Showing papers in "American Journal of Physics in 1969"
220 citations
TL;DR: In this article, a simple nonlinear partial differential equation suitable for study by an undergraduate in applied science is discussed and several physical realizations are outlined and the construction of an analog model is described.
Abstract: A simple nonlinear partial differential equation suitable for study by an undergraduate in applied science is discussed. Several physical realizations are outlined and the construction of an analog model is described. The equation is analyzed to determine nonlinear pulse and periodic waveforms, and the stability of these waveforms is investigated using a recently developed “averaged Lagrangian” technique.
201 citations
TL;DR: In this paper, the spectrum of light scattered by a suspension of particles in a fluid was used to obtain quantitative information about the motion of the particles, including an accurate determination of their diffusion constant.
Abstract: From the spectrum of light scattered by a suspension of particles in a fluid one can obtain quantitative information about the motion of the particles, including an accurate determination of their diffusion constant. If the incident light source is a laser, and the scattered light falls on the photosurface of a photomultiplier tube, then by measuring the spectrum of the photocurrent one obtains the spectrum of the intensity fluctuations of the scattered light. The intensity of the scattered light is determined by the instantaneous superposition of the phases of the waves scattered from each of the diffusing particles and the intensity fluctuates because the particles move. For particles of known diameter one can predict the spectral shape and width from the diffusion equation. We present a calculation of the spectrum of the field and the spectrum of the intensity of the scattered light and an advanced laboratory experiment and lecture demonstration by which the intensity spectrum can be studied.
161 citations
153 citations
TL;DR: In this article, the problem of a particle in a one-dimensional infinite square-well potential with one wall moving at constant velocity is treated by means of a complete set of functions which are exact solutions of the time-dependent Schrodinger equation.
Abstract: The problem of a particle in a one-dimensional infinite square-well potential with one wall moving at constant velocity is treated by means of a complete set of functions which are exact solutions of the time-dependent Schrodinger equation. Comparison is made with a first-order perturbation treatment, and numerical results are presented for a particle initially in the ground state.
115 citations
TL;DR: In this paper, the bound state solutions of a truncated Coulomb potential −e2/(|x|+a), a>0, for small a, the discrete spectrum of this potential contains energy levels which approach arbitrarily close to the discrete levels of the true Coulomb pote...
Abstract: The time-independent Schrodinger equation is solved for the bound state solutions of the one-dimensional Coulomb potential, −e2/|x|. The wave functions obtained are normalizable and continuous. The energy spectrum consists of a set of discrete levels with energies equal to the Bohr energies of hydrogen, and a set of continuum levels with energies lying strictly between the discrete levels. The odd wave functions associated with the discrete levels are differentiable everywhere, but the even wave functions associated with the continuum levels have a cusp with infinite slope at the origin. The energy levels are not degenerate. Following the method of Loudon, the bound state solutions of a truncated Coulomb potential −e2/(|x|+a), a>0, are also obtained. For small a, the discrete spectrum of this potential contains: (1) energy levels which approach arbitrarily close to the discrete levels of the true Coulomb potential as a→0, with odd wave functions identical to the odd wave functions of the true Coulomb pote...
114 citations
98 citations
93 citations
TL;DR: In this paper, the authors examined the center-of-mass law for systems made up of electrostatic charges and magnets, in terms of the requirements of special relativitytheory, and showed that if small "electromagnetic mass" terms are neglected, both conservation of momentum and the center of mass law hold in all cases.
Abstract: Momentum conservation and the validity of the center-of-mass law are examined for systems made up of electrostaticcharges and magnets, in terms of the requirements of special relativitytheory. The approach used is that of a quasimicroscopic electromagnetictheory, in which the interaction of the field with material bodies is described by using models for these bodies which involve charge and current densities. It is shown that if small “electromagnetic mass” terms are neglected, both conservation of momentum and the center-of-mass law hold in all cases. In some cases a “hidden momentum” contained in stationary matter plays an important role, as pointed out recently by Shockley and James [W. Shockley and R. P. James, Phys. Rev. Lett. 18, 876 (1967).] In such cases the center-of-mass law can fail in nonrelativistic theory. This is illustrated by the discussion of a special model. Another case in which a “hidden momentum” required by relativitytheory is important is the explanation of the null result of the Trouton-Noble experiment. This is discussed in Sec. V.
TL;DR: In this article, the single-ended zipper problem is treated as an analog to the one-dimensional analog of the Slater model of KDP, and an interesting simiality with the work of Nagle on the onedimensional analog is established.
Abstract: Two systems of biomolecules in solution are known to be represented by simple models which can be solved to give phase transitions in one dimension. The systems are double-stranded DNA and the helical polypeptides. We treat the very simple problem of the single-ended zipper. There is an interesting simialrity with the work of Nagle on the one-dimensional analog of the Slater model of KDP.
TL;DR: In this paper, a tutorial review of the theory of crystals with large-amplitude, highly anharmonic vibrational motion is given and applications are discussed to the lighter solid rare gases, particularly helium, as well as to the ferroelectric-lattice structural transformation.
Abstract: A tutorial review is given of the theory of crystals with large-amplitude, highly anharmonic vibrational motion. Applications are discussed to the lighter solid rare gases, particularly helium, as well as to the ferroelectric-lattice structural transformation. The single-particle and the collective pictures of the starting coordinate basis set are developed and compared. Formulas are presented for the phonon damping in the collective picture. A survey is outlined of Jastrow function treatments of short-range correlation due to hard-core interatomic repulsion in solid helium.
TL;DR: In this paper, the basic experiments, theory, and recent investigations about radio frequency plasmoids and resonance-sustained gas discharges are reviewed, as well as their properties.
Abstract: The progress made in the last decade towards a better understanding of the resonance properties of bounded plasmas has shed some light on the physical behavior of the radio frequency plasmoid, which was discovered in 1929 but never satisfactorily explained. A few years ago it was shown that the plasmoid is a particular aspect of a much more general class of discharge such that the steady state is controlled by a resonance in the plasma. In this article the basic experiments, theory, and the recent investigations about radio frequency plasmoids and resonance-sustained gas discharges are reviewed.
TL;DR: The Wham-O Super-Ball as discussed by the authors is a rough ball which conserves kinetic energy and exhibits unexpected behavior after a single bounce and bizarre behavior after three bounces against parallel surfaces.
Abstract: A rough ball which conserves kinetic energy exhibits unexpected behavior after a single bounce and bizarre behavior after three bounces against parallel surfaces. The Wham-O Super-Ball® (registered by Wham-O Corporation, 835 E. El Monte St., San Gabriel, Calif.91776), appears to approximate this behavior and provides an inexpensive and readily available model of kinematics quite different from that of a point mass or smooth ball. The analysis is most strikingly illustrated by the fact that the ball returns to the hand after three collisions with the floor, the underside of a table, and the floor. Some questions are raised concerning the dynamics of the collision.
TL;DR: In this paper, a solution for the electrostatic field strength and force acting on a nonconducting dielectric sphere near a grounded conducting plane was derived, which is one of the relatively few that are exact and apply to a physically realizable geometry.
Abstract: Because of the short charge relaxation time for water, an electrostatic solution for conductors usually applies. But to extend the analysis to very short interaction times, a solution is derived for the electrostatic field strength and force acting on a nonconducting dielectric sphere near a grounded conducting plane. This solution has more general interest, since it is one of the relatively few that are exact and apply to a physically realizable geometry.
TL;DR: A comprehensive tutorial-review of theoretical and experimental work pertaining to helicon wave propagation in solids is presented in this article, where the authors investigate the behavior of a local free-electron metal in a magnetic field to demonstrate the conditions necessary for helicon propagation.
Abstract: This paper is a comprehensive tutorial-review of theoretical and experimental work pertaining to helicon waves in solids. The discussion of helicon work is divided into two general categories comprising helicon propagation in the “local” and “nonlocal” regimes. We investigate the behavior of a local free-electron metal in a magnetic field to demonstrate the conditions necessary for helicon propagation and to determine the essential characteristics of the helicon wave. These concepts are carried over to a discussion of the behavior of a general anisotropic metal. Solutions to various boundary-value problems are given. For a nonlocal free-electron metal, there are two collisionless mechanisms for the damping of a helicon wave, Doppler-shifted cyclotron resonance, and Landau or transit-time damping. Both of these mechanisms are described and the influence of a finite carrier mean-free-path on these mechanisms is discussed. All of the experimental methods commonly used to study helicon waves are described and...
TL;DR: In this paper, the problem of the electrostatics problem of a point charge between two infinite parallel conducting planes is solved by the method of images, and a Sommerfeld-Watson transformation is then used to obtain an integral representation for the potential.
Abstract: The electrostatics problem of a point charge between two infinite parallel conducting planes— i.e., the Green function for a parallel plate capacitor—is solved by the method of images. A Sommerfeld-Watson transformation is then used to obtain an integral representation for the potential. An asymptotic expression is derived for the region far from the charge, and the field is found to fall off exponentially.
TL;DR: In this paper, the authors discuss ambiguities and sources of confusion in the presentation of electromagnetic induction in introductory texts and explicitly show that in these examples no exceptions occur, and give a general prescription for evaluating induced emf's.
Abstract: The first part of this article is a discussion of some ambiguities and sources of confusion in the presentation of electromagnetic induction in introductory texts. Particular attention is paid to the use of special relativity theory in these presentations. The second part of the paper discusses various examples of electromagnetic induction that have acquired reputations as “exceptions to the flux rule”. The origin of these exceptions is traced to an inappropriate choice of contour or its motions. We explicitly show that in these examples no exceptions occur, and give a general prescription for evaluating induced emf's.
TL;DR: In this paper, an interpretation of the process of measurement is proposed which can be placed wholly within the quantum theory, and the entire system including the apparatus and even the mind of the observer can be considered to develop according to the Schrodinger equation.
Abstract: An interpretation of the process of measurement is proposed which can be placed wholly within the quantum theory. The entire system including the apparatus and even the mind of the observer can be considered to develop according to the Schrodinger equation. No separation, in principle, of the observer and the observed is necessary; nor is it necessary to introduce either the type I process of von Neumann or wave function reduction.
TL;DR: The varied investigations involve both German and U. S. A. wartime efforts and subsequent efforts in such diverse laboratories as university, military, and commercial, are doubtless this diversification that has enabled so many successes to be achieved.
Abstract: In 1930, a meeting to discuss photoelectric cells indicated that photoconductive cells were of marginal value. In 1954, interest in photoconductivity was sufficient to warrant a meeting to discuss that topic exclusively. The impetus for this change came largely from the military in its desire to develop a sensitive, reliable infrared detector. The varied investigations involve both German and U. S. A. wartime efforts and subsequent efforts in such diverse laboratories as university, military, and commercial. It is doubtless this diversification that has enabled so many successes to be achieved.
TL;DR: In this article, the diffraction of a full thermal neutral atomic beam by a single slit has been observed, and the experimental pattern was reproducible and was in good general agreement with the prediction of de Broglie's hypothesis and simple scalar Fresnel diffraction theory.
Abstract: The diffraction of a full thermal neutral atomic potassium beam by a single slit has been observed. Four experimental diffraction patterns of a 23.0(±0.4)μ diffracting slit were obtained with an atomic-beam apparatus which had a 2.5(±1)μ source slit, a 3.0(±0.1)μ detector wire, a source-to-slit distance of 96 cm, a slit-to-detector distance of 100 cm, and an oven temperature of 533° K. The experimental pattern was reproducible and is in good general agreement with the prediction of de Broglie's hypothesis and simple scalar Fresnel diffraction theory. The effect of diffraction is clearly evident; two prominent diffraction fringes are present on the top corners of the beam profiles. The theoretical prediction, calculated with the aid of a computer, included the effects of finite source and detector widths and the Maxwellian speed distribution of the K beam. Additional theoretical calculations showed that no major improvement in the clarity of the diffraction fringes could be obtained by using a velocity-sel...
TL;DR: A joint symposium of the AAPT and APS on the history and philosophy of physics, held during the 1969 AAPT-APS annual meeting as discussed by the authors, was presented on 5 February 1969.
Abstract: This paper was presented on 5 February 1969 at a joint symposium of the AAPT and APS on the history and philosophy of physics, held during the AAPT-APS annual meeting.
TL;DR: In this paper, the physical mechanisms by which echoes are produced in a system of many charged particles gyrating in a static magnetic field are outlined, and it is shown how these ideas carry over to large systems of (almost) harmonic oscillators and are therefore applicable to many other physical systems.
Abstract: The physical mechanisms by which echoes are produced in a system of many charged particles gyrating in a static magnetic field is outlined. It is then shown how these ideas carry over to large systems of (almost) harmonic oscillators and are therefore applicable to many other physical systems.
TL;DR: In this paper, the usual least-squares procedure includes the assumption that the independent variables are absolutely error free, but this assumption is invalid for most physical problems and can be removed.
Abstract: The usual least-squares procedure includes the assumption that the independent variables are absolutely error free. This assumption is invalid for most physical problems and can be removed. The resulting set of equations is given in a form suitable for computer solution, and advantages in using the correct method are discussed briefly.