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May 2013

Volume 81, Issue 5, pp. 325-399

Spotlight Figure

American Journal of Physics -- May 2013 -- Volume 81, Issue 5, pp. 351

Justin Peatross, John P. Corson, and Grayson Tarbox
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2013 AAPT Award Citations at the Winter Meeting, New Orleans, Louisiana

American Journal of Physics -- May 2013 -- Volume 81, Issue 5, pp. 325

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01.10.-m Announcements, news, and organizational activities
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The symplectic egg in classical and quantum mechanics

Maurice A. de Gosson

American Journal of Physics -- May 2013 -- Volume 81, Issue 5, pp. 328

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Symplectic geometry is the language of Classical Mechanics in its Hamiltonian formulation, and it also plays a crucial role in Quantum Mechanics. Symplectic geometry seemed to be well understood until 1985, when the mathematician Gromov discovered a surprising and unexpected property of canonical transformations: the non-squeezing theorem. Gromov's result, nicknamed the “principle of the symplectic camel,” seems at first sight to be an abstruse piece of pure mathematics. It turns out that it has fundamental—and unsuspected—consequences in the interpretations of both Classical and Quantum Mechanics, because it is essentially a classical form of the uncertainty principle. We invite the reader to a journey taking us from Gromov's non-squeezing theorem and its dynamical interpretation to the quantum uncertainty principle, opening the way to new insights.
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02.40.-k Geometry, differential geometry, and topology
03.65.-w Quantum mechanics
45.00.00 Classical mechanics of discrete systems

Uncertainty analysis for a simple thermal expansion experiment

Dimitri R. Dounas-Frazer, Punit R. Gandhi, and Geoffrey Z. Iwata

American Journal of Physics -- May 2013 -- Volume 81, Issue 5, pp. 338

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We describe a simple experiment for measuring the thermal expansion coefficient of a metal wire and discuss how the experiment can be used as a tool for exploring the interplay of measurement uncertainty and scientific models. In particular, we probe the regimes of applicability of three models of the wire: stiff and massless, elastic and massless, and elastic and massive. Using both analytical and empirical techniques, we present the conditions under which the wire's mass and elasticity can be neglected. By accounting for these effects, we measure Nichrome's thermal expansion coefficient to be 17.1(1.3) μm/m⋅K, which is consistent with the accepted value at the 8% level.
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01.50.Pa Laboratory experiments and apparatus
65.40.De Thermal expansion; thermomechanical effects

Solving for three-dimensional central potentials using numerical matrix methods

B. A. Jugdutt and F. Marsiglio

American Journal of Physics -- May 2013 -- Volume 81, Issue 5, pp. 343

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We present a numerical matrix method to find quantum stationary states and energies for three-dimensional central forces. The method can be used both for familiar, exactly solvable potentials and for those that are not solvable by analytical methods. As examples, we include the Coulomb potential, the finite spherical well, and the Yukawa potential. This method requires much less mathematical expertise than traditional analytical methods, although it does require some familiarity with numerical matrix diagonalization software.
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02.70.-c Computational techniques; simulations
03.65.-w Quantum mechanics

Classical connection between near-field interactions and far-field radiation and the relevance to quantum photoemission

Justin Peatross, John P. Corson, and Grayson Tarbox

American Journal of Physics -- May 2013 -- Volume 81, Issue 5, pp. 351

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Interference in the far-field radiation pattern emitted from a classical current distribution implies near-field work between different spatial portions of the distribution. We examine this relationship and the essential role of system geometry for the case of two oscillating dipoles and for a Gaussian current distribution. This analysis offers a compelling argument as to why the radiation from a large single-electron quantum wave packet should not exhibit the same destructive interference as that associated with a comparable classical charge density. Our discussion draws attention to the ad hoc heuristics motivating the original derivation of a quantum electron's radiation profile.
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41.00.00 Electromagnetism; electron and ion optics

Measurement of electric fields and estimation of dielectric susceptibility

Yasuyuki Nogi, Kiyomitsu Suzuki, and Yasunori Ohkuma

American Journal of Physics -- May 2013 -- Volume 81, Issue 5, pp. 359

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We describe a method of measuring the spatial structures of electric fields produced by charge distributions such as those on strip electrodes, small disk electrodes, and long double-plate electrodes. An electric-field sensor with high sensitivity to ac fields is fabricated for the measurement using a thin copper sheet. The reliability of the sensor is confirmed using a parallel-plate capacitor. The electric fields are oscillated at a frequency of 300 kHz to operate the electric-field sensor successfully. The structures of the measured fields coincide well with those of theoretical fields derived from Coulomb's law. When a dielectric is inserted in an electric field, polarization charges appear on the surface of the dielectric and modify the electric field in empty space. We measure the modified field and confirm the well-known linear relation between the polarization of a dielectric and the electric field. Dielectric susceptibilities are estimated from the linear relation for four types of dielectric.
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01.50.Pa Laboratory experiments and apparatus
41.00.00 Electromagnetism; electron and ion optics

Image method in the calculation of the van der Waals force between an atom and a conducting surface

Reinaldo de Melo e Souza, W. J. M. Kort-Kamp, C. Sigaud, and C. Farina

American Journal of Physics -- May 2013 -- Volume 81, Issue 5, pp. 366

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After a brief survey of van der Waals forces, we review a method recently proposed by Eberlein and Zietal to compute the dispersion van der Waals interaction between a neutral but polarizable atom and a perfectly conducting surface of arbitrary shape. This method has the advantage of relating the quantum problem to a corresponding classical one in electrostatics in an enlightening way so that all one needs is to compute an appropriate Green function. We show how the image method of electrostatics can be conveniently used together with the Eberlein and Zietal method (when the image solution is known). We then illustrate this method in some simple but important cases, including the atom-sphere system. Finally, we present an original result for the van der Waals force between an atom and a boss hat made of a grounded conducting material.
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41.20.Cv Electrostatics; Poisson and Laplace equations, boundary-value problems
51.00.00 Physics of gases

Advanced optics experiments using nonuniform aperture functions

Lowell T. Wood

American Journal of Physics -- May 2013 -- Volume 81, Issue 5, pp. 377

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A method to create instructive, nonuniform aperture functions using spatial frequency filtering is described. The diffraction from a single slit in the Fresnel limit and the interference from a double slit in the Fraunhofer limit are spatially filtered to create electric field distributions across an aperture to produce apodization, inverse apodization or super-resolution, and apertures with phase shifts across their widths. The diffraction effects from these aperture functions are measured and calculated. The excellent agreement between the experimental results and the calculated results makes the experiment ideal for use in an advanced undergraduate or graduate optics laboratory to illustrate experimentally several effects in Fourier optics.
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42.00.00 Optics

Gamma spectroscopy of environmental samples

P. B. Siegel

American Journal of Physics -- May 2013 -- Volume 81, Issue 5, pp. 381

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We describe experiments for the undergraduate laboratory that use a high-resolution gamma detector to measure radiation in environmental samples. The experiments are designed to instruct the students in the quantitative analysis of gamma spectra and secular equilibrium. Experiments include the radioactive dating of Brazil nuts, determining radioisotope concentrations in natural samples, and measurement of the 235U abundance in uranium rich rocks.
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01.50.Pa Laboratory experiments and apparatus
23.00.00 Radioactive decay and in-beam spectroscopy
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A qualitative approach to teaching capacitive circuits

David P. Smith and Paul van Kampen

American Journal of Physics -- May 2013 -- Volume 81, Issue 5, pp. 389

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We have investigated students' qualitative understanding of dc circuits containing resistors and a capacitor. We found that a year after traditional lecture instruction as part of an introductory physics course, most students were unable to predict the behavior of a series circuit consisting of a battery, a bulb, and a capacitor. Among the difficulties identified we found that almost half of the students implicitly abandoned the idea that a complete circuit is necessary for a bulb to light when a capacitor is introduced into the circuit. We have developed curriculum that enables students to construct a phenomenological model in which they liken the behavior of a capacitor to that of a wire, a switch, and a battery; this allows them to qualitatively describe circuits with batteries, bulbs, and capacitors. We have also developed curriculum on the determination of RC times. Post-test results show a significant increase in understanding of capacitive circuits.
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01.40.Fk Research in physics education
84.00.00 Electronics; radiowave and microwave technology; direct energy conversion and storage
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Elementary Particles.

Enrico Fermi and Luisa Bonolis, Reviewer

American Journal of Physics -- May 2013 -- Volume 81, Issue 5, pp. 397

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01.30.Vv Book reviews
10.00.00 THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

BOOKS RECEIVED

American Journal of Physics -- May 2013 -- Volume 81, Issue 5, pp. 399

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