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Aug 2000

Volume 68, Issue 8, pp. 689-778

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Answer to Question #15. What space scales participate in cosmic expansion?

Hans C. Ohanian

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 689 | Cited 1 time

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98.80.Jk Mathematical and relativistic aspects of cosmology
98.80.Qc Quantum cosmology
04.20.Gz Spacetime topology, causal structure, spinor structure

Answer to Question #68. 60.000 Hz? Synchronization of the power grid

Loren Lockwood

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 690

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84.70.+p High-current and high-voltage technology: power systems; power transmission lines and cables

Answer to Question #73. S is for entropy, Q is for charge

Ralph Baierlein

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 691

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06.20.F- Units and standards

Answer to Question #75. “Permittivity” and “permeability”—Where do the names come from?

Ari Sihvola

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 691

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77.22.Ch Permittivity (dielectric function)

Answer to Question #75. “Permittivity” and “permeability”—Where do the names come from?

Steven T. Ratliff

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 692

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77.22.Ch Permittivity (dielectric function)

Answer to Question #76. Neutrino mass and helicity

Luis J. Boya

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 692 | Cited 2 times

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12.10.-g Unified field theories and models
14.60.Pq Neutrino mass and mixing
11.30.Er Charge conjugation, parity, time reversal, and other discrete symmetries
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Institutional access to the online version of the American Journal of Physics

Robert H. Romer

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 694

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01.20.+x Communication forms and techniques (written, oral, electronic, etc.)
01.50.-i Educational aids
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American Association of Physics Teachers: Citations for Distinguished Service, 2000

Thomas L. O’Kuma

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 695

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01.10.Cr Announcements, news, and awards
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A class of inverse problems in physics

Ashley H. Carter

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 698 | Cited 4 times

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If physics students are exposed at all to inverse problems, it is usually in the context of specialized treatments of quantum scattering processes. Inverse problems are, however, important in a wide variety of applications, such as gravitational lensing, seismological exploration, and underwater acoustic tomography. Students can be introduced to inverse problems in undergraduate courses in mechanics, optics, and quantum mechanics. This paper presents some simple examples whose solution in each case involves Abel’s integral equation, illustrating the ubiquity of this mathematical relation in diverse areas of physics. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
02.30.Rz Integral equations
03.65.Ge Solutions of wave equations: bound states

An accurate determination of the acceleration of gravity g in the undergraduate laboratory

A. Dupré and P. Janssen

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 704 | Cited 1 time

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A rod, connected with a horizontal hinge to the vertical axle of a motor, will deviate from the vertical at angular frequencies of the motor above a certain minimum value. The acceleration of gravity is related in a simple way to the speed of the motor, the length of the rod, and its angle with the vertical. It turns out that g can be measured in this way with an accuracy of about 0.1% without the use of sophisticated technology or the application of corrections to the result. The system has some other interesting features which make it particularly appropriate for the undergraduate laboratory. © 2000 American Association of Physics Teachers.
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01.50.Pa Laboratory experiments and apparatus
96.12.Fe Gravitational fields

Completeness of the energy eigenfunctions for the one-dimensional δ-function potential

S. H. Patil

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 712 | Cited 7 times

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We develop energy eigenfunctions for the one-dimensional δ-function potential, with well-defined parity and appropriate orthogonalization. We use these elementary functions to present an explicit demonstration of the completeness of the energy eigenfunctions. It provides a simple illustration of an essential quantum mechanical property, which is pedagogically important. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.-w Quantum mechanics

Bound states of a finite periodic potential

D. W. L. Sprung, J. D. Sigetich, Hua Wu, and J. Martorell

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 715 | Cited 14 times

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We locate the bound states for a one-dimensional potential which consists of N identical cells, by the transfer matrix method. Our expressions involve only the Bloch phase and a scattering phase, both of which are properties of the single cell. The method applies to an arbitrary but nonoverlapping potential shape, and thereby emphasizes generic properties over specific details. It gives useful qualitative insight without tedious calculations. We discuss the evolution of the bound states as the intercell spacing is varied, and the occurrence of surface states as bound states in a forbidden zone. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.Ge Solutions of wave equations: bound states

Einstein’s mistake and the cosmological constant

Alex Harvey and Engelbert Schucking

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 723 | Cited 11 times

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A brief history of the cosmological constant in the equations of general relativity is presented. Particular attention is paid to (a) a misunderstanding by Einstein of both its function as a repulsive force and new vacuum state rather than the relativistic analog of an exponential potential cutoff he thought he had introduced and to (b) a common misunderstanding of the function of the cosmological constant. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
98.80.Jk Mathematical and relativistic aspects of cosmology
98.80.Qc Quantum cosmology
04.20.Cv Fundamental problems and general formalism
95.30.Sf Relativity and gravitation

What quantum mechanics is trying to tell us

Ulrich Mohrhoff

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 728 | Cited 5 times

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This article presents a novel interpretation of quantum mechanics. It extends the meaning of “measurement” to include all property-indicating facts. Intrinsically, space is undifferentiated: There are no points on which a world of locally instantiated physical properties could be built. Instead, reality is built on facts, in the sense that the properties of things are extrinsic, or supervenient on property-indicating facts. The actual extent to which the world is spatially and temporally differentiated (that is, the extent to which spatiotemporal relations and distinctions are warranted by the facts) is necessarily limited. Notwithstanding that the state vector does nothing but assign probabilities, quantum mechanics affords a complete understanding of the actual world. If there is anything that is incomplete, it is the actual world, but its incompleteness exists only in relation to a conceptual framework that is more detailed than the actual world. Two deep-seated misconceptions are responsible for the interpretational difficulties associated with quantum mechanics: the notion that the spatial and temporal aspects of the world are adequately represented by sets with the cardinality of the real numbers, and the notion of an instantaneous state that evolves in time. The latter is an unwarranted (in fact, incoherent) projection of our apparent “motion in time” into the world of physics. Equally unwarranted, at bottom, is the use of causal concepts. There nevertheless exists a “classical” domain in which language suggestive of nomological necessity may be used. Quantum mechanics not only is strictly consistent with the existence of this domain but also presupposes it in several ways. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.Ta Foundations of quantum mechanics; measurement theory
02.50.Cw Probability theory
01.70.+w Philosophy of science

Areas of the event horizon and stationary limit surface for a Kerr black hole

C. A. Pickett and J. D. Zund

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 746 | Cited 1 time

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We present an elementary evaluation of the surface areas of the event horizon and stationary limit surface for an uncharged Kerr black hole. The latter appears not to have been previously given in the literature, and permits us to suggest new geometrical/physical interpretations of these areas. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
97.60.Lf Black holes
04.70.-s Physics of black holes

One model for an integrated math/physics course focusing on electricity and magnetism and related calculus topics

Jason W. Dunn and Julius Barbanel

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 749 | Cited 5 times

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Over the last decade, there has been an increasing, widespread pedagogical interest in developing various types of integrated curricula for science and engineering programs. Over the last three years, a year-long Integrated Math/Physics course has been developed at Union College. This paper will focus on a model for a one-quarter integrated course organized around a traditional set of electricity and magnetism (E&M) physics topics, integrated with appropriate mathematical topics. Traditional, nonintegrated E&M physics students often struggle with challenging vector calculus ideas which may have been forgotten, not yet encountered, or introduced with different notation in different contexts. Likewise, traditional vector calculus mathematics students are often unable to gain intuitive insight, or fail to grasp the physical significance of many of the vector calculus ideas they are learning. Many of these frustrations are due to the fact that at many schools, the physics and calculus teachers teaching separate courses probably have little or no idea what their fellow educators are actually doing in these courses. Substantial differences in context, notation, and philosophy can cause breakdowns in the transfer of knowledge between mathematics and physics courses. We will discuss the methods, philosophy, and implementation of our course, and then go on to present what we feel were the substantial strengths and insights gained from a thoughtful integration of the two subjects. In addition, some problem areas and recommendations for probable student difficulties will be addressed. © 2000 American Association of Physics Teachers.
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01.40.Di Course design and evaluation
01.50.-i Educational aids
02.30.-f Function theory, analysis

Simple chaotic systems and circuits

J. C. Sprott

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 758 | Cited 39 times

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Many new chaotic systems with algebraically simple representations are described. These systems involve a single third-order autonomous ordinary differential equation (jerk equation) with various nonlinearities. Piecewise linear functions are emphasized to permit easy electronic implementation with diodes and operational amplifiers. Several new simple and robust chaotic electrical circuits are described and evaluated. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
05.45.-a Nonlinear dynamics and chaos
02.60.Lj Ordinary and partial differential equations; boundary value problems
02.30.Hq Ordinary differential equations

Motion of a hanging chain after the free end is given an initial velocity

Herb Bailey

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 764 | Cited 3 times

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One end of a chain is attached to the ceiling and the free end is given a sharp horizontal blow. The resulting pulse travels to the top of the chain, and a few seconds later the reflected pulse causes the free end to give a kick. The free end kicks again and again at regular intervals. The time between kicks is constant and has been accurately predicted by the solution of an ordinary differential equation. Close observation of the nature of successive kicks shows that they are not always in the same direction, but they do follow a pattern that repeats every four kicks. We have modeled this experiment by solving the wave equation with variable tension and summing the resulting series solution. The lateral deflection as a function of time and distance along the chain was calculated. The predicted deflection of the free end is in good agreement with experimental results obtained from a movie of the chain motion. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
45.05.+x General theory of classical mechanics of discrete systems
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Investigating collisional broadening of spectral lines using a tuning fork: An undergraduate laboratory

Anne L. Boreen, Renae L. Coons, Darin J. Ulness, and Bryan A. Luther

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 768 | Cited 1 time

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An intuitive laboratory experiment designed to study the phenomenon of collisional (or pressure) broadening is presented. Molecular collisions are modeled by striking a tuning fork with a mallet. The response of the tuning fork is recorded via microphone by a computer. These time domain data can be transformed numerically to reveal the frequency spectrum. Results corresponding to a range of pressures from 0 to 111 kPA are presented. © 2000 American Association of Physics Teachers.
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01.50.Pa Laboratory experiments and apparatus
33.70.Jg Line and band widths, shapes, and shifts
34.50.-s Scattering of atoms and molecules

Impact cratering study performed in the laboratory without a fast recording camera

S. Kasas, G. Dumas, and G. Dietler

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 771 | Cited 1 time

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Abstract Unavailable
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01.50.Pa Laboratory experiments and apparatus
96.12.Kz Surfaces

The rail gun: A popular demonstration of the Lorentz force

R. Jones

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 773 | Cited 1 time

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01.50.My Demonstration experiments and apparatus
85.70.Rp Magnetic levitation, propulsion and control devices
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Magnetars

Kirk T. McDonald

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 775 | Cited 1 time

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Abstract Unavailable
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01.50.-i Educational aids
97.60.Gb Pulsars
98.70.Rz γ-ray sources; γ-ray bursts
97.10.Ld Magnetic and electric fields; polarization of starlight
97.10.Kc Stellar rotation
98.70.Qy X-ray sources; X-ray bursts
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Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations

John Nye, Author and Francis J. Wright, Reviewer

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 776

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Abstract Unavailable
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01.50.-i Educational aids
01.30.Vv Book reviews

Quantum Chaos: An Introduction

Hans-Jürgen Stöckmann, Author and Martin C. Gutzwiller, Reviewer

American Journal of Physics -- August 2000 -- Volume 68, Issue 8, pp. 777

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01.30.Vv Book reviews
05.45.-a Nonlinear dynamics and chaos
03.65.-w Quantum mechanics
01.50.-i Educational aids
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