Volume 48, Issue 10, October 1980
 Letters To The Editor



Universality anyone?
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Physics for the amateur
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Applicability of least‐squares formula
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Review articles for the nonspecialist
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 Editorial


Editorial: Changes in the Journal Format
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 Papers


Confirming the Planck–Einstein equation h v=(1/2)mv ^{2}
View Description Hide DescriptionNote is taken of the implausibility of Planck’s early views and papers on the quantum theory, of the interaction, though not collaboration, of Planck and Einstein in the nascent period of the theory, and of the essential roles played by two crucial experiments—schematically simple but technically formidable in their time—in bringing about the general acceptance of a theory of quanta. In particular, David Webster’s hitherto unreported work in this connection is put on record.

Graphical introduction to the special theory of relativity
View Description Hide DescriptionAn approach to special relativity employing space‐time diagrams and elapsed time intervals recorded by a pair of stationary observers is presented. The conceptual simplicity of the approach does not preclude its use to obtain all of the usual results. The clock paradox as well as a length paradox are discussed as an illustration of the pedagogical technique.

Experimental study of Brownian motion in the limit of small time intervals by means of an ideal gas simulator
View Description Hide DescriptionA simulator of an ideal gas and its use for the study of Brownian displacements in the limit of small time intervals is described. The study was carried out to identify either the Einstein or Ornstein formula as best describing Brownian motion. The results are consistent with the Ornstein formula rather than the familiar Einstein formula.

Minimum and absolute minimum spherical aberration of a simple, thin lens
View Description Hide DescriptionTraditional treatments of third‐order spherical aberration of a thin lens express the results in terms of a function L _{ s }, involving a lens shape factor q and an object‐image position factor p. The function L _{ s } is defined in terms of the difference of the reciprocal paraxial and zonal image distances instead of the difference in distances, which is actually the longitudinal spherical aberration. The treatments show that a lens will have minimum spherical aberration for a shape q determined by minimizing L _{ s } relative to q for a given p. In the present work it is shown that the same lens will actually exhibit smaller spherical aberration for values of p<0 determined by minimizing L _{ s } relative to p. An equation is derived for minimizing the aberration itself, instead of the function L _{ s }, and on the basis of the equation the object‐image distances can be found for which a given lens will exhibit an absolute minimum spherical aberration. The results of the analyses are in good agreement with the results of mathematical ray tracing. also, some interesting graphical properties of the function L _{ s } related to the refractive index of the lens are investigated.

Integral equations and the bound‐state problem
View Description Hide DescriptionAn integral equation for the s‐wave bound‐state solution is derived and then solved for a square‐well potential. It is shown that the scattering solutions continue to exist at negative energies, and when evaluated at the energy of a bound state these solutions do reduce to the bound‐state solution. The bound‐state energies of a square‐well potential are deduced also from orthogonality considerations. Finally, the existence of bound states for an arbitrary short‐range potential is related to the occurrence of zeros of the Jost function or poles of the S matrix for that potential.

Bandwidth and spectrum analysis
View Description Hide DescriptionWhen complex waveforms are analyzed in undergraduate laboratory courses by examining oscillograms from simple resonant circuits, interpretation problems often occur. It is suggested that these problematic oscillograms are explainable by recognizing that typical resonant filters pass significant amounts of several harmonics adjacent to the one intended. The effect of such adjacent harmonics is computed, and the resulting Fourier partial sum compares favorably with oscillographic observation.

Dielectric loss measurements on raw materials
View Description Hide DescriptionThis paper describes a relatively simple experiment which can be performed by undergraduate students to study the dielectric properties of materials. Values of the dielectric loss tangent can be determined at low frequencies from Lissajous figures formed on an oscilloscope. Sample results for mineral rock specimens are presented. Some of these specimens show Debye‐type relaxation peaks at frequencies in the region of 1 to 500 Hz. Such losses can be reasonably represented by an equivalent circuit.

Zero‐point term in cavity radiation
View Description Hide DescriptionWe show that if one accepts the reality of a zero‐point term (1/2)h/ω per normal mode in the spectral distribution of cavity radiation, then the Planck law can be derived with no further nonclassical assumptions; we do this in two different ways, both based on Einstein’s work at the beginning of the century. The argument is intuitive and clarifies some conceptual difficulties; we point out where more elaborate theoretical work is required. A related derivation of the Planck law due to Boyer is examined.

Integrating microcomputers and microelectronics into the physics curriculum
View Description Hide DescriptionThis paper describes a highly successful interdisciplinary microcomputer and microelectronics program offered jointly by the Physics and Computer Science Departments of East Texas State University. The program operates on both the graduate and undergraduate level. The content as well as the structure of the program are discussed.

Reflection of rarefaction wave in one‐dimensional gas flow
View Description Hide DescriptionA one‐dimensional gas flow is generated by a piston which moves at a constant velocity out of a pipe filled with gas. The piston causes a rarefaction wave which is reflected against the closed end of the pipe. According to the theory as described by Landau and Lifshitz the reflection process is governed by the solution of a linear partial differential equation with the adiabatic exponent γ as a parameter. Explicit solutions are obtained for γ=5/3 and γ=7/5, corresponding to the theoretical values for monoatomic and diatomic ideal gases, respectively. In this paper an explicit solution for arbitrary γ is given and applied specifically to the case γ=4/3, corresponding to a polyatomic ideal gas.

Raising and lowering operators and spectral structure: A concise algebraic technique
View Description Hide DescriptionWe show that it is possible to give to any (linear and Hermitian) operator with discrete spectrum, acting on a Hilbert space, a canonical form in terms of the commutator and anticommutator of a pair of adequately constructed raising and lowering operators. This construction enables one to investigate in a very compact way the (discrete) spectrum of the given operator, which becomes determined by a set of consistency conditions. We apply the method to several important problems of quantum mechanics.

Plane electromagnetic waves in material media: Are they transverse waves?
View Description Hide DescriptionWe study the polarizationproperties of electromagnetic waves in material media, such as a solid, a liquid, a gas, or a plasma. The waves are excited by direct incidence of light at the surface of the medium, at an arbitrary angle of incidence. Contrarily to a common misconception, the electric field E, the magnetic field B, and the wave vector q are n o t perpendicular to each other (as is the case in vacuum). In fact, because of dissipative and/or free‐charge effects, these three quantities must be represented by complex vectors. We find that, at any given point, the tips of the electromagnetic vectors Re E and Re B describe ellipses as a function of time. The planes of these ellipses are n o t parallel; neither plane is normal to the direction of the refracted beam (Re q); and Re E is n o t perpendicular to Re B. Thus e l e c t r o m a g n e t i c w a v e s i n m a t e r i a l m e d i a a r e n o t t r a n s v e r s e w a v e s, in general. The only exception is the case of normal incidence of light. In the special case of p(s)‐polarized incidence Re B(E) is linearly polarized and transverse, while Re E(B) has ’’longelliptical’’ polarization. By this we mean that the direction of propagation of the light is p a r a l l e l to the plane of the polarization ellipse (itself parallel to the plane of incidence).

Concepts of nonequilibrium thermodynamics in discrete model of heat conduction
View Description Hide DescriptionExamples of thermodynamic evolutions toward stationary states are exhibited in a one‐dimensional heat conduction problem. A computer simulation technique is employed to solve the Fourier partial differential equation and compute the evolution of the three terms in the entropy balance equation. Some concepts of linear nonequilibrium thermodynamics are analyzed in the framework of the model: the meaning of the entropy balance equation, the disticntion between free and fixed forces, the role of the Onsager’s relations, and the relationship between the structural adaptation of a linear system to the externally imposed constraints and the entropic concept of ’’order.’’

Experimental studies of the He–Ne laser: resonators and self‐locking
View Description Hide DescriptionHe–Ne laser experiments suitable for an undergraduate laboratory are described. The topics covered are cavity stability, self‐mode‐locking coherent interactions between pulses and laser medium, and spontaneous transverse mode locking.
