# Showing papers in "American Journal of Physics in 1988"

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6,036 citations

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TL;DR: The pages of this expensive but invaluable reference work are dense with formulae of stupefying complexity as discussed by the authors, where definite/indefinite integral properties of a great variety of special functions are discussed.

Abstract: The pages of this expensive but invaluable reference work are dense with formulae of stupefying complexity. Chapters 1 and 2 treat definite/indefinite integral properties of a great variety of special functions, Chapters 3 and 4 (which are relatively brief) treat definite integrals of some piece-wi

3,784 citations

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TL;DR: In this paper, a new class of solutions of the Einstein field equations is presented, which describe wormholes that, in principle, could be traversed by human beings, and it is essential in these solutions that the wormhole possess a throat at which there is no horizon.

Abstract: Rapid interstellar travel by means of spacetime wormholes is described in a way that is useful for teaching elementary general relativity. The description touches base with Carl Sagan’s novel C o n t a c t, which, unlike most science fiction novels, treats such travel in a manner that accords with the best 1986 knowledge of the laws of physics. Many objections are given against the use of black holes or Schwarzschild wormholes for rapid interstellar travel. A new class of solutions of the Einstein field equations is presented, which describe wormholes that, in principle, could be traversed by human beings. It is essential in these solutions that the wormhole possess a throat at which there is no horizon; and this property, together with the Einstein field equations, places an extreme constraint on the material that generates the wormhole’s spacetime curvature: In the wormhole’s throat that material must possess a radial tension τ0 with the enormous magnitude τ0∼ (pressure at the center of the most massive of neutron stars)×(20 km)2/(circumference of throat)2. Moreover, this tension must exceed the material’s density of mass‐energy, ρ0 c 2. No known material has this τ0>ρ0 c 2property, and such material would violate all the ‘‘energy conditions’’ that underlie some deeply cherished theorems in general relativity. However, it is not possible today to rule out firmly the existence of such material; and quantum field theory gives tantalizing hints that such material might, in fact, be possible.

2,169 citations

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TL;DR: In this paper, it is shown that the harmonic oscillator potential can be solved by using raising and lowering operators, which can be generalized with the help of supersymmetry and the concept of shape invariant potentials, allowing one to calculate energy eigenvalues and eigenfunctions of essentially all known exactly solvable potentials in a simple and elegant manner.

Abstract: It is well known that the harmonic oscillator potential can be solved by using raising and lowering operators. This operator method can be generalized with the help of supersymmetry and the concept of ‘‘shape‐invariant’’ potentials. This generalization allows one to calculate the energy eigenvalues and eigenfunctions of essentially all known exactly solvable potentials in a simple and elegant manner.

379 citations

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TL;DR: In this paper, a small plasma focus (3.3 kJ) is designed from the viewpoint of simplicity, reliability, and cost effectiveness to act as a source of pulsed high-density plasmas.

Abstract: A small plasma focus (3.3 kJ) is designed from the viewpoint of simplicity, reliability, and cost effectiveness to act as a source of pulsed high‐density plasmas. The simplicity of the device and associated diagnostics coupled with its rich variety of plasma phenomena makes this device ideal for the teaching of plasma nuclear fusion particularly for developing countries where such facilities are at present rarely available. Six sets of the device have been constructed and tested in various gases with better than 95% reliability and reproducibility in various plasma phenomena including neutron production of 0.5–1.0×108 per discharge when operated in 3‐Torr deuterium. The design principles, procedures, and parameters are discussed and test results shown.

258 citations

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185 citations

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TL;DR: In this paper, the difference in force expressions between electric current loop models and separated magnetic charge models for a magnetic dipole has been investigated for the determination of the nature of the neutrondipole moment and the Aharonov-Casher effect.

Abstract: The classical magnetic force on a magnetic dipole depends upon the model for the dipole. The usual electric current loop model for a magnetic dipole leads to the force F=∇(m⋅B) on a magnetic dipole m in a magnetic fieldB. The separated magnetic charge model for a magnetic dipole leads to the force F=(m⋅∇)B on a magnetic dipole. The latter expression is analogous to the force experienced by an electric dipole in an electric field. Here, some elementary examples are given where the force expressions yield entirely different forces on a magnetic dipole. Electromagnetism textbooks usually do not emphasize the difference between these force expressions; however, occasionally the difference is important for understanding experimental results. In the 1930s and 1940s the difference in force expressions was involved in a determination of the nature of the neutrondipole moment. At present, in the 1980s, the difference in the force expressions is central to a controversy over an experiment to test the proposed Aharonov–Casher effect.

152 citations

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TL;DR: The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific Statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Abstract: The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific Statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

146 citations

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122 citations

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TL;DR: The Formulaire Reference Record was created on 2004-09-07, modified on 2016-08-08 as discussed by the authors, and is based on the formulaire reference record (FRS).

Abstract: Keywords: Mathematique ; Formulaire Reference Record created on 2004-09-07, modified on 2016-08-08

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TL;DR: In this article, an alternative analysis for the magnetic braking experiment of Wiederick et al. is presented, taking into account the fringing streamlines of eddy currents for a rectangular ‘‘footprint’’ of the magnetic field.

Abstract: An alternative analysis is presented for the magnetic braking experiment of Wiederick et al., taking into account the fringing streamlines of eddy currents for a rectangular ‘‘footprint’’ of the magnetic field.

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TL;DR: In this article, the statistical properties of various harmonic oscillator states that are linear superpositions of its energy eigenfunctions are described using only elementary quantum-mechanical concepts and the principles underlying the production of squeezed electromagnetic waves via parametric amplification or four-wave mixing, their measurement by homodyne detection, and the connection between squeezing and non-Poissonian counting statistics.

Abstract: Using only elementary quantum‐mechanical concepts, the statistical properties of various harmonic oscillator states that are linear superpositions of its energy eigenfunctions are described. These superpositions include coherent states and squeezed (or two‐photon coherent) states. The resulting Gaussian, minimum‐uncertainty wave packets are shown to oscillate back and forth for both coherent and squeezed states, but with an oscillating ‘‘width’’ for the squeezed states. Also examined are the principles underlying the production of squeezed electromagnetic waves via parametric amplification or four‐wave mixing, their measurement by homodyne detection, and the connection between squeezing and non‐Poissonian counting statistics.

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TL;DR: In this article, a general description of the ballistic trajectory of a flying spinning ball acted on, in addition to the forces of gravity and drag, by the so-called Magnus force is presented.

Abstract: A general description is presented of the calculation of the ballistic trajectory of a flying spinning ball acted on, in addition to the forces of gravity and drag, by the so‐called Magnus force By applying the regression analysis to results of wind‐tunnel measurement of the drag and lift coefficients of a spinning ball, a calculation of the nonlinear differential equation of the hodograph was carried out by means of the Runge–Kutta method The theoretical results that can be used to calculate the ballistic trajectories for any ball game were applied to one of the most difficult and most interesting tennis strokes, ie, to the topspin lob Practical results obtained for various distances are presented in a table as well as in graphical form UFAJP

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TL;DR: In this paper, the Coulomb potential is derived in one space-one time dimension and introduced into Dirac and Klein-Gordon equations and the equations are solved and the somewhat surprising result that nonexistence of bound state solutions in the lower dimension is discussed and identified as another fine example of the Klein paradox.

Abstract: The Coulomb potential is derived in ‘‘one space–one time’’ dimension and introduced into Dirac and Klein–Gordon equations. The equations are solved and the somewhat surprising result—nonexistence of bound state solutions in the lower dimension—is discussed and identified as another fine example of the ‘‘Klein paradox.’’

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TL;DR: In this article, a simple analysis of two problems in each of which a different length scale determines the effective screening is presented, and an exact analysis is also presented of the screening for a cylinder of arbitrary thickness, as well as an analogy between screening by normal metals and screening by superconductors.

Abstract: To dispel a widespread but erroneous belief among physicists that the penetration of ac magnetic fields into normal metals is determined by the usual skin depth δ alone, a simple analysis is presented of two problems in each of which a different length scale determines the effective screening. For a cylindrical can of thickness d≪δ and radius R≪λ, where λ is the wavelength, it is shown that the critical thickness for effective screening is dc =δ2/R. For a planar film with thickness d≪δ, dc =c/2πσ, where σ is the conductivity. An exact analysis is also presented of the screening for a cylinder of arbitrary thickness, as well as an analogy between screening by normal metals and screening by superconductors.

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TL;DR: The first published calculation of the gravitational deflection of light based on Newtonian theory and the corpuscular model of light was done around 1784 by Henry Cavendish, almost 20 years earlier than the first published calculated calculation by Johann Georg von Soldner as mentioned in this paper.

Abstract: The gravitational deflection of light based on Newtonian theory and the corpuscular model of light was calculated, but never published, around 1784 by Henry Cavendish, almost 20 years earlier than the first published calculation by Johann Georg von Soldner. The two results are slightly different because, while Cavendish treated a light ray emitted from infinity, von Soldner treated a light ray emitted from the surface of the gravitating body. At the first order of approximation, they agree with each other; both are one‐half the value predicted by general relativity and confirmed by experiment.

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TL;DR: In this article, it was shown that for a potential consisting of two Dirac δ functions of arbitrary strength, a finite portion of the incident particles is transmitted at threshold for certain choices of the set of parameters defining the potential.

Abstract: In one‐dimensional scattering, the portion of particles that is transmitted in general vanishes as the kinetic energy of the incident particles approaches zero. Based upon published results from the literature, the present work shows that for a potential consisting of two Dirac δ functions of arbitrary strength, a finite portion of the incident particles is transmitted at threshold for certain choices of the set of parameters defining the potential. The underlying reasons are shown to be related to the structure of the bound levels of the potential. It is shown that for a potential with a finite range but of general shape the reflection coefficient in general tends to unity near threshold, which is what is usually observed. However, in the presence of a bound level at the onset of the continuum, a finite portion of the incident particles is transmitted at threshold for a potential with a general shape and, furthermore, it can be shown that if the potential V is symmetric with V(x)=V(−x) then resonance transmission is observed, i.e., the reflection coefficient vanishes at threshold.

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TL;DR: In this article, the authors presented analytical solutions for the time-dependent tunneling of wave trains and wave packets through delta function barriers with no approximations to the tunneling currents and density distributions.

Abstract: Analytical solutions for the time‐dependent tunneling of wave trains and wave packets through delta‐function barriers are presented. Tunneling currents and density distributions are calculated with no approximations. A standby mechanism is demonstrated: The particle ‘‘waits’’ some time in front of the barrier before it tunnels through the barrier.

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TL;DR: In this article, an analysis of billiard ball collisions in two dimensions with a full account of frictional effects is presented, and an experiment designed to test the predictions of the analysis is described.

Abstract: An analysis of billiard ball collisions in two dimensions with a full account of frictional effects is presented. An experiment designed to test the predictions of the analysis is described. Data are presented showing that the angle between the directions of travel of billiard balls after a collision in which one ball is initially stationary depends on the impact parameter in a rather complicated way, and is not 90 deg as is commonly claimed.

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TL;DR: In this paper, the Gibbs-Appell equations of motion were derived for a disk rolling on a horizontal plane, and the role of virtual displacements in generating generalized equations was discussed.

Abstract: A particularly simple and direct derivation of the Gibbs–Appell equations of motion is given. In addition to the conventional results, a relatively unknown but elegant and useful form of the equations of motion is also obtained. The role of virtual displacements in generating generalized equations of motion is discussed. The relationship between the Gibbs–Appell equations of motion and Lagrange’s equations of motion is discussed. Auxiliary results that facilitate the application of the Gibbs–Appell equations of motion to rigid bodies are presented. The theory is demonstrated by generating equations of motion for a disk rolling on a horizontal plane.

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TL;DR: In this article, the authors compare the force laws of Ampere and Biot-Savart in magnetostatics using the geometrical model of a closed curve to represent a current loop.

Abstract: The force laws of Ampere and Biot–Savart in magnetostatics are compared using the geometrical model of a closed curve to represent a current loop. The two laws give identical results when forces between separate current loops are considered and also for the force exerted by a current loop on a rectilinear part of itself. According to both laws, these self‐forces diverge wherever the curvature of the curve representing the current loop is not equal to zero. Differences in the predictions of the two laws are shown to appear only as differences in diverging forces when evaluating forces of a current loop on a part of itself and to be entirely due to the oversimplified and unrealistic geometrical model used for the current loop.

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TL;DR: In this paper, a simple pictorial representation of the chirality of an atom is obtained by mapping the electron probability current density in the atom to the electron density map of the atom, and results were shown for a hydrogenic 2p1/2 stationary state.

Abstract: 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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TL;DR: In this paper, a general discussion is given of the relationship of relativistic gravitation and its Newtonian limit with special emphasis on a particular non-Newtonian effect: spatial curvature.

Abstract: The Schwarzschild metric, the general relativistic description of the space‐time outside a spherical mass, has an extremely simple appearance. Because of this many attempts have been made to derive it by combining special relativity with concepts of Newtonian gravitation. It is shown here that such a derivation is impossible. A general discussion is given of the relationship of relativistic gravitation and its Newtonian limit with special emphasis on a particular non‐Newtonian effect: spatial curvature.

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TL;DR: In this paper, generalized virial theorems are developed for central potentials in an N-dimensional space, and the virial relations are then used to find the various spatial moments of the probability distribution, wavefunctions, and their derivatives at the origin of Coulomb and isotropic harmonic oscillator potentials.

Abstract: Generalized virial theorems are developed for central potentials in an N‐dimensional space. The virial relations are then used to find the various spatial moments of the probability distribution, wavefunctions, and their derivatives at the origin of Coulomb and isotropic harmonic oscillator potentials in N dimension.

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TL;DR: Hake et al. as discussed by the authors studied Newton's laws for a 3-week period along with 323 students in a noncalculus-based introductory physics course for science majors, and found substantial increase in conceptual understanding for both professors and students over that obtained by students subjected to conventional instruction.

Abstract: Ten nonphysical‐science professors studied Newton’s laws for a 3‐week period along with 323 students in a noncalculus‐based introductory physics course for science majors. The course contained innovations described in an earlier article [R. R. Hake, Am. J. Phys. 55, 878 (1987)]. Pre‐ and post‐course mechanics exams indicated substantial increase in conceptual understanding for both professors and students over that obtained by students subjected to conventional instruction. The perspectives of the professorial peers on the innovations and various other aspects of the course are quoted at some length. Their major suggestions for instructional improvement of introductory physics courses are: (1) slow the pace at which topics are covered; (2) relate all educational activities to precisely stated course objectives; (3) devote some lecture time to setup and solution of problems with emphasis on models and strategy; (4) use a pedagogically advanced textbook; (5) relate abstract concepts to everyday concrete phe...

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TL;DR: In this paper, the bound-state solutions of the Dirac equation are verified and two theorems regarding the bound state solutions of one-dimensional Dirac equations are verified: 1) there is no degeneracy of energy; 2) when the potential is a Lorentz scalar and the potential does not cross zero, the energy does not degenerate.

Abstract: Two theorems regarding the bound‐state solutions of the one‐dimensional Dirac equation are verified: A—There is no degeneracy of energy; B—When the potential is a Lorentz scalar and the potential is continuously varied, the energy does not cross zero. Some features of the Dirac equation related to these theorems are discussed.

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TL;DR: In this paper, the optical heterodyne principle is described and its history traced, and the optical communication by this technique was frustrated by problems of wavefront degradation and laser frequency instability, however, fiber optics has recently revitalized this as an attractive possibility.

Abstract: The optical heterodyne principle is described and its history traced. Early hopes for optical communication by this technique were frustrated by problems of wavefront degradation and laser frequency instability. However, fiber optics has recently revitalized this as an attractive possibility. In the interim, many other successful applications have been found that exploit different advantages of the heterodyne principle. Several examples are described. A number of simple optical heterodyne experiments utilizing a HeNe laser and electrical spectrum analyzer are presented. Details are furnished concerning experimental requirements and special considerations for optical heterodyne detection.

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TL;DR: In this paper, the exact solution to Schrodinger's equation for a three-dimensional harmonic oscillator confined by two impenetrable walls is presented, and 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.

Abstract: The exact solution to Schrodinger’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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TL;DR: The Wigner-Araki-Yanase theorem is often interpreted as meaning that there must be an error in measurement under certain conditions (when the commutator C between an additive conserved quantity and the discrete-spectrumed measured quantity does not vanish), and that the error may only be reduced by increasing the size of the apparatus as mentioned in this paper.

Abstract: The Wigner–Araki–Yanase theorem is often interpreted as meaning that there must be an error in measurement under certain conditions (when the commutator C between an additive conserved quantity and the discrete‐spectrumed measured quantity does not vanish), and that the error may only be reduced by increasing the size of the apparatus. By explicit example, it is shown that it is possible to have a perfectly accurate measurement if the system being measured is disturbed, regardless of the size of the apparatus. Also illustrated is how the error in an imperfectly accurate measurement may be reduced by decreasing the magnitude of C, without affecting the size of the apparatus.