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Dec 1988

Volume 56, Issue 12, pp. 1063-1157

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Coevolution of science and capitalism

Lawrence Cranberg

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1063

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01.65.+g History of science
01.75.+m Science and society

An offensive spin‐off from the strategic defense initiative

Louis A. P. Balázs

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1063

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45.05.+x General theory of classical mechanics of discrete systems
95.10.-a Fundamental astronomy

Angular acceleration in central force motion

Jacob Neuberger

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1063

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45.05.+x General theory of classical mechanics of discrete systems
95.10.Ce Celestial mechanics (including n-body problems)
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Editorial: Physics for nonscientists—A role for the visiting committee

Robert H. Romer

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1065

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01.40.G- Curricula and evaluation
01.50.-i Educational aids
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The search for gravitational waves

Massimo Tinto

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1066

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This article serves as an introduction to the sources of gravitational waves and their detection. The types of sources expected to generate signals detectable by instruments currently planned, together with the theory governing these detectors, are considered. Order of magnitude estimates for the characteristic wave amplitudes are calculated and compared to the sensitivities of the currently prototyped and future detectors.
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04.80.-y Experimental studies of gravity
04.30.-w Gravitational waves

A simplified proof of Bertrand’s theorem

Yoel Tikochinsky

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1073 | Cited 4 times

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By using a technique borrowed from the inverse problem for one‐dimensional motion, the proof of Bertrand’s theorem concerning the possible central forces leading to closed orbits is considerably simplified.
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04.80.-y Experimental studies of gravity
04.30.-w Gravitational waves

The new physics—Physical or mathematical science?

Robert L. Oldershaw

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1075 | Cited 4 times

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As creators of the new physics have proposed increasingly abstract descriptions of nature, the ‘‘testability’’ of their theoretical constructs has markedly declined. While the current problems are not different in kind from those characterizing other eras in the evolution of physics, they do appear to be substantially different in degree from past experience. This situation, exacerbated by an incongruously strong confidence in the standard paradigms of particle physics and cosmology, is a cause for concern.
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01.70.+w Philosophy of science

Electromagnetic quantities and units derived from classical relativistic electrodynamics

Giovanni Mana

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1081

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The present article deals with a procedure for establishing the systems of electromagnetic quantities and units in the framework of the covariant formulation of electrodynamics. The dimensions and units of electromagnetic quantities are obtained from the action for the field and the charged particles interacting with it. Relations are thus established between the quantities used in the covariant formulation of electrodynamics and those used in the nonrelativistic approximation when SI units are employed. It is pointed out that quantities ϵ0 and μ0 appear explicitly in Maxwell equations written in SI units only to ensure the coherence of this system of units, but that they have no meaning as universal physical constants.
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03.50.-z Classical field theories
06.20.F- Units and standards

Mapping the weak chirality of atoms

R. A. Hegstrom, J. P. Chamberlain, K. Seto, and R. G. Watson

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1086 | Cited 5 times

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Atoms are chiral due to the parity‐violating weak neutral current interaction between the nucleus and the electrons. A simple pictorial representation of the chirality of an atom is obtained by mapping the electron probability current density in the atom. Results are shown for a hydrogenic 2p1/2 stationary state.
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31.90.+s Other topics in the theory of the electronic structure of atoms and molecules (restricted to new topics in section 31)
12.15.Mm Neutral currents
11.30.Rd Chiral symmetries

The total reflection of a compact wave group: Long‐range transmission in a waveguide

Robert F. Gragg

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1092 | Cited 3 times

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This article presents a unified explanation of the reflection of compact wave groups (e.g., pulses and bounded beams) from plane interfaces with application to signal propagation in waveguides. Expressions are developed for the spatial, temporal, and phase shifts that are experienced by such wave groups but not by plane waves.
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42.25.Gy Edge and boundary effects; reflection and refraction
42.79.Gn Optical waveguides and couplers
43.20.Fn Scattering of acoustic waves
41.20.Jb Electromagnetic wave propagation; radiowave propagation

Symbolic derivation of the electrodynamic Green’s tensor in an anisotropic medium

Werner Weiglhofer

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1095

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A symbolic inverse operator technique is used to derive the electromagnetic Green’s tensor of an anisotropic (uniaxial) medium. By using algebraic matrix identities, the tensor differential operator of the governing field equation is inverted in a straightforward way. Thus the correct result is obtained, which has been found elsewhere with the help of a much more complicated analysis.
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03.50.De Classical electromagnetism, Maxwell equations
41.20.Jb Electromagnetic wave propagation; radiowave propagation

Precession of the perihelion of Mercury

Daniel R. Stump

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1097 | Cited 7 times

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The equation of motion for a test mass in the gravitational field of a spherical mass is written in a form that can be used in an undergraduate mechanics course. A simple calculation of the general relativistic precession of the perihelion of Mercury is presented.
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04.20.-q Classical general relativity
95.10.Ce Celestial mechanics (including n-body problems)
96.30.Dz Mercury
96.12.De Orbital and rotational dynamics
96.15.De Orbital and rotational dynamics

A calculus of variations demonstration: The gradient index lens

Kevin M. Jones, Scott Lundgren, and Alak Chakravorty

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1099

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Calculating ray paths in a gradient index lens provides a simple, practical application of the calculus of variations. Inexpensive lenses are available for use as a lecture demonstration.
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01.50.My Demonstration experiments and apparatus
42.15.Eq Optical system design
42.79.Bh Lenses, prisms and mirrors
42.79.Ry Gradient-index (GRIN) devices
42.15.Dp Wave fronts and ray tracing

Coulomb and Fermi holes in a two‐electron model atom

Jan Makarewicz

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1100 | Cited 1 time

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The limitations of the independent particle model in describing electron motion in an atom are shown. To this end, an exact solvable model of a two‐electron atom is studied. The way the interelectron interaction splits the atomic energy levels is shown. Both Coulomb and spin correlations are analyzed and Coulomb and Fermi holes are illustrated.
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31.10.+z Theory of electronic structure, electronic transitions, and chemical binding
31.15.V- Electron correlation calculations for atoms, ions and molecules

An adiabatic reversible process

Raul Rechtman

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1104 | Cited 1 time

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It is argued that an adiabatic reversible process is a subtle thermodynamical concept. It is then shown how such a process may be constructed for the special case of an ideal gas enclosed in a rigid cylinder surrounded by adiabatic walls fitted with a piston that slides without friction.
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05.70.-a Thermodynamics

Equilibrium configurations of parallel repulsive permanent magnets placed inside a circle

D. Pescetti and E. Piano

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1106 | Cited 2 times

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The equilibrium configurations of a plane system of N equal, parallel, repulsive, permanent magnets constrained inside a circle of radius R are considered. Simple demonstration experiments with permanent magnets gliding on an air table are described. One finds that the magnets can gather in various stable patterns, either symmetrical or nonsymmetrical, the actual configuration being a function of the system’s history. The theoretical analysis has been restricted to a comparison between the energies of the following configurations: (A) All N magnets uniformly distributed around the circumference of radius R; (B) N−1 magnets uniformly distributed around the circumference of radius R plus one magnet at the center. It is shown that the energy of configuration A is lower than that of configuration B only for N smaller than a critical value Nc.
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01.50.My Demonstration experiments and apparatus
41.20.Cv Electrostatics; Poisson and Laplace equations, boundary-value problems
41.20.Gz Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems

The measurability of the kinetic momentum of a charged particle in a magnetic field

W. P. Healy

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1109

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Uncertainty relations are derived for the components of the kinetic momentum (mass times velocity) of a charged particle in a magnetic field. In constrast to the components of the canonical momentum, the components of the kinetic momentum do not all commute with each other when the field is not zero. The uncertainty relations are illustrated by two Gedanken experiments in which the kinetic momentum is measured by using (a) the Doppler shift of emitted radiation and (b) the angle of deflection of the particle by the field.
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03.65.Ta Foundations of quantum mechanics; measurement theory

Adiabatic and nonadiabatic processes in classical and quantum mechanics

Humphrey J. Maris and Quan Xiong

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1114 | Cited 2 times

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The problem of two coupled pendulums, one of which has a length that varies with time so that the pendulum passes through resonance with the other is considered. An expression is derived for the amount of energy transferred between the pendulums as a function of the rate of change of the length and the strength of the coupling spring. This is done by making a connection with the quantum mechanical two‐level system.
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03.65.Nk Scattering theory
45.05.+x General theory of classical mechanics of discrete systems

Unbounded orbits of a swinging Atwood’s machine

N. Tufillaro, A. Nunes, and J. Casasayas

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1117

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The motion of a swinging Atwood’s machine is examined when the orbits are unbounded. Expressions for the asymptotic behavior of the orbits are derived that exhibit either an infinite number of oscillations or no oscillations, depending only on a critical value of the mass ratio.
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45.05.+x General theory of classical mechanics of discrete systems

The effect of the mass of the center spring in one‐dimensional coupled harmonic oscillators

David L. Wallach, William Beatty, Karl Beisler, Peter Chronowski, Matthew Holloway, Robert Hutchinson, Diane Kacmarik, Raymond Lesko, James Lutz, Daniel Miller, and Michael Sivak

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1120 | Cited 3 times

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The effect of the mass of the center spring in the one‐dimensional coupled harmonic oscillator is calculated and shown to have a small but noticeable effect on the periods of the normal modes of oscillation. Sophomore engineering students have developed the experimental technique using only stop watches, an analytic balance, and a standard Ealing air track.
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45.05.+x General theory of classical mechanics of discrete systems
01.50.Pa Laboratory experiments and apparatus
01.50.My Demonstration experiments and apparatus

Critique and correction of the textbook comparison between classical and quantum harmonic oscillator probability densities

C. Leubner, Margot Alber, and N. Schupfer

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1123 | Cited 5 times

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This comparison, although well meant, is unsuitable for demonstrating in introductory quantum mechanics the convergence of classical and quantum predictions for large quantum numbers, for it really tries to match ‘‘classical apples’’ with ‘‘quantum pears’’! First, it compares a classical oscillatory state with a quantum stationary state, instead of comparing it to the corresponding quantum nonstationary state. Second, it compares probabilities of different quality, namely, a classical probability of the classical oscillator (which could be circumvented by specifying the initial conditions precisely) with a quantum probability of the quantum oscillator (which cannot be avoided by any means). However, it is shown that both defects can be nicely corrected, illuminating the fact that—if properly formulated— classical and quantum oscillators have more in common than the textbooks are trying to make the beginner believe. The associated quantum position probability density, because it is now truly analogous to the classical situation, agrees much better with the classical curve than the textbook one does, and its analytical form also explains why the textbook quantum curve, derived from an unwarranted comparison, nevertheless resembles the classical curve in some sense.
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03.65.Ta Foundations of quantum mechanics; measurement theory
03.65.Sq Semiclassical theories and applications
45.05.+x General theory of classical mechanics of discrete systems

The harmonic oscillator at finite temperature using path integrals

Å. Larsen and F. Ravndal

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1129 | Cited 1 time

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The statistical mechanics of a quantum harmonic oscillator can easily be formulated in terms of Feynman path integrals in imaginary time. By straightforward integrations, the partition function, the internal energy, and correlation functions are found. When time is discretized, the same results can be obtained directly using Monte Carlo methods on a computer. In the zero temperature limit, the usual quantum mechanical results are recovered.
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03.65.Db Functional analytical methods
03.65.Ge Solutions of wave equations: bound states
05.30.-d Quantum statistical mechanics

On the harmonic oscillator inside an infinite potential well

J. L. Marin and S. A. Cruz

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1134 | Cited 8 times

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The exact solution to Schrödinger’s equation for a three‐dimensional harmonic oscillator confined by two impenetrable walls is presented. The energy levels of this system are obtained as a function of wall separation as well as distance of the center of the oscillator to the walls. The force exerted by the walls on the oscillator is also evaluated, showing a classical behavior.
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03.65.Ge Solutions of wave equations: bound states
03.65.Sq Semiclassical theories and applications

On electric fields produced by steady currents

Harold S. Zapolsky

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1137

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It is well known that an electric (as well as a magnetic) field exists in a reference frame moving relative to a dc circuit that appears to be electrically neutral in its own rest frame. The source of this field is customarily treated as a continuous charge density, which appears in the moving frame as a consequence of the fact that charge and current densities are separate components of a four‐vector, which become mixed under the operation of a Lorentz transformation. It is possible to analyze this situation in a different way, by considering the superposed Lienard–Wiechert fields of a large number of moving point charges in the limit that their spacing becomes infinitesimal. While this analysis is not as simple as the standard one, it does expose some interesting physics that is masked by the standard treatment. It is also a useful approach in resolving a paradox that appears to occur when charge and current densities are treated as static objects.
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41.20.Gz Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems
03.50.De Classical electromagnetism, Maxwell equations
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Method of images and electrostatic screening by a polarized dielectric sphere

Clinton DeW. Van Siclen

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1142 | Cited 2 times

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The electrostatic potential due to a point charge outside a polarized dielectric sphere is calculated by considering the analagous situation for a conducting sphere. (AIP)
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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

Phase and displacement in sound waves

Frank Munley

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1144

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Abstract Unavailable
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43.20.Bi Mathematical theory of wave propagation

The requirement of a sphere rolling without slipping down a grooved track for the coefficient of static friction

Qing‐gong Song

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1145 | Cited 1 time

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

Comment on ‘‘Periastron precession in general relativity’’ [Am. J. Phys. 55, 85 (1987)]

I. M. Ganea

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1146

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It is shown that the derivation of periastron precession can be improved if the exact general relativistic definition of a circular orbit is used. (AIP)
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04.20.-q Classical general relativity
95.10.Eg Orbit determination and improvement

Comment on ‘‘Chaotic dynamics of a bouncing ball’’ [Am. J. Phys. 54, 939 (1986)]

R. L. Zimmerman and Sergio Celaschi

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1147 | Cited 1 time

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Abstract Unavailable
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01.50.Pa Laboratory experiments and apparatus
05.45.-a Nonlinear dynamics and chaos
45.05.+x General theory of classical mechanics of discrete systems

Canonical transformations and time reversal

C. H. Blanchard

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1148

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

Solution to a classical problem in electrostatics in Legendre polynomials expansion

G. A. Estévez, Basab B. Dasgupta, and L. B. Bhuiyan

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1149

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Abstract Unavailable
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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

‘‘Atwood’s’’ oscillator

Thomas B. Greenslade, Jr.

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1151

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Abstract Unavailable
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45.05.+x General theory of classical mechanics of discrete systems
01.50.Pa Laboratory experiments and apparatus
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H. A. Kramers: Between Tradition and Revolution

Max Dresden, Author and Katherine R. Sopka

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1154

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Abstract Unavailable
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01.30.Ee Monographs and collections
01.60.+q Biographies, tributes, personal notes, and obituaries
01.65.+g History of science

Astrophysical Concepts, 2nd ed.

Martin Harwit, Author and Thomas Arny

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1155

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Abstract Unavailable
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01.30.Ee Monographs and collections
95.30.-k Fundamental aspects of astrophysics
98.80.-k Cosmology

Physics at Surfaces

Andrew Zangwill, Author and Dale L. Doering

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1155

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Abstract Unavailable
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01.30.Ee Monographs and collections
82.65.+r Surface and interface chemistry; heterogeneous catalysis at surfaces
68.35.-p Solid surfaces and solid-solid interfaces: structure and energetics

The Problems of Physics

A. J. Leggett, Author and David Park

American Journal of Physics -- December 1988 -- Volume 56, Issue 12, pp. 1156

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Abstract Unavailable
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01.30.Ee Monographs and collections
01.70.+w Philosophy of science
01.55.+b General physics
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