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Feb 2001

Volume 69, Issue 2, pp. 103-237

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Answer to Question #31. Does any piece of mathematics exist for which there is no application whatsoever in physics?

A. C. de la Torre and R. Zamorano

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 103 | Cited 1 time

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01.50.-i Educational aids
02.00.00 Mathematical methods in physics

Answer to Question #51. Applications of third-order and fifth-order differential equations

H. P. W. Gottlieb

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 103 | Cited 1 time

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01.50.-i Educational aids
02.30.-f Function theory, analysis
02.60.Lj Ordinary and partial differential equations; boundary value problems

Answer to Question #58. Is a good long jumper a good high jumper?

Andrew Rex

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 104 | Cited 2 times

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Abstract Unavailable
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01.50.-i Educational aids
01.55.+b General physics
87.19.rs Movement
87.19.ru Locomotion
45.40.-f Dynamics and kinematics of rigid bodies

Answer to Question #58. Is a good long jumper a good high jumper?

Stephen Hanzely

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 105 | Cited 1 time

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Abstract Unavailable
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01.50.-i Educational aids
01.55.+b General physics
87.19.rs Movement
87.19.ru Locomotion
45.40.-f Dynamics and kinematics of rigid bodies

Answer to Question #58. Is a good long jumper a good high jumper?

John D. Barrow

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 105 | Cited 1 time

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01.50.-i Educational aids
01.55.+b General physics
87.19.rs Movement
87.19.ru Locomotion
45.40.-f Dynamics and kinematics of rigid bodies

Answer to Question #65. What conditions determine crystal growth?

Helene F. Perry

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 106

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01.50.-i Educational aids
81.10.Aj Theory and models of crystal growth; physics and chemistry of crystal growth, crystal morphology, and orientation
64.70.D- Solid-liquid transitions
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Heat is not a noun

Robert H. Romer, Editor

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 107 | Cited 14 times

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01.30.Vv Book reviews
05.70.-a Thermodynamics
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An electrical measurement of the speed of light

George W. Clark

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 110 | Cited 2 times

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A pedagogical experiment is described for a determination of the speed of light by measurements of the dimensions and resonance frequency of an LRC circuit. The only calibrated devices employed are instruments for measuring frequency and length. An accuracy of approximately 1% is achieved. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
06.30.Gv Velocity, acceleration, and rotation
07.60.-j Optical instruments and equipment
06.30.Bp Spatial dimensions (e.g., position, lengths, volume, angles, and displacements)
06.30.Ft Time and frequency

Dissipation, fluctuations, and conservation laws

Paul Grassia

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 113 | Cited 6 times

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A large particle moves through a sea of small particles. On the microscale, all particle collisions are elastic. However, on the macroscale, where only the large particle is properly resolved, dissipative forces and fluctuating random forces are observed. These forces are connected by a fluctuation–dissipation theorem proved in two different ways, first via statistical mechanics, and second from fundamental classical mechanical principles of momentum and energy conservation. The novel classical mechanics proof elucidates the relation between micro- and macroscale behaviors, and offers new insights into the physics behind the fluctuation–dissipation result. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
05.20.-y Classical statistical mechanics
45.50.-j Dynamics and kinematics of a particle and a system of particles
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

Two charged particles in a one-dimensional well

Edward A. Salter, Gary W. Trucks, and Daniel S. Cyphert

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 120 | Cited 4 times

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We present numerically exact solutions of the time-independent Schrödinger equation for the following system: two particles of the same charge, repelled by the Coulomb force, confined to a one-dimensional infinite well. The eigenfunctions are expanded in a basis set of product delta functions; the expansion allows the removal of the Coulomb potential’s singularity. We report and discuss our findings regarding correlated behavior in the lowest energy states of a well of length 3 bohr (1 bohr=1 Bohr radius≈0.52 Å). © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.Ge Solutions of wave equations: bound states
02.10.Ud Linear algebra

Cosmological expansion in the classroom

Richard H. Price and Elizabeth Grover

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 125 | Cited 3 times

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A simple demonstration or classroom exercise using the expansion of a latex strip provides an analog computation of the light travel time between distant galaxies in an expanding universe, and gives students insight into the meaning of cosmological expansion. © 2001 American Association of Physics Teachers.
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01.50.My Demonstration experiments and apparatus
98.80.-k Cosmology

Particle size determination: An undergraduate lab in Mie scattering

I. Weiner, M. Rust, and T. D. Donnelly

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 129 | Cited 12 times

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A technique for determining the size of microscopic spherical particles using light scattering is presented as an undergraduate physics lab. Scatterer size is determined from angular scattering distribution measurements of laser light scattered from a dilute suspension of latex spheres with diameters of 4.99±0.05 and 6.038±0.045 μm. Previous experiments of this type used approximate theoretical corrections and required the construction of specialized sample cells to minimize complicating effects. As a significant improvement to these, we generate angular scattering distributions from Mie theory and, using an accurate numerical procedure, correct these distributions for Snell’s law and foreshortening effects. Scatterer size is then determined using a fast, robust fitting algorithm to compare these corrected angular scattering distributions to measured angular scattering distributions. We fit the scatter from a solution of 6.04-μm-diam spheres to spheres of 5.95±0.11 μm diameter, and that from a solution of 4.99-μm spheres to 4.85±0.15 μm. Additionally, scattering data for a 2:1 mixture of spheres of diameters 4.99 and 6.04 μm are taken, and after numerical adjustment for Snell’s law and foreshortening effects, good agreement with theory is obtained. © 2001 American Association of Physics Teachers.
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01.50.Pa Laboratory experiments and apparatus
06.30.Bp Spatial dimensions (e.g., position, lengths, volume, angles, and displacements)
82.70.Kj Emulsions and suspensions
78.35.+c Brillouin and Rayleigh scattering; other light scattering

Waves in locally periodic media

David J. Griffiths and Carl A. Steinke

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 137 | Cited 63 times

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We review the theory of wave propagation in one dimension through a medium consisting of N identical “cells.” Surprisingly, exact closed-form results can be obtained for arbitrary N. Examples include the vibration of weighted strings, the acoustics of corrugated tubes, the optics of photonic crystals, and, of course, electron wave functions in the quantum theory of solids. As N increases, the band structure characteristic of waves in infinite periodic media emerges. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
03.75.-b Matter waves
47.35.-i Hydrodynamic waves

Choosing and rechoosing to have or have not interference

Thomas F. Jordan

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 155 | Cited 4 times

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Loss and restoration of interference similar to that produced in “quantum erasure” can be demonstrated in interference of macroscopic laser beams by using polarization to distinguish light from two slits. You can choose whether to observe interference or identify the light from each slit. The choice can be reversed and repeated an unlimited number of times. It never becomes irreversible. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
42.60.Jf Beam characteristics: profile, intensity, and power; spatial pattern formation
42.25.Hz Interference
42.25.Ja Polarization
42.50.Ar Photon statistics and coherence theory
42.25.Kb Coherence

From rapidity to vibracy (logarithmic frequency)

Daniel Wilkins and Deborah Williams

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 158

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Logarithmic parameters have been been found useful for describing the translational and gravitational states of some systems. These parameters are additive, and may serve to push unwanted singularities off to infinity. The best known of these is rapidity, a speedlike parameter used in special relativity. Another is the so-called “linear time” of Misner and Lévy-Leblond, which applies to general relativistic cosmology. We point out that these two parameters are both logarithmic measures of frequency shift and represent a quantity we call “vibracy.” Majernik’s trigonometric variant of rapidity is found to be an aberration angle. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
03.30.+p Special relativity
98.80.Jk Mathematical and relativistic aspects of cosmology
98.80.Qc Quantum cosmology

Harmonographs. I. Pendulum design

Robert J. Whitaker

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 162 | Cited 2 times

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Mechanical devices that undergo various kinds of repetitive motion and which draw the curves produced from this motion are known as “harmonographs.” One such class of these devices are those that operate by means of pendulum action. These devices range from modifications of a simple pendulum to various physical and compound pendulums. This paper traces the history of the development of this class of apparatus. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
07.10.-h Mechanical instruments and equipment

Harmonographs. II. Circular design

Robert J. Whitaker

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 174

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Devices that produce curves by the rotation of circles (or gears) about one another constitute one class of harmonographs. In the simplest case, a point on one of the circles will trace a cycloidal curve. A number of devices of varying degrees of complexity and which make use of gears or pulleys in their operation have been invented over the years to draw various curves. This paper offers a survey of some of these. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
07.10.-h Mechanical instruments and equipment

Multiple representations of work–energy processes

Alan Van Heuvelen and Xueli Zou

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 184 | Cited 32 times

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An energy process can be represented by verbal, pictorial, bar chart, and mathematical representations. This multiple-representation method for work–energy processes has been introduced and used in the work–energy part of introductory college physics courses. Assessment indicates that the method, especially the qualitative work–energy bar charts, serves as a useful visual tool to help students understand work–energy concepts and to solve related problems. This paper reports how the method has been used to teach work–energy concepts, student attitudes toward this approach, and their performance on work–energy problems. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
45.30.+s General linear dynamical systems
45.05.+x General theory of classical mechanics of discrete systems

A simple cosmology: General relativity not required

Russell Akridge

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 195 | Cited 2 times

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A pedagogical cosmology illustrates general relativity concepts, without requiring general or special relativity. Topics examined are the existence of a global time scale, proper vs coordinate variables, the variation of light speed in an expanding universe, the look-back paradox, the horizon, the red shift, the age of the universe, and the dynamics of the universe. An Appendix is devoted to space and time in general relativity, but can be skipped by readers unfamiliar with general relativity. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
98.80.-k Cosmology
98.62.Py Distances, redshifts, radial velocities; spatial distribution of galaxies

Semiclassical analysis of level widths for one-dimensional potentials

Gert-Ludwig Ingold, Rodolfo A. Jalabert, and Klaus Richter

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 201 | Cited 2 times

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We present a semiclassical study of level widths for a class of one-dimensional potentials in the presence of an ohmic environment. Using a semiclassical approach for the dipole matrix element we obtain the level widths within the golden rule approximation. For potentials with an asymptotic power-law behavior, which may in addition be limited by an infinite wall, we find a universal result: The level widths are proportional to the corresponding quantum number. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.Sq Semiclassical theories and applications
42.50.-p Quantum optics
32.80.-t Photoionization and excitation
03.65.Ge Solutions of wave equations: bound states

How to distinguish identical particles

Fedor Herbut

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 207 | Cited 5 times

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Usually fermions and bosons behave very differently. Regarding distinguishability, they behave in one and the same way. Two-identical-particle quantum theory is discussed on the example of the deuteron and that of distant correlations, as well as on the example of the real interference and quantum erasure experiments in the Hong–Ou–Mandel two-photon interferometer (with and without polarizers and analyzers). Distinguishability and indistinguishability of two identical photons in the experiments are illustrated. It is demonstrated, using a simple formalism valid simultaneously for fermions and for bosons, that there exists an isomorphism giving theoretical foundation to distinguishing two identical particles. But the distinguishing has a limited range of exact applicability. In most cases of interest, only the indistinguishability approach has a first-principle (and universal) validity. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.-w Quantum mechanics

A computer program to visualize gravitational lenses

Francisco Frutos Alfaro

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 218 | Cited 1 time

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Gravitational lenses presently play an important role in astrophysics. By means of these lenses the parameters of the deflector such as its mass, ellipticity, etc., and Hubble’s constant can be determined. Using C, XFORMS, MESA, and IMLIB, a computer program to visualize this lens effect has been developed. This program has been applied to generate sequences of images of a source object and its corresponding images. It has also been used to visually test different models of gravitational lenses. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
95.30.Sf Relativity and gravitation
98.62.Sb Gravitational lenses and luminous arcs
95.75.Pq Mathematical procedures and computer techniques
95.75.Mn Image processing (including source extraction)
42.30.Va Image forming and processing
84.40.Ua Telecommunications: signal transmission and processing; communication satellites

Einstein’s hole argument

Alan Macdonald

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 223

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In general relativity, space and time are inseparable from a gravitational field: no field, no spacetime. This is a lesson of Einstein’s hole argument. We use a simple transformation in a Schwartzschild spacetime to illustrate this. On the basis of the general theory of relativity … space as opposed to “what fills space” … has no separate existence. … There is no such thing as an empty space, i.e., a space without [a gravitational] field. … Spacetime does not claim existence on its own, but only as a structural quality of the field. Albert Einstein, 1952. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
04.20.Gz Spacetime topology, causal structure, spinor structure

On energy absorption in classical electromagnetism

G. H. Goedecke

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 226

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Using only classical electromagnetic energy conservation laws and causality, we show that the net average power absorbed by any mechanically isolated illuminated medium in steady state must be zero, but that for linear model media it is nonzero. This contradiction implies that all media must behave inelastically. We also show in general that the average power absorbed at an incident frequency, which is equal to the total taken from an incident wave minus that scattered elastically, is also equal to the average power scattered inelastically plus that carried off mechanically, if any. Finally, we infer that while the conventional linear theory cannot predict the spectral distribution of inelastic scattering, it may be applied as always to predict the propagation, absorption, and elastic scattering of weak illumination in passive media. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
41.20.Jb Electromagnetic wave propagation; radiowave propagation
02.30.Lt Sequences, series, and summability
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Comment on “The sweet spot of a baseball bat,” by Rod Cross [Am. J. Phys. 66 (9), 772–779 (1998)]

Robert K. Adair

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 229 | Cited 6 times

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Abstract Unavailable
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01.50.-i Educational aids
01.55.+b General physics
45.40.Gj Ballistics (projectiles; rockets)
87.19.rs Movement
87.19.ru Locomotion

Response to “Comment on ‘The sweet spot of a baseball bat’ ” [Am. J. Phys. 69 (2), 229–230 (2001)]

Rod Cross

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 231 | Cited 2 times

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Abstract Unavailable
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01.50.-i Educational aids
01.55.+b General physics
45.40.Gj Ballistics (projectiles; rockets)
87.19.rs Movement
87.19.ru Locomotion

The zeta function method and the harmonic oscillator propagator

F. A. Barone and C. Farina

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 232 | Cited 3 times

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We show how the pre-exponential factor of the Feynman propagator for the harmonic oscillator can be computed by the generalized ζ-function method. Also, we establish a direct equivalence between this method and Schwinger’s proper time method. © 2001 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.Ge Solutions of wave equations: bound states
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Antimatter, the Ultimate Mirror

Gordon Fraser, Author and Richard Kessler, Reviewer

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 236

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Abstract Unavailable
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01.30.Vv Book reviews
95.30.Cq Elementary particle processes
14.00.00 Properties of specific particles

Optics and Photonics: An Introduction

F. Graham Smith, Author, Terry A. King, Author, and Daniel L. Dawes, Reviewer

American Journal of Physics -- February 2001 -- Volume 69, Issue 2, pp. 236

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Abstract Unavailable
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42.55.-f Lasers
01.50.-i Educational aids
42.82.-m Integrated optics
01.30.Vv Book reviews
42.60.-v Laser optical systems: design and operation
85.60.-q Optoelectronic devices
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