Volume 58, Issue 1, January 1990
 Letters To The Editor



Important concerns, incorrect facts: Arons’ critique of the Introductory University Physics Project (IUPP)
View Description Hide Description 
Search the literature!
View Description Hide Description  Top

 Guest Comment


Guest Comment: Why so few women?
View Description Hide Description  Top

 Papers


Less is more: Experiments with an individual atomic particle at rest in free space
View Description Hide DescriptionThis article surveys experiments with individual closely confined atomic particles since their beginning in 1973. Such experiments have improved information on the size of an elementary particle on the same level as a quark, the electron, by at least three orders of magnitude. Their extension to the optical region promises atomic clocks of a reproducibility improved up to 100 000 times. The most important of the techniques developed for continuously detecting, cooling, and spin‐state analyzing a permanently confined individual electron are described in some detail. The electron, trapped in ultrahigh vacuum at liquid helium temperature, is profitably viewed as a man‐made atom, geonium.

The Richtmyer Memorial Lecture (January 1989): Novel magnetic phenomena and high‐temperature superconductivity in lamellar copper oxides
View Description Hide DescriptionThe discovery of high‐temperature superconductivity in lamellar copper oxide materials is one of the most dramatic and unexpected events in physics in the last several decades. In this paper, which is the text of the 48th Richtmyer Lecture, the basic physics of this new phenomenon is discussed and it is explained why the problem is proving to be so difficult in spite of the unprecedented assault on it by many thousands of physicists, chemists, and materials scientists.

Moments to remember—The conditions for equating torque and rate of change of angular momentum
View Description Hide DescriptionIt is a well‐known but frequently forgotten fact that the net external torque on a system of particles is equal to the rate of change of angular momentum only if the point about which moments are taken satisfies certain stringent conditions: The point must have zero acceleration, or it must be the center of mass, or its instantaneous acceleration must be directly toward or away from the center of mass. A simple problem in rigid‐body mechanics has been solved by Crawford, taking moments about the center of mass. It is shown here that the problem may also be solved using a point that does n o t satisfy any of these conditions, in which case a more general equation is required. An external fixed point may also be used for calculating moments. When carefully executed, all correct approaches yield the same solution.

Rigid levitation and suspension of high‐temperature superconductors by magnets
View Description Hide DescriptionA high‐T _{ c }superconductor floating freely above a magnet of low symmetry remains rigidly suspended in the air in almost any position and orientation as if stuck in an invisible heap of sand. This striking effect is due to pinning of the magnetic flux lines inside the superconductor and is often overlooked, since usually magnets with rotational symmetry are used for levitation. Magnets with rotational symmetry allow for nearly undamped orbiting and rotation of the superconductor about the magnet’s symmetry axis. But even in this geometry, flux‐line pinning can be seen, since it forces the orbiting superconductor to turn the same face toward the axis. Superconductors with sufficiently strong pinning may even be suspended below a magnet.

Functional integrals and the BCS theory of superconductivity
View Description Hide DescriptionAs an example of the application of functional integral techniques to condensed matter physics, the partition function for the BCSmodel for superconductivity is derived. The pairing term in the Hamiltonian is linearized by applying the Hubbard–Stratonovich transformation. It is shown that the standard result for the gap equation can be obtained by making a saddle‐point approximation to the functional integral.

The contracting square quantum well
View Description Hide DescriptionThe one‐dimensional square quantum well of varying width is shown to be an instructive example for testing the appropriateness of approximate solutions in quantum mechanics. The range of wall speeds over which the adiabatic approximation is applicable is investigated and related to the initial energy of the quantum system for both expanding and contracting wells. However, of more interest is the applicability of the sudden approximation to these systems. It is shown that this approximation is appropriate for expanding wells at quite modest wall speeds, whereas the approximation cannot be applied for contracting wells no matter how rapidly the well width contracts. The physical reasons for the inapplicability of the sudden approximation for contracting wells is investigated.

The bipolar motor: A simple demonstration of deterministic chaos
View Description Hide DescriptionA simple and inexpensive mechanical model for the demonstration of chaos in a nonlinear deterministic system is described. Periodic, period‐doubled, and chaotic motions are exhibited by the model in agreement with the solutions of its governing differential equation. The model is sufficiently free from long‐term drifts to enable experimental Poincaré plots to be easily constructed. Such a simple mechanical model is shown to be ideal for use as a lecture room demonstration, as well as for a student laboratory.

Asymmetry and convergence in the central limit theorem: An approach for physicists
View Description Hide DescriptionA version of the central limit theorem is presented that allows the study of the rate of convergence to the normal probability density of the average of independent identically distributed random variables. Particular emphasis is put on the effect due to the asymmetry of the probability density of the variables. An example is worked out that gives a convincing visual display of the theorem and its convergence.

A relativistic extension of the concepts of the central and conservative forces
View Description Hide DescriptionUsually in classical dynamics the fundamental quantities of electromagnetism are considered to be the electric and magnetic fields. However, in quantum dynamics, the fundamental quantities of electromagnetism are the potentials. To solve this confusion there is a discussion of how the concepts of the central force and the conservative force in Newtonian dynamics are extended if the Galilean transformation is replaced by the Lorentz transformation. As a result, if only the conservativeness, linearity, and wave nature of field are assumed, a relativistic potential can be axiomatically defined and the dynamical equations that are similar to the equation of motion, the Lorentz condition, and the field equation for the potentials of electromagnetism can be composed. Then, the concept of charge can be introduced leading to electromagnetism without the electric and magnetic fields and the inverse‐square law. Thus even in classical dynamics the fundamental quantities of electromagnetism are the potentials. The discussion above is important in the understanding of the mutual relations among Newtonian dynamics, the special theory of relativity, and electromagnetism.

On the surface charge density of a moving sphere
View Description Hide DescriptionIt is shown that the surface charge density on a spherical conductor (spherical in the l a b frame) is uniform, regardless of its velocity.

A computer‐assisted experiment in single‐slit diffraction and spatial filtering
View Description Hide DescriptionAn intermediate‐level experiment examines Fraunhofer diffraction and its implications for the image formation of a coherently illuminated object. A commercially available software package is used to provide an environment that allows interactive data acquisition and subsequent numerical and graphical analysis.

Simple proof of the symmetrization postulate in quantum mechanics
View Description Hide DescriptionWith the assumption that n complete single‐particle measurements α_{ i } uniquely determine the n‐identical‐particle state ‖α_{1},α_{2},...,α_{ n }〉, the wavefunction ψ(α_{1},α_{2},...,α_{ n }) =〈α_{1},α_{2},...,α_{ n }‖ψ〉 is shown to be either symmetric or antisymmetric under any permutation of its arguments.

A simple device to illustrate angular momentum conservation and instability
View Description Hide DescriptionAn inexpensive and easily constructed spring‐loaded dumbbell that illustrates both angular momentumconservation and mechanical instability is described.

Wind chime physics
View Description Hide DescriptionThe construction of a set of wind chimes tuned to specific pitches is described. A method for the determination of Young’s modulus based on the measured frequencies of vibration of the sample is employed in the construction of the chimes. Some complications dealing with the perception of musical pitch are also discussed.

Generalization of the Hagen–Poiseuille velocity profile to non‐Newtonian fluids and measurement of their viscosity
View Description Hide DescriptionBy using the constitutive equation for the stress tensor that yields a viscosity formula similar to the Eyring formula for non‐Newtonian fluids and solving the hydrodynamicequation for a tube flow of such fluids, a generalization is obtained of the Hagen–Poiseuille formula for velocity profile in tube flow under pressure. The volume flow rate is calculated with the velocity profile, and a method of measuring zero shear rate viscosity is suggested. As the pressure difference increases, the calculated velocity profiles become increasingly flatter in the midportion of the tube than that predicted by the Hagen–Poiseuille formula, which remains parabolic for all values of the pressure difference.
 Top
