagator of a charged particle in the presence of a crossed uniform electromagnetic field in terms of the propagator of a charged particle in the presence of only a magnetic one. Also noted is how the result makes it possible to relate the initial propagator, with E and B, to that of the free particle.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 333 - 339
Time-reversal invariance in multiple collisions between coupled masses
Frank S. Crawford

Physics Department and Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
(Received 8 February 1988; accepted for publication 27 June 1988)
The time evolution of two mechanical oscillators coupled by a spring can (but need not) exhibit an instant t=2t' when the initial conditions at t=0 have been exactly restored. When that is the case, then at t=t' energy and momentum have been exchanged exactly as in an elastic collision between two free particles, and the evolution of the system from t=t' to 2t' is related to that from 0 to t' by time-reversal invariance. A similar ``simulation of elastic scattering'' at t=t' can occur for two free particles coupled via collisions with an intermediary mass that bounces back and forth between the two particles provided the intermediary is left at rest at t=t'. Examined here is the time evolution of the exchange of momentum and energy for these two examples, determining the values of the coupling spring constant (or mass value) of the intermediating spring (or mass) needed to simulate single elastic scattering between free particles, and looking at the manifestation of time-reversal invariance.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 339 - 344
An approximate analytic solution of the spectral inverse problem
Ray Engelke

Los Alamos National Laboratory, Los Alamos, New Mexico 87545
(Received 16 November 1987; accepted for publication 15 May 1988)
An important problem of nonrelativistic quantum theory is: Given a bound-state energy spectrum, determine the space dependence of a potential function that will produce that spectrum. This is sometimes called the ``spectral inverse'' problem. Here, by use of the first-order WKB energy quantization condition, an approximate analytic solution of this problem is given for the case of one-dimensional symmetric oscillators and for a class of radial oscillators. This is done by reformulating the WKB quantization condition as an Abel integral equation that relates the quantum number to the potential's space dependence. The resultant integral equation can be solved exactly. The harmonic oscillator and the hydrogen atom problems are used to demonstrate the method. The solution for the case of one-dimensional asymmetric oscillators is also briefly discussed and the Morse oscillator is used as an example. Finally, the history of the spectral inverse problem is reviewed and the conditions necessary for its exact solution are discussed. In particular, the conditions required for the inversion process to be unique are considered.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 344 - 346
Deriving a formula for nuclear radii using the measured atomic masses of elements
N. Gauthier

Department of Physics, Royal Military College of Canada, Kingston, Ontario K7K 5L0, Canada
(Received 11 January 1988; accepted for publication 30 April 1988)
Most nuclei have a nearly spherical shape and can be characterized by an effective radius R=R[sub 0] A[sup 1][sup /][sup 3], where A is the nucleon number and R[sub 0] is a constant to be determined from experimental data. Traditionally, the data came from experiments on muonic or pionic x-ray emission, high-energy electron scattering, optical or x-ray isotope shifts, beta emission by mirror nuclei, alpha decay, or neutron scattering. Because this type of information is not readily available in textbooks or the pedagogical literature, it is difficult to ask students to establish the radius formula on their own. However, as shown here, one may easily circumvent the difficulty by using the readily available and highly accurate masses of the mirror nuclei. Results are presented for all existing pairs of mirror nuclei.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 346 - 351
Heuristic methods for counting and sizing of molecules in the liquid state
R. E. Crandall
T. G. Dunne

Departments of Physics and Chemistry, Reed College, Portland, Oregon 97202
(Received 25 August 1986; accepted for publication 29 April 1988)
Though the liquid state is highly complex, there are global classical properties that liquids enjoy. Heuristic liquid-state relations may be derived from the fundamental physics of surface energy and volume energy. It has long been known that the dimensional difference between these two measures can be exploited to yield estimates of molecular count and size. Herein is described an alternative approach in which a key parameter is the temperature coefficient of surface tension. This parameter circumvents the need for awkward volume energy measurements. Here indicated is how simple experiments, or even pretabulated chemical data, may be used to estimate such quantities as Avogadro's number.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 351 - 352
A classroom exercise to determine the Earth-Moon distance
E. Roger Cowley

Department of Physics, Camden College of Arts and Sciences, Rutgers, The State University of New Jersey, Camden, New Jersey 08102
(Received 8 March 1988; accepted for publication 16 May 1988)
A simple indoor exercise to obtain the value of the Earth-Moon distance, in terms of the Earth's radius, is described. The student measures on a photograph the ratio of the diameter of the Moon to the diameter of the shadow of the Earth during a lunar eclipse. A simple but adequate reduction of the measurement is given.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 352 - 359
Redesigning courses and textbooks for the twenty-first century
Gordon J. Aubrecht,II

American Association of Physics Teachers, Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742 and Department of Physics, Ohio State University, Marion, Ohio 43302 and Columbus, Ohio 43210
(Received 20 April 1987; accepted for publication 8 May 1988)
There is evidence that a confluence of pressures to change the current physics syllabus is building from many sources. Texts for science and engineering students do not usually have much contemporary physics content. There is a need to update textbooks to include areas of current interest in physics research, to include important facets of 20th-century physics that have gone virtually unnoticed in the present generation of physics textbooks. The consequence of additions of topics must be restructuring of the physics curriculum and may lead to corresponding deletions among topics presently discussed.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 359 - 362
A remark on the gravitational field produced by an infinite straight string
G. Francisco
G. E. A. Matsas

Instituto de Fisica Teorica, Universidade Estadual Paulista, Rua Pamplona 145, Sao Paulo 01405, Brazil
(Received 21 December 1987; accepted for publication 3 May 1988)
The results predicted by Newtonian gravity and general relativity are compared regarding the field produced by an infinite gauge string with constant density lambda . A simple gedankenexperiment is suggested to stress the remarkable differences between these two theories. The existence of the usual Newtonian limit is discussed in this case.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 362 - 365
Exercises in the synthesis of electrical impedances
Robert L. Collier

305 West 20th, Austin, Texas 78705
(Received 28 October 1987; accepted for publication 20 May 1988)
Two general circuits are developed for the synthesis of user-variable electrical impedances. One circuit permits user-variable enlargement of any existing impedance without affecting its phase characteristics. This circuit facilitates such devices as floating capacitors and inductors which are continuously variable over wide ranges. The other circuit permits simulation of user-variable floating impedances whose phase and frequency characteristics are widely subject to design objectives. In addition to all conventional impedance functions, it poses access to an infinite set of alternatives for the simulation of resistance and reactance functions of frequency. Included is a theoretical approach for predicting parasitic impedances reported in earlier works on similar devices known as gyrators.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 366 - 370
Measurement of refractive index by double-exposure speckle pattern recording
P. K. Buah-Bassuah
F. Francini
G. Molesini

Istituto Nazionale di Ottica, Firenze 50125, Italy
(Received 3 August 1987; accepted for publication 21 June 1988)
An experimental approach is presented to the measurement of the refractive index of materials based on the optical properties of speckle patterns. The sample being characterized is shaped in the form of a plane parallel plate and so inserted in a speckle-forming beam. Speckles are recorded on a photographic plate with a double-exposure technique producing a twin speckle pattern. Decoding of such a recorded pattern leads to the desired information.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 370 - 373
An experiment on the physical reality of edge-diffracted waves
Salvatore Ganci

Gruppo Nazionale Didattica della Fisica, Consiglio Nazionale delle Ricerche, Dipartimento di Fisica dell'Universita, 33 Via Dodecaneso, Genova, 16146, Italy
(Received 16 November 1987; accepted for publication 27 April 1988)
An experiment that deals with the physical reality of the edge-diffracted wave in the boundary wave theory of diffraction is described in this article. The basic philosophy is simple and the experimental evidence is strong.

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 374 - 375
Calculating the parameters of Earth's orbit
M. G. Calkin

Department of Physics, Dalhousie University, Halifax, Nova Scotia B3H 3J5, Canada
(Received 25 January 1988; accepted for publication 18 May 1988)

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 375 - 376
Still more on the Coulomb potential
Wayne A. Bowers

Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27514
(Received 23 May 1988; accepted for publication 28 June 1988)

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 376 - 377
Determination of the generalized Laplace-Runge-Lenz vector by an inverse matrix method
Takeshi Yoshida

Department of Applied Mathematics and Physics, Kyoto University, Kyoto 606,Japan
(Received 1 December 1987; accepted for publication 15 May 1988)

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 378 - 378
Another method for the Gantmakher formula
Oliver Keyes

209 West 13th Street, New York, New York 10011
(Received 15 December 1987; accepted for publication 11 July 1988)

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 378 - 379
Comment on ``Unified vector derivation on Gantmakher's, rotation, and charged particle deflection formulas,'' by P. K. Aravind [Am. J. Phys. 55, 744 (1987)]
Lars Falk

Swedish Geological Co., P. O. Box 1424, S-751 44 Uppsala, Sweden
(Received 15 December 1987; accepted for publication 11 July 1988)

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 379 - 381
Inefficiency and irreversibility in the Bucher diagram
J. Wallingford

Department of Physical Science, Pembroke State University, Pembroke, North Carolina 28372
(Received 25 January 1988; accepted for publication 8 May 1988)

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 381 - 382
The correct relation between wavefunctions in two gauges
R. J. Swenson

Department of Physics, Montana State University, Bozeman, Montana 59717
(Received 31 August 1987; accepted for publication 13 June 1988)

Am. J. Phys., Vol. 57, No. 4, April 1989 Pages 383 - 384
Incompleteness, Nonlocality, and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics
Michael Redhead,Author
Leslie E. Ballentine


For more information please send a mail to Dan.MacIsaac@nau.edu.