Volume 40, Issue 9, September 1972
 PAPERS


NonDispersive Mirror Wavepackets
View Description Hide DescriptionWe argue for greater use of the nodispersion approximation in introductory courses on quantum mechanics for the following two basic reasons: (i) the approximation yields in many situations a simple serniclassical picture of the time development of localized wavepackets; (ii) it makes explicit the fundamental importance of phase relations in the quantum model.

Electromagnetic Induction: A ComputerAssisted Experiment
View Description Hide DescriptionMinimal equipment is used in a sophomore laboratory experiment demonstrating Faraday's Law. A complicated mathematical expression for the induced EMF is solved with an electronic desk calculator or computer for comparison with experimental results. Data are given for a typical experiment.

Signal Averaging at Modest Cost
View Description Hide DescriptionWe describe how to perform signal averaging using a multichannel analyzer without internal modification. It thus becomes possible to average signals with the aid of “borrowed” equipment. Required equipment, in addition to a multichannel analyzer, consists of approximately $100 worth of transistor circuitry and a voltage to frequency converter.

Satyendranath Bose: CoFounder of Quantum Statistics
View Description Hide DescriptionSatyendranath Bose's recognition of the fact that the photons in a cavity radiator are indistinguishable led him to a derivation of the Planck law free from any assumptions of classical electrodynamics. His result, published in 1924, was a significant vindication of the photon concept that Einstein had championed since 1905. It also laid the foundations of quantum statistics, as was freely acknowledged by Einstein and Dirac, among others. Various aspects of Bose's career, including his apparent failure to understand the full implications of his work, may be of interest both to physicists and historians of science.

The ProductIntegral Calculus Formulation in Quantum Mechanics
View Description Hide DescriptionIn this paper we investigate the advantages of using the productintegral calculus rather than the usual successive approximation perturbative expansion in three branches of quantum physics. The mathematics of the calculus is fully developed, and its superiority over the perturbative expansion is explored in specific examples from physics. All of timedependent perturbation theory in quantum mechanics can be written in terms of the calculus, as well as the most general solution for the density operator in quantum statistical mechanics.

A Simple Approach for the Calculation of Energy Levels of Light Atoms
View Description Hide DescriptionConsiderable insight into elementary atomic theory is generated by constraining the atomic Hamiltonian of atoms with few electrons by demanding that the electrons be as far apart as possible. This and other simplifying assumptions allow us to separate Schrödinger's equation by reducing the problem to a geometrical analog. The analogous problem is to locate dots symmetrically on the surfaces of concentric spheres consistently with the Pauli principle and with the dots as far apart as possible. The resulting equations permit calculation of effective nuclear charges which are used to find the total energy of the system from a hydrogenlike energy formula. The energies so determined are compared to experimental values, and derived screening terms are compared to those of Slater's rules. Our energies are consistently lower than experimental values. Several unanswered questions opened by this technique are proposed as possible further research on a level suitable for an undergraduate paper.

A Different Proof of the MaxwellBoltzmann Distribution
View Description Hide DescriptionThe MaxwellBoltzmann Distribution (MBD) for a classical ideal gas is obtained as the mean over phase space of the number of momentum components less than some value p, without making any assumptions beyond those implicit in the microcanonical ensemble. The variance of the fluctuations of actual distributions of the momentum around the average given by the MBD is shown to go to zero as , where is the number of particles. This proof of the MBD has the advantage over the usual type of proof in that it does not employ a subdivision of phase space into cells, a trick which gives rise to certain difficulties discussed in the introduction. Moreover, it is more complete in that the problem of the fluctuations is treated at an elementary level.

The Resistive Net and FiniteDifference Equations
View Description Hide DescriptionThe application of finitedifferenceequations in the solution of repetitive multiloop resistive circuits in oneand twodimensional configurations is discussed in both finite and infinite cases. The technique of solution involves only ordinary algebra and trigonometry. Yet one can see the emergence of simple orthogonal functions and the finitedifference approximations of the CauchyRiemann equations and Laplace's equation.Boundaryvalue problems can be presented and understood at a simple level of physics and mathematics. Such repetitive structures can serve as discrete approximative models for various physical properties of continuous media. The implications for the teaching of boundaryvalue problems in electricity are brought out.

Energy Quantization and the Simple Harmonic Oscillator
View Description Hide DescriptionTwo methods for obtaining the ladder spectrum characteristic of the simple harmonic oscillator are widely used in elementary quantum mechanics. In the first method, that of series solution, quantization is shown to follow from the requirement that the wave function be normalizable. In the second, it is common to derive quantisation in an operator formalism based on factorization of the wave equation. In this latter method the role of normalizability is not customarily discussed. We show explicitly that the same boundary condition implicit in the operator manipulations leads to quantization in both methods.

A Special Class of Ideal Quantum Gases
View Description Hide DescriptionThis essay is motivated to add a useful note to the contemporary literature of ideal gases. For brevity, a new description is given for a special class of ideal quantum gases (the “qsuper ideal gases”) which are characterized here by two compact equations of state. Within such a framework all fundamental properties of these gases are readily expressed in terms of two constants known as the state indices. In order to test our results of deduction, six typical examples are given with comparable numerical values. While all the examples must otherwise have resort to statistical calculations, our evaluation for them turns out to be straightforward as well as heuristic.

Neutron Diffusion as a Random Walk Problem
View Description Hide DescriptionThe onedimensional random walk problem has been generalized to allow for absorption at lattice sites, and then this technique has been used to study one velocity neutron diffusion. We show that most of the results that are normally obtained by solving the diffusion equation under appropriate boundary conditions, can be obtained directly. Various special cases have been considered, including leakage from a finite lattice and neutronwave propagation in an infinite lattice.

A Unique MS Program for Graduates of FourYear Colleges
View Description Hide DescriptionA large and increasing gap exists between the level and sophistication of the physics encountered by a student in his undergraduate work at a fouryear college with no graduate program and the level and sophistication of the physics with which he must work in the PhD program of a large university. In order to help bridge this gap, Wichita State University designed an MS program especially for graduates of fouryear colleges, with the intention of preparing them for PhD study at larger universities. This article describes the workings and results of the program and gives some insight into the planning of students for their careers in physics.

A New Emphasis in Diffraction Theory and Experiments
View Description Hide DescriptionScalar diffraction theory is usually presented as a closed subject in current textbooks. Actually, the theory is extremely unsettled and open to original investigation, and the authors feel that student understanding and motivation could be significantly enhanced if the problematic nature of the theory were stressed. With this in mind, the Kirchhoff, Huygens and Rayleigh theories are reviewed, emphasizing the fundamental inconsistencies and contradictions which are often ignored. Instructive and provocative experiments are then described which confirm the unwarranted success of the theoretical solutions under extreme conditions. The investigations are based on the diffraction of microwaves by a circular aperture, and are on a level suitable for undergraduate work.

Poincaré's Rendiconti Paper on Relativity. Part III
View Description Hide DescriptionThis is the concluding part of a modernized rendition of Poincaré's Rendiconti paper on relativity, of which the first two parts appeared in the November 1971 and June 1972 issues of this Journal. It covers the last section of that paper, in which Poincaré develops in masterful, even if incomplete, fashion, a generalization of Newtonian gravitational theory, involving retarded actionatadistance interaction that is covariant under the Lorentz group. As the first such attempt it is of obvious historical significance. In addition, just as the first two parts, so this part, too, contains material of independent interest to the historian of the genesis of special relativity.

A Computer Simulation for the Study of Waves
View Description Hide DescriptionThe computer program described, designed for use in the second quarter of the beginning course for science and engineering majors at the University of California, Irvine, simulates an experimental investigation of a pulse in a rope. The student is provided with a “measurement” facility: If he enters time and position he is told the rope displacement. His problem is to discover enough about the disturbance to answer numerical questions about its behavior. Auxiliary facilities such as plotting and listing are provided. Checks are made as to the reasonableness of the student strategy, and suggestions are given based on these checks. It is hoped that through this simulation students can in many cases “discover” the preservation of “shape,” the dependence of the pulse.

An Illustrative Example for the Undergraduate Thermodynamics Curriculum
View Description Hide DescriptionIntrinsic disorder of a simple type is discussed and recommended for inclusion in the undergraduate thermodynamics curriculum as a practical example. The concentration of intrinsic defects is calculated as a function of temperature. The dc conductivity and diffusion coefficient are also examined.

Keller vs Lecture Method in General Physics Instruction
View Description Hide DescriptionA description of the use of the Keller method of instruction in a general physics class of 100 students is presented. This teaching technique is critically evaluated by comparing the performance of the students in the program with that of 100 students in a concurrent control group run by the traditional lecture method. It is found that performances are not significantly different and the cost of running the program is not excessive. Furthermore, student reaction to the program is found to be quite favorable.

A Statistical Experiment Using Resistors
View Description Hide DescriptionIn undergraduate laboratories we frequently ask the student to use error theory to evaluate his results without giving him the opportunity to measure and analyze a large statistical sample to see how well it follows theoretical models. In the experiment described here, the student investigates the statistics of a set of resistors. In the process he gets some practice in the use and interpretation of histograms, and gains some insight into the relation of the Gaussian error curve and a real statistical distribution as well as the significance of standard deviation and standard error..

Image Location and Magnification in Holography
View Description Hide DescriptionA method is presented for determining the location and magnification of images formed by holographicreconstruction. The method is based upon the similarity between a hologram and a zone plate. An undergraduate student familiar with introductory optics should be able to understand the method presented.

Phase Waves of Louis deBroglie
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