Volume 52, Issue 9, September 1984
 Papers


Elementary derivation of the wake pattern of a boat
View Description Hide DescriptionAn elementary derivation is given for the shape of the wake pattern of a boat traveling at constant velocity in deep water. We find essentially the same results as those found in standard treatments, but our mathematics is easier. All results follow from the fact that the group velocity is half the phase velocity.

Forging, cooking, trimming, and riding on the bandwagon
View Description Hide DescriptionRecent accusations of scientific fraud have raised serious questions both for science policy and science itself. If experimental results cannot be trusted then science becomes virtually impossible. Four cases from twentieth‐century physics are examined to see if the normal procedures of science provide adequate safeguards against fraud. I conclude that repetition of experiments, particularly for those of theoretical importance, does provide a sufficient safeguard.

An up‐to‐date approach to physics
View Description Hide DescriptionA unified approach to science teaching based upon a certain class of quantities which play fundamental roles in classical and modern physics is introduced. These quantities share the property of being substance‐like, that is, each can be pictured to be contained in bodies and to flow from one body to another like a kind of ‘‘stuff.’’ Such quantities include, for example, energy (=mass), momentum, angular momentum,electric charge, particle number (=amount of substance), and entropy. When emphasizing substance‐like quantities, the breakup of physics into sub‐branches is nothing more than a classification of natural processes according to the substance‐like quantity playing the dominant role in each case. The method of presentation, however, remains the same from one sub‐branch to another: different natural processes can be simply visualized and quantitatively described according to the same formal rules in terms of the increasing, decreasing, and flowing of the respective substance‐like quantities in each case. Thus knowledge of a single branch of physics already provides an analogy for the ways and means by which processes are described in other branches (including chemistry and biology) as well. These claims are illustrated with the help of a few simple examples.

Inexpensive demonstration of an anharmonic oscillator
View Description Hide DescriptionA simple circuit comprising an operational amplifier and an R C feedback network is configured into a resonant circuit. It behaves as a simple harmonic oscillator for small input signals and changes to an anharmonic oscillator when slew limiting occurs. The circuit is analyzed and the theoretical gain is compared to experimental data for the two cases.

Modification of the general theorem of equipartition: Application to the relativistic ideal gas
View Description Hide DescriptionAccording to the general theorem of equipartition 〈χ∂H/∂χ〉=k T, where χ is any appropriate coordinate or component of momentum. More generally, if f is any suitable function of the coordinates and momenta 〈 f∂H/∂χ〉=k T〈∂f/∂χ〉. This relation is used to obtain by elementary means relations describing the dependence of the energy of a relativistic ideal gas upon the parameter k T/m c ^{2}.

Elementary approach to scattering theory
View Description Hide DescriptionExpressions for the time‐dependent scattering wave function,S‐matrix elements, and the transition rate are derived using simple time‐dependent perturbation theory as it is presented in elementary quantum‐mechanics texts.

Classical approach to the problem of an electron in a periodic potential
View Description Hide DescriptionMotion of an electron in a periodic potential is analyzed with use of a simple classical model. A calculation and a demonstration experiment described show the usefulness of the model in the teaching of solid‐state physics.

Aspects of scientific method in the natural sciences—physics
View Description Hide DescriptionIn this paper the distinction between ‘‘science’’ and ‘‘nonscience’’ is considered, and the essential ingredients which characterize scientific method such as the construction of models, hypotheses, theories, and paradigms in the physics enterprise are discussed.

Coriolis acceleration: A laboratory experiment
View Description Hide DescriptionUsing a common laboratory apparatus and a spark timer, consecutive positions of a moving object with respect to time in a rotating frame of reference can be obtained. Experimental data are analyzed by means of a simple graphic method, directly based on the vectorial definitions of mean velocity and acceleration. Thus the Coriolis acceleration vector can be directly obtained on every point of the trajectory and the relation for the Coriolis acceleration can be clearly verified.

Unified formulation of quantum and statistical mechanics
View Description Hide DescriptionUsing one and the same simple variational principle for average energy, a new equation is obtained equivalent to the set of two equations: the time‐independent Schrödinger equation and that describing canonical Gibbs distribution.

Experimental picture of the band structure formation in a solid
View Description Hide DescriptionAn experimental illustration of the formation of a band structure in a solid is presented. It is based on the structure analysis of the x‐ray excited photoelectron valence bandspectra recorded for a series of molecules with increasing length, the linear normal‐alkanes (C_{ n }H_{2n+2} , where 1≤n≤∞). This experiment shows how a single atomic carbon 2s electronic level evolves to molecular orbitals, and then to a band, as the number n of carbon atoms increases in the molecule and simulates at the end a 1‐D solid. It is thought that such a simple picture might help to understand and illustrate a solid state physics course about band structures.

Solitons in a wave tank
View Description Hide DescriptionA wave tank experiment (first described by the nineteenth‐century engineer and naval architect John Scott Russell) relates a linear eigenvalue problem from elementary quantum mechanics to a striking feature of modern nonlinear wave theory: multiple generation of solitons. The tank experiment is intended for lecture demonstrations.

Self‐catalysis in solid hydrogen—A computer simulation
View Description Hide DescriptionWe describe a Monte Carlo simulation of self‐catalysis of orthohydrogen molecules in solid hydrogen in one‐ and two‐dimensional lattices at low temperatures in the absence of molecular diffusion. The problem is useful for illustrating the importance of lattice geometry and near neighbor relationships in such calculations. The simulations were performed on a small computer and may be of use in teaching Monte Carlo techniques.

Electrostatic energy when dielectrics are present: A general integral approach
View Description Hide DescriptionA detailed discussion of electric energy storage in the presence of dielectrics is presented. The discussion is general and is aimed at the introductory–intermediate levels, when an integral representation of the laws of electrostatics is more familiar to the student. The case where a discrete set of point charges is slowly transported into the vicinity of an arbitrary dielectric is first considered and then an extension to the continuous distribution is presented. A simple model of atomic polarization is introduced and used to illustrate dielectric nonlinearities and the concept of self‐interaction. It is shown that the energy density E⋅D/2 is restricted to the case of linear dielectrics and a novel way of introducing Maxwell’s displacement current term at a more advanced level is suggested as a natural extension of the electrostatic case.

Time‐dependent theory of alpha decay
View Description Hide DescriptionUsing Green’s function techniques a time‐dependent theory of α decay in the standard one‐body model is developed. Formulas are obtained for the decay rate and α energy. These formulas are combined with experimental information to show that to a good approximation the i n i t i a l α‐particle wave function vanishes on or near the nuclear surface.

Study on diffusion and recombination of minority carriers by the method of photoconductive decay
View Description Hide DescriptionThis paper describes an experiment relating to the diffusion of charge carriers in homogeneous semiconductor material.Diffusion theory, as outlined in this paper, is applied to deduce from measurements a quantity called the bulk lifetime of excess minority carriers: a quantity which is independent of the size, shape, and surface condition of the semiconductor sample. Because of this independence, the bulk lifetime is used as one of the characterizing quantities of semiconductor material. In performing this experiment, the student will gain a working knowledge of diffusion theory as applied to semiconductor carriers, and at the same time become acquainted with an important technique for the characterization of semiconductor material. The actual duration of involvement will depend upon the amount of setting up of equipment, sample preparation, etc., that is expected of the student. An oscilloscope of fast rise time (200–MHz bandwidth), and a xenon flash tube with pulse duration of a few microseconds (General Radio 1542‐B electronic stroboscope is a proven possibility), are the major items of equipment needed.

A recursive method for solving the Schrödinger equation
View Description Hide DescriptionA recursion equation for computing the total reflectance amplitude from a given potential is derived. It is shown that the poles of the total reflectance amplitude are the bound eigenvalues of the problems. The method avoids complicated boundary value problems usually encountered in computing the bound eigenvalues of the Schrödinger equation. The utility of the method is demonstrated by two examples. A simple algorithm for the numerical approach is derived. Finally the physical meaning in terms of standing waves is discussed.
