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Feb 1987

Volume 55, Issue 2, pp. 103-191

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Comment on ‘‘ ‘Counterrevolutionary’ physics’’[Am. J. Phys. 54, 776 (1986)]

Jay M. Pasachoff

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 103

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01.50.My Demonstration experiments and apparatus
07.60.Dq Photometers, radiometers, and colorimeters
92.60.Sz Air quality and air pollution

Wavefunction: Physical or mathematical?

Robert D. Eagleton

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 103

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03.65.Ta Foundations of quantum mechanics; measurement theory

On Roemer and navigation by the moons of Jupiter

Cynthia W. Peterson

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 103

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95.30.Sf Relativity and gravitation
96.30.L- Jovian satellites
01.65.+g History of science

Descartes and the concept of density

Herman Erlichson

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 104

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01.65.+g History of science
06.30.Dr Mass and density

Comment on Letter by O. Haszpra[Am. J. Phys. 54, 679 (1986)]

Alton K. Schultz

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 104

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06.20.F- Units and standards

What is g?

Mario Iona

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 104

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06.20.F- Units and standards
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Editorial: Heisenberg, February 1927, and physics

John S. Rigden

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 107

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01.65.+g History of science
03.65.Ta Foundations of quantum mechanics; measurement theory
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An investigation of student understanding of the real image formed by a converging lens or concave mirror

Fred M. Goldberg and Lillian C. McDermott

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 108 | Cited 32 times

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Student understanding of the real images produced by converging lenses and concave mirrors was investigated both before and after instruction in geometrical optics. The primary data were gathered through interviews in which undergraduates taking introductory physics were asked to perform a set of prescribed tasks based on a simple demonstration. The criterion used to assess understanding was the ability to apply appropriate concepts and principles, including ray diagrams, to predict and explain image formation by an actual lens or mirror. Performance on the tasks, especially by students who had not had college instruction in geometrical optics, suggested the presence of certain naive conceptions. Students who had just completed the study of geometrical optics in their physics courses were frequently unable to relate the concepts, principles, and ray‐tracing techniques that had been taught in class to an actual physical system consisting of an object, a lens or a mirror, and a screen. Many students did not seem to understand the function of the lens, mirror, or screen, nor the uniqueness of the relationship among the components of the optical system. Difficulties in drawing and interpreting ray diagrams indicated inadequate understanding of the concept of a light ray and its graphical representation.
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01.40.G- Curricula and evaluation
42.30.Va Image forming and processing
42.15.Dp Wave fronts and ray tracing
42.79.Bh Lenses, prisms and mirrors

Carnot’s function: Origins of the thermodynamic concept of temperature

William H. Cropper

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 120 | Cited 3 times

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This paper traces an important chapter in the evolution of the temperature concept in classical thermodynamics. The centerpiece in the story is the temperature function discovered by Carnot, and gradually developed over a period of 30 yr by Clapeyron, Holtzmann, Helmholtz, Joule, Rankine, Thomson (Kelvin), and Clausius. In Thomson’s final resolution of the problem, Carnot’s function simply determined the thermodynamic temperature scale.
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05.70.Ce Thermodynamic functions and equations of state
01.65.+g History of science

Slinky whistlers

Frank S. Crawford

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 130 | Cited 1 time

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See Also: Erratum

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Delightful sounds, produced in simple experiments, agree with an elementary theoretical analysis.
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01.50.My Demonstration experiments and apparatus
43.20.Px Transient radiation and scattering
43.25.Zx Measurement methods and instrumentation for nonlinear acoustics

The Casimir effect revisited

Frederik J. Belinfante

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 134 | Cited 3 times

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Using Wick’s normal‐ordered expression for the quantum‐mechanical energy of a radiation field, so that in absence of matter the zeropoint energy of a radiation field would vanish, the Casimir effect of attraction between uncharged condenser plates in absence of photons will still follow, due to a nonvanishing but finite zeropoint radiation energy in the presence of these plates. If we assume the plates to be transparent for electromagnetic waves of sufficiently high frequency, the remaining zeropoint energy density itself will be finite (and not merely its variation under a change of the distance between the plates). These results are obtained by a more careful consideration of where in sums over modes of vibration one should use sums over running waves with a periodicity condition, where one should sum over standing waves with nodes at conducting boundaries, and where these sums may be replaced by integrals.
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03.70.+k Theory of quantized fields

The Kepler problem recast: Use of a transverse velocity transformation and the invariant velocities

Ferdinand J. Shore

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 139 | Cited 1 time

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For conservative central forces the constancy of angular momentum provides a more natural substitution than is normally used to transform the force law into a differential equation. This is a transverse velocity substitution, which emphasizes angular rather than radial dependence for dynamical variables, implying a functional rotation. The method gives the standard results in new forms and they are expressed in more natural units of length, time, velocity, and energy than appears in other approaches. For the inverse square force the transverse velocity explicitly depends on the two invariant velocities, and the total energy is the difference of the kinetic energies for the two velocities. The invariant angular momentum is the sum of two variable angular momenta for the two velocities. The Laplace–Runge–Lenz vector is one of a triplet of orthogonal invariant vectors, the cross product of the invariant momentum and angular momentum. For noncircular trajectories this triplet and the scalar total energy are constants of the motion.
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45.05.+x General theory of classical mechanics of discrete systems

The total probability current and the quantum period

Jean‐Marc Lévy‐Leblond

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 146 | Cited 1 time

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Starting from the standard current density of probability for a quantum particle in a potential V(r), the total probability current in a stationary state is considered and investigated. Its physical interpretation leads to a natural definition of the time period for such a quantum stationary state. A simple and elegant formula relates the total current to the energy level of the state. This formula is shown to be consistent with the Correspondence Principle. The results are applied to the hydrogen atom and the harmonic oscillator.
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03.65.Ta Foundations of quantum mechanics; measurement theory

Fluid flow and particle trajectories around simple bodies: Impaction of snowflakes on car windshields

W. D. King and S. Dujmovic

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 149 | Cited 1 time

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The airflow around a simple automobile shape is calculated using a distributed source–sink technique. This is then used to determine the trajectories of snowflakes, and it is shown that, for a given snowflake size, there is a range of travel speeds that minimizes the impaction of snowflakes on the windshield.
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47.15.km Potential flows
92.60.Jq Water in the atmosphere

On the molecular distribution of a hard‐sphere gas

J. Güémez and S. Velasco

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 154 | Cited 6 times

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Given a gas of N0 hard‐sphere molecules in a vessel of volume V0, one shows in a simple way that the probability WN0(N,V,V0) that N molecules are located in a subvolume V of V0 is given by the hypergeometric distribution. One shows that this distribution can be written as the product of the binomial distribution, which characterizes the ideal gas, and a factor which takes into account the size of the molecules. In the limit of low densities, one checks in two cases of practical interest that the derived distribution presents slight deviations from the corresponding ideal behavior.
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05.20.-y Classical statistical mechanics

Minimum‐energy charge configurations

M. G. Calkin, D. Kiang, and D. A. Tindall

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 157 | Cited 3 times

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In two dimensions the minimum energy configuration of a finite set of equal point charges confined to a circle does not necessarily have all the charges on the circumference. In three dimensions, however, we show that the minimum energy configuration of a similar set of charges confined by a surface has all of the charges located on the surface. The pseudo‐two‐dimensional analog of the three‐dimensional case, provided by an array of parallel line charges confined to a cylinder, is also investigated.
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41.20.Cv Electrostatics; Poisson and Laplace equations, boundary-value problems
41.20.Gz Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems

Classical limit of the path‐integral formulation of quantum mechanics in terms of the density matrix

Pimon Ajanapon

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 159 | Cited 3 times

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Instead of regarding the classical limit as the limit ℏ→0, an alternative view based on the physical interpretation of the elements of the density matrix is proposed. The derivation of the classical limit of quantum mechanics is carried out in two stages. First, the statistical classical limit is derived, and then, with an appropriate initial condition, the deterministic classical limit is obtained. The derivation hinges on the use of the Feynman path‐integral formulation of quantum mechanics in terms of the density matrix. It is shown that deterministic (Hamilton’s or Newton’s) classical mehanics is not the classical limit of Schrödinger’s wave mechanics. The classical limit of Schrödinger’s wave mechanics is only statistical and corresponds to the classical Liouville equation. In order to obtain the deterministic classical limit, it is necessary to start out initially with a quantum mechanical mixture.
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03.65.Ca Formalism
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The Runge–Lenz vector and Einstein perihelion precession

T. Garavaglia

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 164 | Cited 6 times

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Abstract Unavailable
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95.10.Eg Orbit determination and improvement
04.20.-q Classical general relativity

Tidal disruption of a solid body

James Conwell and Daniel Wilkins

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 165

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95.10.-a Fundamental astronomy
96.30.Cw Comets

Limits, average values, and the magnetic field of a current through a hollow cylinder

James L. Monroe

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 166

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Abstract Unavailable
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41.20.Gz Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems

Eigenvalues of a nonuniform string

Frank S. Crawford

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 168

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A modified WKB approximation is used to calculate the eigenvalues for the transverse modes of a nonuniform strength. (AIP)
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43.20.Ks Standing waves, resonance, normal modes
43.40.Cw Vibrations of strings, rods, and beams

The use of stereographic projections for finding the eigenvector of a general rotation

Eric Stanley

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 170

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Abstract Unavailable
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02.40.Dr Euclidean and projective geometries
07.07.Hj Display and recording equipment, oscilloscopes, TV cameras, etc.

A simple model for water‐wave dispersion relations

Frank S. Crawford

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 171 | Cited 2 times

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The dispersion relation between angular frequency and wave number is derived for both deep and shallow water waves. (AIP)
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41.20.Jb Electromagnetic wave propagation; radiowave propagation
47.35.-i Hydrodynamic waves

Particle in a square well with a δ‐function perturbation

I. Richard Lapidus

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 172 | Cited 7 times

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Abstract Unavailable
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03.65.Ge Solutions of wave equations: bound states

Note on the derivation of the Lorentz transformation by Lévy‐Leblond

A. W. Ross

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 174 | Cited 3 times

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Abstract Unavailable
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03.30.+p Special relativity

Compton shift in energy and wavelength—A laboratory experiment

N. M. Badiger and S. R. Thontadarya

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 175 | Cited 1 time

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Abstract Unavailable
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01.50.Pa Laboratory experiments and apparatus
78.70.-g Interactions of particles and radiation with matter

Diagrams for the acoustic Doppler effect and shock wave cones

Manfred Bucher

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 176

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43.25.-x Nonlinear acoustics
43.25.Cb Macrosonic propagation, finite amplitude sound; shock waves

A disappearing rod

Terrence P. Toepker

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 177

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44.90.+c Other topics in heat transfer (restricted to new topics in section 44)

Effective elastic constant and effective mass of an oscillating spring: An energy approach

Maurice Leclerc

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 178

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Abstract Unavailable
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45.05.+x General theory of classical mechanics of discrete systems

Elementary derivation of the law of equipartition of energy

Frank S. Crawford

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 180 | Cited 3 times

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In a freshman physics course the classical law of equipartition of energy is usually stated without proof, because its usual derivation assumes knowledge of the Maxwell–Boltzmann distribution function, which is not always included in a first course. Here, instead, is a nonrigorous but plausible derivation based on simple mechanical models. It does not use the distribution function and it shows roughly how long it takes to reach thermal equilibrium.
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05.20.Dd Kinetic theory

Velocity amplification in vertical collisions

Joseph L. Spradley

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 183 | Cited 1 time

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Abstract Unavailable
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45.05.+x General theory of classical mechanics of discrete systems

Fun with missing fundamentals

T. M. Kalotas and A. R. Lee

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 184

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Abstract Unavailable
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01.50.My Demonstration experiments and apparatus
43.75.Wx Electronic and computer music
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Microcomputer‐controlled signal integration

B. R. Reddy

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 185

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Abstract Unavailable
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01.50.ht Instructional computer use
84.30.Sk Pulse and digital circuits
84.30.Vn Filters

F center experiments from soft x rays

R. Rodríguez and A. Clark

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 186 | Cited 1 time

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Abstract Unavailable
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01.50.Pa Laboratory experiments and apparatus
61.72.jn Color centers
61.80.Cb X-ray effects
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Science and Gender: A Critique of Biology and Its Theories on Women

Ruth Bleier, Author and Irene M. Engle

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 188

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Abstract Unavailable
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01.30.Ee Monographs and collections
01.75.+m Science and society
87.90.+y Other topics in biological and medical physics (restricted to new topics in section 87)

One World

John C. Polkinghorne, Author and James T. Cushing

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 188

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Abstract Unavailable
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01.30.-y Physics literature and publications
01.70.+w Philosophy of science

POST‐USE REVIEW: Modern Physics

Kenneth S. Krane, Author, John F. Devlin, and Victor K. Wong

American Journal of Physics -- February 1987 -- Volume 55, Issue 2, pp. 190

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Abstract Unavailable
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01.30.mp Textbooks for undergraduates
01.55.+b General physics
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