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Apr 1970

Volume 38, Issue 4, pp. 407-553

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Resource Letter TLA-1 on Technology, Literature, and Art since World War II

William H. Davenport

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 407

Online Publication Date: Jul 2005

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Prepared at the request of the AAPT Committee on Resource Letters.
This is one of a series of Resource Letters on different topics, intended to guide college physicists to some of the literature and other teaching aids that may help them improve course contents 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. Please send such communications to Professor Joel Gordon, Chairman, Resource Letter Committee, Department of Physics, Amherst College, Amherst, Massachusetts 01002.
Additional copies: Available from the Executive Secretary, American Association of Physics Teachers, 335 East 45 Street, New York, N. Y. 10017. When ordering, request Resource Letter TLA-1 and enclose 25 cents per copy (not in stamps), together with a self-addressed stamped envelope.

The Potential of a Point Charge between Capacitor Plates

M. L. Glasser

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 415 | Cited 2 times

Online Publication Date: Jul 2005

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The potential of a point charge between two grounded conducting plates is expressed as a definite integral, simplifying a previous formula due to Pumplin. The potential is obtained exactly in closed form along a line passing through the charge.

A Helicon Solid-State Plasma Experiment for the Advanced Laboratory

J. R. Merrill, D. Pierce, and D. Giovanielli

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 417

Online Publication Date: Jul 2005

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This paper reports an advanced undergraduate laboratory experiment concerning the helicon solid-state plasma wave. Student results are reported. The experiment is performed as an inexpensive dip in a liquid helium storage vessel. The experiment is made possible by the design of a small, superconducting magnet. The magnet is capable of attaining 18 kG and costs about $25. The whole experiment can be built by students in a week's time. When the experiment is completed, the student not only understands helicon propagation but also understands the use of the helicon to measure magnetoresistance and Hall coefficients in pure metals.

Relations among Systems of Electromagnetic Equations

Chester H. Page

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 421

Online Publication Date: Jul 2005

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The equations of electromagnetism, whether written in the electrostatic, electromagnetic, or symmetric system, whether in rationalized or nonrationalized form, express an invariant set of physical relationships. The same set of letter symbols is employed in each, system of equations; these symbols represent related, but different, quantities in the various systems. The relationships among corresponding symbols are given and applied to precise statements about the relation between the oersted and the ampere per meter, the abampere and the ampere, etc.

Experiments with Cholesteric Liquid Crystals

James L. Fergason

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 425

Online Publication Date: Jul 2005

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The following set of experiments was designed for students just beginning to study cholesteric liquid crystals. It contains all of the information on materials and apparatus needed to perform thermal mapping. Wherever possible, materials which are readily available have been chosen. The experiments progress, each one somewhat more difficult than the preceding. No attempt has been made to give an outline of the properties of liquid crystal phases, but the reader is referred to A. Saupe's review article [Angew. Chem. Internat. Edit. 7, No. 2, 97 (1968)] on the subject.

Laser Mode Structure Experiments for Undergraduate Laboratories

Richard A. Phillips and Robert D. Gehrz

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 429 | Cited 1 time

Online Publication Date: Jul 2005

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Experiments dealing with laser mode structure are presented which are suitable for an upper division undergraduate laboratory. The theory of cavity modes is summarized. The mode structure of the radiation from a helium-neon laser is measured by using a photodiode detector and spectrum analyzer to detect intermode beating. Off-axial modes can be visually detected in the expanded laser beam and their presence correlated with signals displayed on the spectrum analyzer in agreement with the theory.

The Virial Theorem and the Equation of State of a Two-Dimensional Plasma

G. Knorr

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 433

Online Publication Date: Jul 2005

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The virial theorem is used for an elementary derivation of the exact equation of state of a two-dimensional plasma.

I Am Curious (Transport Coefficients)

E. A. Mason, J. R. Dorfman, and Robert Zwanzig

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 435 | Cited 2 times

Online Publication Date: Jul 2005

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Some aspects of the kinetic theory of transport coefficients are discussed in terms of simplified models. These models are a gas of one-dimensional rods and a gas of d-dimensional rigid parallel “cubes.” The collision process is taken to be such that two molecules exchange velocities upon collision. For these models the elementary mean-free-path results are exact, up to an unknown factor of order unity appearing in a correction term.

A Reformulation of Newtonian Dynamics

C. Gregory Hood

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 438

Online Publication Date: Jul 2005

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It is postulated that all dynamical laws must be formulated in terms of variables measured relative to interacting particles. This implies that the two-particle system is the fundamental interaction unit. When this postulate is applied to Newtonian mechanics, a radically new conceptual structure is revealed. The two major changes which result are the absence of the law of inertia and a broadening of the space and time invariance to include accelerated observers. Although energy and angular momentum remain conserved in this reformulation, the usual linear momentum theorem does not appear. It is further shown that the theory can be expressed in the Lagrangian and Hamiltonian formalisms in a straightforward manner. Finally, applications are made to several simple two-body and three-body systems which demonstrate that many-particle interactions can be formulated without reference to the dynamics of a single particle.

Absorption and Emission of Energy at Electron Cyclotron Resonance

S. C. Bloch, H. R. Brooker, and G. J. KeKelis

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 443

Online Publication Date: Jul 2005

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Experiments are described in which the absorption and emission of energy at and near electron cyclotron resonance may be studied with simplified equipment. The magnetic field is measured by electron spin resonance, thus bringing out aspects of spin as well as orbital angular momentum; the magnetic field may also be measured by the radius of the electron orbit, rendered visible by low-pressure hydrogen. It is observed that, in a gas-focused electron beam tube, the frequencies of maximum electron cyclotron resonance absorption and emission (as determined by the zero crossing of the derivative of the line shape) are generally different from the frequency of electron spin resonance, and the frequency shifts are functions of electron beam current. The line shapes are asymmetric and are also functions of beam current. These effects are tentatively identified with plasma effects in the gas-focused beam.

A Progress Report on Open-End Laboratories

John I. Shonle

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 450

Online Publication Date: Jul 2005

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This paper reports our experiences with open-end introductory-physics laboratories after three semesters. All available indications show that they are successful. The method of evaluation of the effectiveness of the open-end laboratories and the results are given. Organizational details and changes in the organization made for 1969–1970 are also included. An important device used to start the student on an open-end experiment is a required preset exercise.

How Good Is the Hartree-Fock Approximation? II. The Case of Closed Shells

A. Calles and M. Moshinsky

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 456 | Cited 1 time

Online Publication Date: Jul 2005

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In the present paper, we analyze the problem of an arbitrary number of particles A in a harmonic-oscillator common potential interacting through a harmonic-oscillator force. The particles have spin ½ and obey Fermi statistics. The exact lowest eigenstate and energy are derived for values of A corresponding to closed subshells. An approximate analysis is also made using determinantal wave functions formed from single-particle harmonic-oscillator states, giving the eigenstates and energies of a simple form of the Hartree-Fock approximation. The exact and Hartree-Fock energies and eigenstates are compared both when potential and force have the same sign, and when they have opposite sign. We discuss the results for models which we call pseudonuclei and pseudoatoms, and we indicate some of the inferences for the real thing.

Explicit Construction of Unitary Operators in Nonrelativistic Quantum Mechanics

Choi-Lai Chan

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 468 | Cited 1 time

Online Publication Date: Jul 2005

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The Moravek-Joseph method [P. H. Moravek and D. W. Joseph, J. Math. Phys. 4, 1363 (1963)] for the construction of unitary operators in quantum field theory is found to be applicable also to nonrelativistic quantum mechanics. Some simple examples are given.

One-Dimensional Atom

James J. Klein

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 471

Online Publication Date: Jul 2005

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A one-dimensional model of an atom is proposed that simulates some of the wavelike characteristics of the hydrogen atom. The model consists of an elastic string under tension in which the transverse waves simulate the ψ wave of the electron in an atom, and the waves of varying tension simulate the electromagnetic waves interacting with the atom. Because of its simplicity, the model may be useful, for teaching purposes, in introductory quantum mechanics courses.

Thermoelectric Power Experiment for the Advanced Laboratory

Thomas B. Greenslade, Jr.

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 480 | Cited 1 time

Online Publication Date: Jul 2005

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Apparatus suitable for measurements of the thermoelectric power of wires in the temperature region from 77 to 300 K is described. An outline of the theoretical treatment of thermoelectric power is presented and typical results are given for aluminum, gold, and iron. This experiment has been used in the undergraduate advanced laboratory.

Position Expectation Values for an Electron in an Infinite Tilted Well

Noble M. Johnson and John N. Churchill

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 487

Online Publication Date: Jul 2005

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A numerical technique is used to determine the manner in which the expectation values of position for an electron in an infinite tilted well depend on the potential gradient and quantum state of the system. The results are compared to the classical case and to the exact analytic expression for the special case in which the total energy of the electron is equal to the maximum value of the linear potential.

The Merry-Go-Round and Schwarzschild Coordinates: A Comparison

B. E. Laurent

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 492

Online Publication Date: Jul 2005

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The behavior of the Schwarzschild metric inside the gravitational radius is compared to the behavior of the flat space metric in rotating coordinates when rω > 1. In both cases the time is imaginary and the spatial line element indefinite with regard to sign. In both cases the physical interpretation is the same: Observers at rest (in the coordinate system) do not exist.

Euler Potentials

David P. Stern

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 494 | Cited 13 times

Online Publication Date: Jul 2005

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The representation of a magnetic field by the cross product of the gradients of two scalars has recently seen wide use in plasma physics and in the study of energetic particles in space. The properties of such a representation are reviewed and examples of its application are given.

Electromagnetic Momentum of Charged Particles

Jack Cohn

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 502

Online Publication Date: Jul 2005

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The current definition of the comomentum associated with a moving charge is discussed, and it is shown to be unsuitable for a charge undergoing nonuniform motion. An alternative definition is then proposed for a charged particle of vanishingly small size, and it is demonstrated that this definition is satisfactory for a charge in arbitrary motion.

Circuit Response Using Fourier Series with Experimental Verification

H. W. Jones and J. S. Wallingford

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 507

Online Publication Date: Jul 2005

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As an illustration of a general method for calculating the circuit response of a network subjected to a periodic signal, the case of an RC circuit driven by a square-wave generator is worked out in complete detail for three values of a circuit parameter. A computer is used to add a sufficient number of Fourier sinusoidal terms and to plot out the circuit response. A criterion for the number of terms needed is given. For comparison, the exact solution is also presented. Experimental verification is achieved by photographing the screen of an oscilloscope which is connected across the proper circuit element. The resulting photographs are enlarged (in effect) to the exact size of the computer plots onto transparent film. An overlay of the transparencies on the computer plots give excellent agreement.

Energy Levels of the Hydrogen Atom as a Relativistic Clock-Retardation Effect?

J. Dorling

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 510

Online Publication Date: Jul 2005

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It is proven that the energy level, according to the Dirac equation, of any stationary state of the hydrogen atom can be written in the form
math
, where m0 is the electron-rest mass, β is the Dirac-β operator, v is the instantaneous electron velocity in the corresponding orbit in Sommerfeld's relativistic old quantum theory, ν is an “electron apparent frequency” satisfying
math
, and 〈 〉 denotes expectation value or time-average value, as appropriate. In spite of the physically suggestive character of this result, it is argued on theoretical grounds that it must be regarded merely as an interesting mathematical accident.

A “Derivation” of Maxwell's Equations

Elliott Krefetz

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 513

Online Publication Date: Jul 2005

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Herein is presented a student-teacher oriented examination of how one might arrive at Maxwell's equations via a number of reasonable assumptions.

Coherent States in Superfluids: The Ideal Einstein-Bose Gas

James R. Johnston

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 516 | Cited 3 times

Online Publication Date: Jul 2005

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It is argued that the grand canonical ensemble is not appropriate for describing local properties of a closed system when the system has off-diagonal long-range order over distances of the order of the dimensions of the system (e.g., when there is a condensation into a single-particle state). It is shown that the local dispersion in number in the condensed part of an ideal Einstein-Bose gas is “small” (appropriate to a Poisson distribution), contrary to the usual result obtained using the grand canonical ensemble. This leads to an approximation in which the condensed part of the system is represented locally by a coherent state. It is further argued that these considerations serve as a rationale for breaking gauge symmetry whereas the usual arguments (based on analogy with ferromagnetism) are not appropriate.
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Instructional Uses of the Computer: The Harmonic Oscillator in APL

Mary F. Gourley

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 529

Online Publication Date: Jul 2005

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Realistic One-Dimensional Example of the Failure of Lattice Dynamics in the Harmonic Approximation

S. B. Trickey

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 529

Online Publication Date: Jul 2005

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A Simple Laboratory Experiment for Studying the Compton Shift

H. Sanjeevaiah, S. Gopal, P. Venkataramaiah, and B. Sanjeevaiah

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 530

Online Publication Date: Jul 2005

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Trouble with a Ballistic Pendulum

J. Strnad

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 532

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Some Observations on Variable-Geometry Phase Methods of Measuring Sound Wavelength

I. C. Romer, Jr.

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 534

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The Double-Simple Pendulum Problem

S. M. Lee

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 536

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Experimental Determination of Moments of Inertia by the Bifilar Pendulum Method

John W. Then and Kang-rong Chiang

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 537

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The Dimensionality of Time

J. Dorling

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 539

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Period of Low Orbits

R. H. Good

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 540

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Utilizing Automatic Balances for Poggendorff's Experiment on the Second Law of Motion

L. Cintra do Prado

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 541

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A Simple Calculation Concerning Electron Shake-Off during Internal Conversion

E. J. Seykora and A. W. Waltner

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 542 | Cited 1 time

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Abstract Unavailable
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Jaki on Goethe

Otto Blüh

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 544

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Re: “Jaki and Goethe”

Stanley L. Jaki

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 545

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A Practical Difference between Rods and Clocks

J. C. Hafele

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 546 | Cited 1 time

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Thermodynamics of Systems with Internal Adiabatic Constraints

Harvey S. Leff

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 546

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Letter re: “Demonstrating Phase Velocity and Group Velocity”

J. Mawdsley

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 547

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Torques and Angular Momentum in a System at Equilibrium in Special Relativity: A Reply

W. K. H. Panofsky and Melba Phillips

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 547 | Cited 2 times

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The Optics of Dipole Magnets

John J. Livingood, Author and Harald A. Enge, Reviewer

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 548

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Exploration of the Universe, Second Edition and Brief Edition

George Abell, Author and Robert T. Mathews, Reviewer

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 549

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An Introduction to Field Quantization

Y. Takahashi, Author and C. L. Hammer, Reviewer

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 550

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Geometrical Optics, An Introduction

Allen Nussbaum, Author and Allen L. King, Reviewer

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 550

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Electronic and Ionic Impact Phenomena

H. S. W. Massey, Author, E. H. S. Burhop, Author, and E. W. McDaniel, Reviewer

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 551

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The Calculus of Physics

McAllister H. Hull, Jr., Author and M. E. Oakes, Reviewer

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 551

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Illinois Section

Homer E. Easley

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 552

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Michigan Section

Henry E. Hooper

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 553

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Colorado-Wyoming Section

Mario Iona

American Journal of Physics -- April 1970 -- Volume 38, Issue 4, pp. 553

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