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Feb 2000

Volume 68, Issue 2, pp. 103-202

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From innovation to change: Forging a physics education reform agenda for the 21st century

Sheila Tobias

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 103 | Cited 3 times

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Abstract Unavailable
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01.40.-d Education
01.55.+b General physics
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Resource Letter IMCF-1: Inertially and magnetically confined fusion

Richard F. Post

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 105 | Cited 2 times

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This Resource Letter is intended to introduce the reader to the history of fusion research, and to provide references covering the research since its first beginnings and up to the present for those who wish to dig deeper. © 2000 American Association of Physics Teachers.
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01.65.+g History of science
01.50.-i Educational aids
52.58.-c Other confinement methods
52.55.-s Magnetic confinement and equilibrium
01.30.Tt Bibliographies

On the interpretation of the redshift in a static gravitational field

L. B. Okun, K. G. Selivanov, and V. L. Telegdi

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 115 | Cited 8 times

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The classical phenomenon of the redshift of light in a static gravitational potential, usually called the gravitational redshift, is described in the literature essentially in two ways: On the one hand, the phenomenon is explained through the behavior of clocks which run faster the higher they are located in the potential, whereas the energy and frequency of the propagating photon do not change with height. The light thus appears to be redshifted relative to the frequency of the clock. On the other hand, the phenomenon is alternatively discussed (even in some authoritative texts) in terms of an energy loss of a photon as it overcomes the gravitational attraction of the massive body. This second approach operates with notions such as the “gravitational mass” or the “potential energy” of a photon and we assert that it is misleading. We do not claim to present any original ideas or to give a comprehensive review of the subject, our goal being essentially a pedagogical one. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
04.20.Cv Fundamental problems and general formalism

The loop-gas approach to Bose–Einstein condensation for trapped particles

William J. Mullin

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 120 | Cited 2 times

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We examine Bose–Einstein condensation (BEC) for particles trapped in a harmonic potential by considering it as a transition in the length of permutation cycles that arise from wave-function symmetry. This “loop-gas” approach was originally developed by Feynman in his path-integral study of BEC for a homogeneous gas in a box. For the harmonic oscillator potential it is possible to treat the ideal gas exactly so that one can easily see how standard approximations become more accurate in the thermodynamic limit (TDL). One clearly sees that the condensate is made up of very long permutation loops whose length fluctuates ever more widely as the number of particles increases. In the TDL, the Wentzel–Kramers–Brillouin approximation, equivalent to the standard approach to BEC, becomes precise for the noncondensate; however, this approximation neglects completely the long cycles that make up the condensate. We examine the exact form for the density matrix for the system and show how it describes the condensate and behaves in the TDL. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.75.Hh Static properties of condensates; thermodynamical, statistical, and structural properties
03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow
37.10.De Atom cooling methods
37.10.Gh Atom traps and guides

Dropped objects and other motions relative to the noninertial earth

Martin S. Tiersten and Harry Soodak

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 129 | Cited 2 times

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Earth is a noninertial frame of reference due to its spin and its orbital free-fall acceleration in the gravity fields of the sun, moon, and other external attractors. Three particularly interesting aspects of motion relative to the earth are discussed: (a) the effect of the sun and the moon and other external gravitational attractors; (b) the Foucault pendulum at middle latitudes; (c) the venerable and surprising problem of the deviation of the path of a dropped object away from the plumb line. A selective review of the twentieth century physics literature on motion relative to the earth demonstrates that errors and omissions abound. A fourth example is also presented, the interesting textbook problem of the free motion of a particle on a frictionless horizontal plane, as a simple illustration of carelessly incorrect treatment in much of the literature. © 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

Two-particle interference

Kurt Gottfried

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 143 | Cited 2 times

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The superposition principle leads to coherence phenomena that have no counterpart in classical optics. A gedanken experiment, due to Horne and Zeilinger, provides an especially clear illustration of such phenomena, and is presented in a manner suitable to an introductory quantum mechanics course. The experiment displays an interference pattern in the correlation between two particles produced in a momentum-conserving decay, but no interference pattern when either particle is observed separately; it also has interesting Einstein–Podolsky–Rosen-type correlations. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.Ta Foundations of quantum mechanics; measurement theory

Napier’s logarithms

Ian Bruce

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 148

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The development of Napier’s logarithms is traced from their beginnings in the construction of tables of numbers in geometric progression. These numbers are found using a kinematic model. The equivalent of a first-order differential equation arises. This is integrated numerically to give another set of corresponding numbers (logarithms) in arithmetic progression. The two sets of numbers are presented as a calculating device in the form of tables. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
02.60.-x Numerical approximation and analysis

Using Feynman diagrams to solve the classical harmonic oscillator

Alan Thorndike

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 155 | Cited 2 times

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The method of Feynman diagrams is used to solve the classical oscillator and a coupled oscillator problem. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.Ge Solutions of wave equations: bound states

Criterion for existence of a bound state in one dimension

K. R. Brownstein

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 160 | Cited 4 times

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Let V(x)≢0 be a one-dimensional potential which vanishes outside some interval. A well-known fact is that a bound state must exist if V(x)⩽0 for all x or even if V(x) satisfies the weaker condition ∫V(x)dx<0. Previously, Simon has shown that a bound state must exist if V(x) satisfies the even weaker condition ∫V(x)dx⩽0 [including the interesting case ∫V(x)dx=0]. In the present paper, using a simple trial function, we obtain a criterion for the existence of a bound state in one dimension, a special case of which gives the Simon result ∫V(x)dx⩽0. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.Ge Solutions of wave equations: bound states

Multiple-prism arrays in laser optics

F. J. Duarte

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 162 | Cited 1 time

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At present, multiple-prism arrays play an important and pervasive role in laser optics. From intracavity beam expansion to pulse compression these integrated optical elements have given a new and expanded meaning to the word prism. In this article we offer a pedagogical introduction to the physics and mathematics of practical multiple-prism arrays. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
42.79.Bh Lenses, prisms and mirrors
42.55.-f Lasers
42.60.Fc Modulation, tuning, and mode locking

Algebraic identities relating first- and second-quantized operators

W. E. Lawrence

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 167

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Second-quantized operators are derived algebraically from first-quantized counterparts, thus providing an alternative to all existing methods, most of which rely upon demonstrating the equivalence of matrix elements of the two operators. This derivation establishes an operator identity between a second-quantized operator and a first-quantized operator whose domain of definition is extended explicitly from an N-particle Hilbert space to Fock space. The existence of such an identity eliminates the need to address the issue of the representations used for the two operators, which often obscures the underlying simple relationship between them. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.-w Quantum mechanics

Representations of electric and magnetic fields

F. Herrmann, H. Hauptmann, and M. Suleder

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 171 | Cited 3 times

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We propose for the graphical representation of fields not to limit ourselves to field lines but also to draw the orthogonal surfaces. Just as the ends of the electric or magnetic field lines tell us where the sources of the flux of a field are located, the borders of the orthogonal surfaces indicate to us the sources of the field’s circulation. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
41.20.-q Applied classical electromagnetism

The intriguing properties of the equivalent resistances of n equal resistors combined in series and in parallel

Antoni Amengual

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 175 | Cited 1 time

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We found that the different values of equivalent resistance of all the possible combinations of n equal unitary resistors in series and/or in parallel form a list composed by a set of numbers and their inverses. This property is demonstrated and used to justify the symmetry and the peaks and valleys observed in the histogram representing the distribution of the values on the real axis. The number of different values obtained with n resistors is approximately 2.55n, defining a geometric series with a ratio smaller than the one that could be expected. The characteristics of the histograms, when some connections other than series or parallel as well as when nonplanar arrangements are allowed, is also suggested. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids

Optical Bloch equations: Informal motivation without the Schrödinger equation

James M. Supplee

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 180

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We briefly review the classical model of a Lorentz atom interacting with an optical field. We then ask how the equations describing the atom’s behavior should be modified to include atomic energy level quantization. Simply discussing what modifications make sense provides a strong plausibility argument for the optical Bloch equations. Contrasted with the standard derivation, this argument is less rigorous but has a certain pedagogical appeal: It simply assumes two atomic states with energy difference ℏω, rather than invoking the Schrödinger equation. Also, because our goal is more-or-less to guess the correct equations with minimal formalism, this discussion focuses on the physical meaning of the Bloch equations. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
42.50.-p Quantum optics
32.80.-t Photoionization and excitation

Phase shifts in multilayer dielectric beam splitters

M. W. Hamilton

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 186 | Cited 3 times

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Some properties of the reflectivity and transmissivity of multilayer dielectric optical coatings are derived from energy conservation applied to a beam splitter acting as a beam combiner. It is shown that dispersion in the phase shifts of the beam splitter coatings influences which quadrature amplitude is measured in a homodyne detector, and, in a Michelson interferometer, how the white-light fringe pattern is disposed about the zero-path-difference condition. The functions of reflectivity and transmissivity that determine these properties are shown to be not completely constrained by considerations of energy conservation and time reversibility, in contrast to commonly employed models for beam splitter reflectivity and transmissivity. Some representative beam splitter coating designs are used to illustrate this point. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
42.79.Wc Optical coatings
78.66.-w Optical properties of specific thin films
07.60.Ly Interferometers

Lifting of magnetic degeneracy in a parity-nonconserved atom by arbitrarily polarized light

Georges H. Wagnière

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 192 | Cited 1 time

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We show that in a one-electron atom in which parity-nonconserving interactions are operative, electromagnetic radiation of arbitrary polarization lifts the magnetic degeneracy of a spin–orbit coupled state. This result, arising from basic symmetry principles, occurs to second (and higher) order in the interaction of the atom with the electromagnetic field. It is a manifestation of the inverse magnetochiral effect. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
31.30.jg QED corrections to parity nonconserving transition amplitudes and CP violations
37.10.Gh Atom traps and guides
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Demonstration of viscous damping in the undergraduate laboratory

Josué Njock Libii

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 195 | Cited 4 times

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Abstract Unavailable
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01.50.-i Educational aids
45.30.+s General linear dynamical systems
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The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory

Brian Greene, Author and John H. Schwarz, Reviewer

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 199

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Abstract Unavailable
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01.30.Vv Book reviews
01.50.-i Educational aids
98.80.Cq Particle-theory and field-theory models of the early Universe (including cosmic pancakes, cosmic strings, chaotic phenomena, inflationary universe, etc.)

The Quantum Beat

Fouad G. Major, Author and Stuart B. Crampton, Reviewer

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 200

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Abstract Unavailable
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01.30.Vv Book reviews
01.50.-i Educational aids
06.20.F- Units and standards
06.30.Ft Time and frequency

Testing Quantum Mechanics on New Ground

Partha Ghose, Author and Raymond Y. Chiao, Reviewer

American Journal of Physics -- February 2000 -- Volume 68, Issue 2, pp. 201

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Abstract Unavailable
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01.30.Vv Book reviews
01.50.-i Educational aids
03.65.-w Quantum mechanics
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