bluuebunny/crossref_metadata_2025 huggingface dataset:
The Mercury-Drag Effect, a Demonstration of Transport Phenomena
Authors: Martin D. H. , Teese R. B.
Published: August 2005

A demonstration of the mercury-drag effect is presented as an example of transport phenomena in dilute gases, in which one gas or vapor diffuses through a second gas, creating a viscous drag on this gas. In the demonstration, mercury vapor from a pool of liquid mercury diffuses through nitrogen gas (pressure 10−5–10−4 Torr), passing through tubes of two different radii (0.69 and 0.33 cm) to liquid nitrogen-cooled cold traps. The pressure changes of the nitrogen gas on the mercury-deficient side of the cold traps is observed and compared with theoretical and experimental values from the literature. Possible reasons for differences are discussed.
Electron Eigenstates in Uniform Magnetic Fields
Authors: Rensink Marvin E.
Published: August 2005

The purpose of this paper is to show in detail how the electron energy-eigenvalue spectrum changes from the form εB = (N+12)ħωc+Pz2/2M in a finite magnetic field to the free-particle form ε0 = P2/2M in zero magnetic field. We consider an electron confined to a “box” of finite volume and calculate the exact eigenstates for arbitrary magnetic field strengths. When the electron cyclotron radius rc = (2ħ/Mωc)1/2 is small compared to the dimensions of the box, we get the spectrum εB, and when it is large we get ε0. The key to this demonstration is a mathematical identity which relates the magnetic eigenfunctions to the free-particle eigenfunctions. Magnetic corrections to the spectrums ε0 are obtained without the use of quantum mechanical perturbation theory.
Response of Ideal Circuit Elements to Sinusoidal Excitations
Authors: Zaky A. A. , Lisboa C.
Published: August 2005

Some of the ambiguities inherent in most textbook presentations of the response of purely resistive, inductive, or capacitive circuit elements to sinusoidal excitations are discussed. Only by analyzing explicitly the difference between ideal and real circuit elements can the student obtain a clear picture of why inductive and capacitive circuit parameters behave as they do in the sinusoidal steady state.
The Generalized Ohm's Law when the Gyro Frequency Exceeds the Collision Frequency
Authors: Browne P. F.
Published: August 2005

The generalized Ohm's law for a partially ionized gas in the case when the gyro frequency exceeds the collision frequency is derived by consideration of the external force drifts of guiding centers. When the opposition to the electric drift comes from collisions with non-drifting neutral atoms, a chain of reactions develops, causing currents alternately in the direction of the electric field and in the direction of the drift. The currents form geometric series, which are summed.
The Symmetry Number in Classical Statistical Mechanics
Authors: Nishioka Kazumi , Pound G. M.
Published: August 2005

The quantum statistical treatment of the symmetry number is briefly reviewed in the Introduction for comparison with the classical statistical treatment. The concept of a localized system is discussed as a convenient method to calculate the classical partition function. The symmetry number in classical statistical mechanics is then defined, and it is applied to some examples. The classical phase integral is discussed as a limiting case of the canonical partition function in quantum statistical mechanics in the Appendix in order to make the meaning of the classical phase integral clear with respect to identity of particles, which is needed for the present purpose.
Polarization of Thermal Radiation in a Symmetric Cavity
Authors: Boudreau Robert D.
Published: August 2005

Formulas are derived for expressing the state of polarization of thermal radiation in an axially symmetric cavity. These formulas are then used to demonstrate that thermal emission from the cavity is unpolarized when the cavity is in thermodynamic equilibrium and that any state of polarization may exist in a diathermanous medium which is enclosed by perfectly reflecting walls. It is also demonstrated that formulas which prescribe the emittance or reflectance of the cavity, neglecting polarization effects, are inherently erroneous.
An Undergraduate Experiment on the Analysis and Synthesis of Musical Tones
Authors: Kammer D. W. , Glathart J. L.
Published: August 2005

A description is given of an experiment involving the analysis and synthesis of musical tones suitable for the laboratory of a beginning calculus-level physics course. Musical tones are recorded, and the waveforms, obtained photographically, are subject to Fourier analysis. The tones are reconstructed graphically and aurally by use of several audio oscillators and compared to the original tones.
A Course on the Physics of Urban and Environmental Problems
Authors: Marston Edwin H.
Published: August 2005

A physics course for social scientists is described. It presents the physics usually taught in a physical science course for liberal arts majors within the context of several urban and environmental problems. The problems considered include transportation, air pollution, thermal pollution of water, and scarcity of resources. They are analyzed in a physical, quantitative way, but in addition the legal, political, and social aspects are presented and discussed.
Secondary Structure in High-Energy Scattering Amplitudes
Authors: Harrington David R.
Published: August 2005

The dependence of the high-energy large-angle scattering amplitude on the detailed shape of the partial wave distribution or impact parameter shape factor is considered. Transformations of the partial wave series and impact parameter representations are derived which make explicit the dependence on the “smoothness” of these shapes. The transformations are also used to construct examples of partial wave distributions and shape factors leading to analytic expressions for the scattering amplitude showing clearly the dependence on the “surface thickness” of the distributions.
Frequency Shifting of Light by means of a Kerr Cell
Authors: Burdette Ernest L. , Hughes Gordon
Published: August 2005

A frequency shift was produced in a He-Ne laser beam by a time dependent change in the index of refraction of a Kerr cell. The shift was detected by measuring the beat frequency obtained by combining the parallel and perpendicularly polarized components of the laser beam transmitted by the cell. A beat frequency varying between 19 and 2 sec−1 was noted.
Comparison of Correlated Wave Functions in the Helium Sequence
Authors: Mires Raymond W.
Published: August 2005

The method of calculating ground state energies of heliumlike atoms by use of a variational wave function is well known. The usual procedure is to start with an uncorrelated wave function multiplied by a correlation factor containing several variational parameters. The variational principle is then used to determine the parameters which give minimum energy. It has been the practice to use the same uncorrelated function and then compare the results when several different correlation factors were used. In this work, the same correlation factor is retained, and the effect of using two different uncorrelated functions is investigated. The correlation factor used was 1+c1r12+c2(r1−r2)2, where c1 and c2 are variational parameters. The uncorrelated wave functions used were hydrogenic functions and Hartree-Fock functions. Results are presented for the He-like ions with Z = 2−10, and it will be seen that the hydrogenic functions give the best results when electron correlation is included.
Paragas
Authors: Ben-Abraham Shelomo I.
Published: August 2005

A hypothetical gas of identical spinless particles obeying r-parastatistics is dealt with. The method allows a unified treatment of both the Fermi and the Bose gases. The partition function, the equation of state, and the thermodynamic functions are simple generalizations of those for the physical quantum gases, which are included as special cases. All paragases have a Fermi energy and a Bose-Einstein condensation. A quantitative criterion of degeneracy for the physical quantum gases is proposed. The fluctuations of occupation numbers and density are also discussed. Expansions for high and low temperatures are given to third order.
Demography and Thermodynamics
Authors: Fein Elihu
Published: August 2005

The use of physics for demographic analyses is not a form of alchemy. A brief reflection on the use of abstract structures to organize knowledge suggests a commonness to both social and physical science. Population distribution is examined using the structure of thermodynamics.
White Light Fringes Obtained with the Michelson Interferometer
Authors: Young P. A. , O'Connor D. E.
Published: August 2005

Circular white light fringes are seen when a dispersing medium is placed in one arm of a Michelson interferometer. A formula for the number of fringes as a function of the bandwidth of the source and the dispersion of the medium is obtained which agrees well with experiment. The phenomenon has been made into a student experiment on wave groups.
An Individualized Approach to Introductory Physics
Authors: Rigden John S.
Published: August 2005

Introductory physics courses are typically specialized in that they are designed for a very specific audience; physics majors, premeds, liberal arts students, etc. The categories are numerous. Further, these courses are usually highly structured with homework assignments, laboratories, and lectures establishing the cadence. The majority of students respond by progressing in lock-step fashion through the course. In this course at tne University of Missouri—St. Louis, there is no specialized audience and there is no cadence—more correctly, the cadence is drastically muted. The students supply the rhythm as the learning of physics is made an individual matter. A variety of learning devices are made available, and the student opts those that hold promise for him. No attempt is made to survey the subject of physics; rather, two major topics form the subject content. One of these topics is developed in a quasihistorical fashion to give the student some feel for physics in its verb sense. The conceptual structure of physics is sweepingly potent and alluringly intelligible—this course is designed to convey these facts.
Nuclear Magnetic Resonance Line Shapes in Solids
Authors: Parker G. W.
Published: August 2005

The local field model introduced by Bloembergen, Purcell, and Pound is shown by direct calculation in a specific case to produce a Gaussian local field distribution which shape is often characteristic of nuclear magnetic resonance lines in solids. That this result is obtained is shown to be due to the fact that the binomial distribution describes the local field distribution of a system of spin 12 particles provided they are more or less uniformly distributed in space and that there is a sufficiently large number of them. In the limit of a large number of spins this distribution is known to become Gaussian in shape so that the local field model can be said to predict a Gaussian line shape under rather general conditions.
A Note on Certain Integrals Which Appear in the Theory of the Ideal Quantum Gases
Authors: Hill Robert Nyden
Published: August 2005

Integrals of powers of the energy over the Bose-Einstein and Fermi-Dirac distributions are special cases of Lerch's zeta function. As a consequence, various results for these integrals follow directly from results recorded in the mathematical literature on special functions. The low-temperature series for the Fermi-Dirac case is considered as an example and derived from results recorded in the Bateman project. Alternative rigorous derivations of this series, useful for classroom presentation, are also given.
Propagators
Authors: Terrall J. R.
Published: August 2005

This is a straightforward discourse that starts with a radio antenna and winds up with the propagator for Dirac particles. From the radio antenna we obtain the physical idea of a propagator and show its nature for Klein-Gordon particles (with photons as a special case). Then, from the Klein-Gordon propagator we easily obtain the propagator for Dirac particles, merely by imposing what might be called the “Dirac condition.” We hope the approach has simplicity and physical appeal.
Anniversaries in 1970 of Interest to Physicists
Authors: Barr E. Scott
Published: August 2005

During the year 1970 there are major anniversaries of the birth or death of seven men whose accomplishments and influence have been of importance to the development of physics. They are: Alexandre Edmond Becquerel, Henry Andrews Bumstead, Heinrich Gustav Magnus, Jean Baptiste Perrin, William John Macquorn Rankine, Simon Stevin, and John Tyndall. Brief accounts of their careers are given here.
Removing the “Cook Book” from Freshman Physics Laboratories
Authors: Prescott J. R. , Anger C. D.
Published: August 2005

A freshman physics laboratory is being developed, in which an attempt has been made to eliminate as far as possible the type of experiment with detailed instructions, commonly known as the “cook-book” variety. The experiments fall into groups that form integrated sequences, e.g., “measurement,” “two-dimensional motion,” and “circuit elements.” Frequent reference is made back to the results found in earlier laboratory periods. Students are encouraged to devise their own experimental designs, within the framework of the equipment provided, which is kept simple enough for this to be practicable. While explicit instructions are rarely given, each laboratory exercise is accompanied by a number of leading questions that are intended to guide the student in deciding how to design and execute his experiment and interpret his results. Student reaction is favorable, but a significant amount of time must be devoted to training of the graduate teaching assistants who participate in the course.
Introduction of Special Physics Topics (Geophysics) through the Use of Physics Laboratory Projects
Authors: Parker R. H. , Whittles A. B. L.
Published: August 2005

A method is presented in which topics of a direct technological application are studied by students in technology taking a general physics course. It is found that student motivation is enhanced, and their interest in the over-all course increased, by such a presentation. The development of the specific laboratory projects also gives the staff member of a technical teaching institute the opportunity to spend some time on work close to his own field of specialization. A list of the project labs is available, and specific comments on an example of each of three types offered (paper, bench top model, and field) are given.
An Instructive Example of the Sudden Approximation in Quantum Mechanics
Authors: Schlitt D. W. , Stutz C.
Published: August 2005

Some features of the sudden approximation are examined and applied to the example of a particle in a suddenly expanded box. Among the points illustrated are the form of the work energy relation in quantum mechanics, the application of the energy-time uncertainty relation, some pitfalls in the use of theorems that apply only to Hermitian operators, and the periodic time-dependence of expectation values.
Factorization in the Production of Resonances Having Spin
Authors: Resnick L.
Published: August 2005

In the production and decay of a spinless resonance or unstable particle, a factorization of the amplitude for the process is intuitively clear and is useful for phenomenological analysis. The intuitive picture in the case of a resonance having nonzero spin is less clear. It is shown under what conditions an equivalent factorization occurs in the cross section for this latter case.
On the Fundamental Equations of Electromagnetism
Authors: Hauser Walter
Published: August 2005

A corollary of Helmholtz's equation for four-vectors is shown to facilitate the derivation of Maxwell's equations.
Relativistic Quantal Oscillator
Authors: Lipas P. O.
Published: August 2005

The Klein-Gordon equation is solved approximately for the three-dimensional harmonic-oscillator potential. Mathematically, the radial equation has the form of the nonrelativistic equation with an r4 anharmonic term added. We carry the calculation to lowest relativistic order and get an energy spectrum with the following, intuitively expected, features: the level spacing decreases with increasing energy and the l degeneracy is broken. The same result is also obtained by putting the relativistic kinetic energy into the Schrödinger equation and expanding in p2.
Use of an Operational Amplifier for Measuring Magnetic Flux Densities
Authors: Gordon J. E. , Marín M. Javier
Published: August 2005

A search coil which is connected to the input of an integrating operational amplifier can be used to measure magnetic fields with an accuracy which varies from 3%–4% at 10 G to 1%– 2% at fields of 1 kG or more. The apparatus is inexpensive, compact, and easy to operate. The method can also be used to study the magnetic properties of paramagnetic and superconducting materials.
The Effective Mass of an Oscillating Spring
Authors: Fox J. G. , Mahanty J.
Published: August 2005

We have calculated the effective mass of the spring in an oscillating mass-spring system. It varies from 4/π2 to 13 the mass of the spring as the suspended mass varies from 0 to ∞. This and the various predicted modes can be easily verified experimentally.
Supplementary Note on Brownian Motion
Authors: Bess L.
Published: August 2005

A modified Fokker-Planck equation is derived to describe Brownian motion for the case of large viscosity. The derivation uses the quasi Huygens relation developed by Chandrasekhar as a starting point. The modified relation is shown to be capable of directly yielding the Smoluchowski equation. Moreover, the momentum-conservation equation to which it gives rise is also investigated.
Aharonov-Bohm Effect—Quantum Effects on Charged Particles in Field-Free Regions
Authors: Erlichson Herman
Published: August 2005

The Aharonov-Bohm effect is relatively little known, but it poses fundamental questions in quantum theory. It concerns physical effects on charged particles in field-free regions. The present paper provides an over-all critical review and commentary on the literature of the Aharonov-Bohm effect. The two fundamental questions raised by the effect concern the role of the force concept in quantum mechanics, and the localizability of physical effects principle. A recent letter from Professor Bohm concerning his evaluation of the significance of the effect is included in the Appendix.
Foucault Pendulum Experiment by Kamerlingh Onnes and Degenerate Perturbation Theory
Authors: Schulz-DuBois E. O.
Published: August 2005

The paper pays homage to H. Kamerlingh Onnes by pointing out that he constructed the first properly functioning model of the Foucault pendulum. His success was largely due to an analysis which takes into account the unavoidable mechanical asymmetry of the pendulum. Based on the analysis he was able to eliminate the asymmetry and to obtain the desired performance which earlier workers had realized only to a limited extent. Onnes' analysis is reproduced with more modern tools such as vector notation and, especially, the concept of eigenfunctions. His analysis is probably one of the earliest examples of a particular type of doubly degenerate perturbation theory. Two different effects compete for lifting the degeneracy, one favoring “circular polarization,” the other “linear polarization.” The resulting eigenfunctions represent “elliptical polarization.” The tutorial significance of this perturbation theory is emphasized by mentioning other fields where it is applied if perhaps disguised by a different jargon and analytic technique. Examples include electromagnetic theory (microwave cavities for circular polarization), laser optics (mode analysis of ring lasers for rotation sensing), and quantum theory (quenching of orbital angular momentum by crystalline field).
Energy and Observables in Electromagnetic Theory
Authors: Janis Allen I.
Published: August 2005

A comparison is made of two ways of introducing auxiliary variables into Maxwell's equations. The first is the usual introduction of potentials. The second introduces twice the usual number of potentials. Although both formalisms lead to the usual vacuum-field equations when expressed in terms of the original variables (the components of the electromagnetic field tensor), they are found to describe physically distinct theories. It is seen that the second formalism leads to a different stress-energy tensor and to the prediction of new observable quantities, which apparently have no counterpart in nature.
Special Relativity and Diagonal Transformations
Authors: Parker Leonard , Schmieg Glenn M.
Published: August 2005

We discuss the form of the special Lorentz transformation, and the corresponding transformation of the electromagnetic field, in which the transformation matrix is diagonal. We derive the diagonal form of the special Lorentz transformation directly, in a simple way, and show that it is sometimes more convenient to apply than the algebraically equivalent conventional form of the transformation. The convenience is especially evident in deriving the linear Doppler effect, and the relativistic addition of more than two parallel velocities. By writing Maxwell's equations in terms of linear combinations of coordinates which have simple transformation properties, we arrive at the transformation equations of the Maxwell fields in a diagonal form, as well as at the plane wave solutions, in a natural manner. The derivations and applications described above should be of use in a course on relativity because of their simplicity and directness.
Simplified Microwave Frequency Electron Spin Resonance Spectrometer
Authors: Rupp L. W. , Walsh W. M. , Steinfeld Allan
Published: August 2005

A self-oscillating microwave frequency spectrometer incorporating a solid-state Gunn diode is described. Its simplicity, sensitivity, and relatively low expense make it suitable for instructional laboratory use.
On Statistical Analysis in the General Physics Laboratory
Authors: White Locke
Published: August 2005

Most general-physics laboratory manuals and textbooks give inadequate and/or erroneous procedures for assessing the validity of experimental data. This paper advocates a procedure both less time consuming and more rewarding than those usually recommended for general physics laboratories. It uses the range of the results of a limited number of repeated measurements to obtain confidence limits about the probable over-all average of repeating the same procedure a great many times. This procedure is well established among statisticians, but appears not to be well known to physicists.
Lorentz Transformation of Thermodynamic Quantities
Authors: Yuen C. K.
Published: August 2005

In this paper we review the recent controversy concerning relativistic thermodynamics. The diversity of viewpoints can be attributed to the numerous ways in which thermodynamic quantities are defined. The advantages of each approach are discussed.
Four Electromagnetic Shock Tube Experiments to Demonstrate Some High-Temperature High-Speed Flow Phenomena
Authors: Scholz P. D. , Anderson T. P.
Published: August 2005

Four experiments are discussed that demonstrate some basic phenomena associated with electromagnetic shock tubes. The experiments utilize simple techniques and are appropriate for a senior level or first year graduate course in experimental physics or gas dynamics. The experiments include determining the spark breakdown characteristics of the shock tube electrodes, the local shock speed, the local average electrical conductivity of the driver gas, and the stand-off ratio of a hypersonic shock wave formed around a spherical blunt body. Each experiment, with the exception of the first, is supported by a first-order theory. Sample results of each experiment are included that indicate that the simple theoretical models qualitatively agree with the experimental results. The experiments are neither inclusive nor closed ended and can provide a continued source of challenge to inquisitive students.
Invariance and Conservation Laws for a Classical Relativistic Particle
Authors: Denman Harry H. , Kiefer Harold M.
Published: August 2005

The general equation of motion of a classical relativistic particle, moving in one dimension, is examined to determine what results are implied by the invariance of this equation to a number of well-known space-time transformations, i.e., the space and time translations, scale changes and inversions, and the Lorentz transformations. While the invariance of the equation to a translation or Lorentz transformation alone generates a conservation law, invariance to the others does not. Conditions on the Lagrangian describing the system for invariance to these transformations are also given. While invariant Lagrangians yield equations of motion with the same invariance, Lagrangians exist that are not invariant to certain transformations but that produce invariant equations of motion. For the Lorentz transformations, the invariance of ∫Ldt is also examined. Further, it is shown that invariance of the equation of motion to Lorentz transformations provides a definition of the relativistic linear momentum that is independent of the Lagrangian or any assumed conservation law.
A Note Concerning Dispersion Forces between Neutral Molecules
Authors: Brown J. S.
Published: August 2005

An explicit expression is obtained for the dispersion force between neutral molecules including retardation, based on the integral relation first proposed by Casimir and Polder. It is shown that the relation presented here reduces to the Casimir-Polder and London results in the appropriate limits.
Seminar/Autolecture Experiences
Authors: Berman Arthur I. , Baez Albert V.
Published: August 2005

Seminar/Autolecture, an open-ended learning system, combines current advances in educational technology with recent findings in behavioral science. Its dominant features are: (1) maximum student involvement through a potentially error-free and low-distraction medium with emphasis on structure, visual and aural stimuli, a personal approach, and programmed-instructional sequences; (2) simplicity, flexibility, and low cost of production and revision; (3) student interchanges and critiques, (4) individual self-paced instruction, rapid feedback, and retrieval; (5) an interpersonal learner-teacher relationship even at high student-faculty ratios; and (6) possibilities for teacher training. The S/A system has been tested and has met with encouraging success at Rensselaer Polytechnic Institute, The Goddard Space Flight Center, The Technical University of Denmark, and Harvard University.
Dependence of the Power Output of He-Ne Lasers on the Cavity Configuration
Authors: Malacara Daniel
Published: August 2005

The dependence of the power output of He-Ne lasers, operating in the TEM00, on the cavity configuration, is analyzed. The main assumption is that the power output increases linearly with the mode volume. Hints for the optimum design of He-Ne lasers based on these considerations, as well as on the alignment tolerances, are given.
Uses of Desk-Top Computers in Introductory Laboratories
Authors: Merrill John R.
Published: August 2005

This note describes three of many uses to which the desk-top computer has been put in the introductory physics laboratory. The three uses involve an ac circuit laboratory, an equipotential mapping experiment, and an N-slit diffraction experiment. Typical desk-top computer-produced theory plots are shown; the student often compares his experimental measurements to theory by plotting his points directly on the computer plot.
CAI Physics Experiments
Authors: Lindsay Robert E.
Published: August 2005

A novel instructional method for physics and related fields is introduced. The materials presented are discussed with regard to content, mediation (mechanics of communication), and scoring and control. Several examples are given along with results from student evaluation.
The Lewis-Tolman Lever Paradox
Authors: Butler J. W.
Published: August 2005

When a rigid right-angled lever experiences equal and opposite torques as measured by an observer O′ at rest with respect to the lever in frame S′, the usual transformation of these torques to another Lorentz frame S makes it appear that the torques are not balanced for an observer 0 at rest in S. This paradox was first pointed out by Lewis and Tolman. The consensus among textbook authors is that a net torque does exist on the lever according to the general Lorentz observer. The present paper is a basic reexamination of both the Lewis-Tolman lever paradox and another, closely related, paradox: equal and opposite torques applied at the same point on a rigid square. The basic approach herein is to construct for observer O a four-tensor Iμν to represent the relative four-torque about a point P′ fixed in frame S′ which has a constant speed ν = βc along the +x axis of S. For some unknown reason, this tensor seems never to have been defined before. The space part of Iμν reduces to the corresponding classical definition of torque in three-space if ν = 0. Based on Iμν a comparison of the torque components for two different Lorentz observers shows that no torque exists on the square or on the lever for any Lorentz observer if no net torque exists for the observer at rest with respect to the square or lever. This analysis suggests a new (covariant) definition for the torque I about a point P′a in three-space: I = l × f, where l is the space part of the four-vector lμ = (γ2lx, ly, lz, iγ2βlx) and where f is the space part of the four-vector fμ = (γF, iγβFx). Here, a force F is applied at a point P′b (stationary in S′) whose displacement from P′a (also stationary in S′) is 1. Both the force F and the displacement 1 are as measured by observer O at rest in S; and I is the torque about P′a according to O.
The Green's Function Theory of the Spin 12 Ferromagnetic Crystal Utilizing Exchange Plus Dipole-Dipole Interaction Hamiltonian in the Single Excitation Limit
Authors: Lawson J. O. , Glass Solomon J.
Published: August 2005

The Green's function technique (including dipole-dipole interactions) is applied to a bulk ferromagnet to obtain an expression for the magnetization at low temperatures. Only the lowest order Green's functions are used in the calculations, allowing only for single excitations. The result obtained is identical with the Holstein and Primakoff result and the Haas result, both of which were intended to be more inclusive than the present calculation—Holstein and Primakoff via diagonalizing the Hamiltonian, and Haas via symmetrically decoupling generated higher order Green's functions.
Resource Letter TLA-1 on Technology, Literature, and Art since World War II
Authors: Davenport William H.
Published: August 2005

Prepared at the request of the AAPT Committee on Resource Letters.

This is one of a series of Resource Letters on different topics, intended to guide college physicists to some of the literature and other teaching aids that may help them improve course contents in specified fields of physics. No Resource Letter is meant to be exhaustive and complete; in time there may be more than one letter on some of the main subjects of interest. Comments and suggestions concerning the content and arrangement of letters as well as suggestions for future topics will be welcomed. Please send such communications to Professor Joel Gordon, Chairman, Resource Letter Committee, Department of Physics, Amherst College, Amherst, Massachusetts 01002.

Additional copies: Available from the Executive Secretary, American Association of Physics Teachers, 335 East 45 Street, New York, N. Y. 10017. When ordering, request Resource Letter TLA-1 and enclose 25 cents per copy (not in stamps), together with a self-addressed stamped envelope.
A Helicon Solid-State Plasma Experiment for the Advanced Laboratory
Authors: Merrill J. R. , Pierce D. , Giovanielli D.
Published: August 2005

This paper reports an advanced undergraduate laboratory experiment concerning the helicon solid-state plasma wave. Student results are reported. The experiment is performed as an inexpensive dip in a liquid helium storage vessel. The experiment is made possible by the design of a small, superconducting magnet. The magnet is capable of attaining 18 kG and costs about $25. The whole experiment can be built by students in a week's time. When the experiment is completed, the student not only understands helicon propagation but also understands the use of the helicon to measure magnetoresistance and Hall coefficients in pure metals.
Relations among Systems of Electromagnetic Equations
Authors: Page Chester H.
Published: August 2005

The equations of electromagnetism, whether written in the electrostatic, electromagnetic, or symmetric system, whether in rationalized or nonrationalized form, express an invariant set of physical relationships. The same set of letter symbols is employed in each, system of equations; these symbols represent related, but different, quantities in the various systems. The relationships among corresponding symbols are given and applied to precise statements about the relation between the oersted and the ampere per meter, the abampere and the ampere, etc.
Experiments with Cholesteric Liquid Crystals
Authors: Fergason James L.
Published: August 2005

The following set of experiments was designed for students just beginning to study cholesteric liquid crystals. It contains all of the information on materials and apparatus needed to perform thermal mapping. Wherever possible, materials which are readily available have been chosen. The experiments progress, each one somewhat more difficult than the preceding. No attempt has been made to give an outline of the properties of liquid crystal phases, but the reader is referred to A. Saupe's review article [Angew. Chem. Internat. Edit. 7, No. 2, 97 (1968)] on the subject.
Laser Mode Structure Experiments for Undergraduate Laboratories
Authors: Phillips Richard A. , Gehrz Robert D.
Published: August 2005

Experiments dealing with laser mode structure are presented which are suitable for an upper division undergraduate laboratory. The theory of cavity modes is summarized. The mode structure of the radiation from a helium-neon laser is measured by using a photodiode detector and spectrum analyzer to detect intermode beating. Off-axial modes can be visually detected in the expanded laser beam and their presence correlated with signals displayed on the spectrum analyzer in agreement with the theory.
The Virial Theorem and the Equation of State of a Two-Dimensional Plasma
Authors: Knorr G.
Published: August 2005

The virial theorem is used for an elementary derivation of the exact equation of state of a two-dimensional plasma.
I Am Curious (Transport Coefficients)
Authors: Mason E. A. , Dorfman J. R. , Zwanzig Robert
Published: August 2005

Some aspects of the kinetic theory of transport coefficients are discussed in terms of simplified models. These models are a gas of one-dimensional rods and a gas of d-dimensional rigid parallel “cubes.” The collision process is taken to be such that two molecules exchange velocities upon collision. For these models the elementary mean-free-path results are exact, up to an unknown factor of order unity appearing in a correction term.
A Progress Report on Open-End Laboratories
Authors: Shonle John I.
Published: August 2005

This paper reports our experiences with open-end introductory-physics laboratories after three semesters. All available indications show that they are successful. The method of evaluation of the effectiveness of the open-end laboratories and the results are given. Organizational details and changes in the organization made for 1969–1970 are also included. An important device used to start the student on an open-end experiment is a required preset exercise.
How Good Is the Hartree-Fock Approximation? II. The Case of Closed Shells
Authors: Calles A. , Moshinsky M.
Published: August 2005

In the present paper, we analyze the problem of an arbitrary number of particles A in a harmonic-oscillator common potential interacting through a harmonic-oscillator force. The particles have spin 12 and obey Fermi statistics. The exact lowest eigenstate and energy are derived for values of A corresponding to closed subshells. An approximate analysis is also made using determinantal wave functions formed from single-particle harmonic-oscillator states, giving the eigenstates and energies of a simple form of the Hartree-Fock approximation. The exact and Hartree-Fock energies and eigenstates are compared both when potential and force have the same sign, and when they have opposite sign. We discuss the results for models which we call pseudonuclei and pseudoatoms, and we indicate some of the inferences for the real thing.
Explicit Construction of Unitary Operators in Nonrelativistic Quantum Mechanics
Authors: Chan Choi-Lai
Published: August 2005

The Moravek-Joseph method [P. H. Moravek and D. W. Joseph, J. Math. Phys. 4, 1363 (1963)] for the construction of unitary operators in quantum field theory is found to be applicable also to nonrelativistic quantum mechanics. Some simple examples are given.
Position Expectation Values for an Electron in an Infinite Tilted Well
Authors: Johnson Noble M. , Churchill John N.
Published: August 2005

A numerical technique is used to determine the manner in which the expectation values of position for an electron in an infinite tilted well depend on the potential gradient and quantum state of the system. The results are compared to the classical case and to the exact analytic expression for the special case in which the total energy of the electron is equal to the maximum value of the linear potential.
Energy Levels of the Hydrogen Atom as a Relativistic Clock-Retardation Effect?
Authors: Dorling J.
Published: August 2005

It is proven that the energy level, according to the Dirac equation, of any stationary state of the hydrogen atom can be written in the form E = m0c2〈β| = m0c2〈(1 − v2/c2)1/2| = h〈ν|, where m0 is the electron-rest mass, β is the Dirac-β operator, v is the instantaneous electron velocity in the corresponding orbit in Sommerfeld's relativistic old quantum theory, ν is an “electron apparent frequency” satisfying ν = ν0(1 − v2/c2)1/2, with hν0 = m0c2, and 〈 〉 denotes expectation value or time-average value, as appropriate. In spite of the physically suggestive character of this result, it is argued on theoretical grounds that it must be regarded merely as an interesting mathematical accident.
Coherent States in Superfluids: The Ideal Einstein-Bose Gas
Authors: Johnston James R.
Published: August 2005

It is argued that the grand canonical ensemble is not appropriate for describing local properties of a closed system when the system has off-diagonal long-range order over distances of the order of the dimensions of the system (e.g., when there is a condensation into a single-particle state). It is shown that the local dispersion in number in the condensed part of an ideal Einstein-Bose gas is “small” (appropriate to a Poisson distribution), contrary to the usual result obtained using the grand canonical ensemble. This leads to an approximation in which the condensed part of the system is represented locally by a coherent state. It is further argued that these considerations serve as a rationale for breaking gauge symmetry whereas the usual arguments (based on analogy with ferromagnetism) are not appropriate.
A Study of Brownian Motion Using Light Scattering
Authors: Clark Noel A. , Lunacek Joseph H. , Benedek George B.
Published: August 2005

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.
The Porous Plug Experiment—A Lot of Mileage on a Little Gas
Authors: Tykodi R. J.
Published: August 2005

The porous plug experiment may be used to illustrate the usefulness of the enthalpy function, irreversibility, steady-state ideas, and a classical relativity principle.
Scattering from a Separable Nonlocal Potential
Authors: Husain D. , Ali S.
Published: August 2005

An analysis has been made of elastic scattering from a nonlocal separable complex potential, using coordinate representation. A neat but exact expression has been obtained from the partial wave-phase shifts. The validity of the analysis has also been checked.
The Trolley Problem
Authors: Page Chester H.
Published: August 2005

A rectangular current circuit in which one conductor is moving along its own axis is Lorentz equivalent to a two-trolley loop sliding along a stationary wire. The body and surface densities of charge and current are deduced on the basis of a simplifying idealization.
Functional Integrals in Statistical Physics
Authors: Revzen M.
Published: August 2005

The radiation field is used as an example for functional integration calculations. Calculations of fluctuations of both thermal and quantum origin are given. The Landau-Ginzburg functional is used to define the concept of mean function. Fluctuations about the mean functions are discussed. The formal notation of functional integration is used to obtain the statistical-mechanics analog of Noether's theorem. The approach is heuristic, rather than rigorous, throughout.
On the Dynamics of the Swing of a Golf Club
Authors: Jorgensen Theodore
Published: August 2005

The Lagrangian method is used to obtain two coupled differential equations describing the motion of a simple model of the swing of a golf club. These equations are simplified by a special treatment of the gravitational torques and are put in a form such that different constant torques applied by the golfer give solutions differing only in a scale factor. The equations are solved numerically for various suitable boundary conditions. It is shown that the clubhead speed achieved for a swing with a constant torque applied by the golfer increases with the hindrance to the uncocking of the wrists during the swing, and that the backswing of the club may be decreased substantially with a correspondingly small decrease in clubhead speed.
The Classical Atom Revisited
Authors: Tutsch J. H.
Published: August 2005

The existence of nonplanetary periodic orbits in the classical model of the n-electron atom is demonstrated.
The Poor Man's Nitrogen Laser
Authors: Phillips David T. , West John
Published: August 2005

A small, simple, pulsed ultraviolet N2 laser is described with wavelength 3371 Å, peak power 103 W, pulse duration 6×10−9 sec, and pulse-repetition rate 120 Hz.
Microscopic Quantum Theory of the Helium Liquids
Authors: Feenberg Eugene
Published: August 2005

A highly developed microscopic theory of the helium liquids exists based on the Schrödinger equation involving realistic forms of the interaction potential between pairs of neutral atoms. This report is a tutorial review of the microscopic theory with emphasis on the method of correlated basis functions. Among the topics considered are potentials, distribution functions, consequences of the correspondence principle, working approximations for the three-particle distribution function, useful matrix elements, sum rules, the paired-phonon function space, trial forms for the ground state of the boson system, distribution of particles in momentum space, elementary excitations, basis functions, and matrix elements for liquid He3 and for the dilute solution of He3 in liquid He4.
A Monte Carlo Simulation of Brownian Motion in the Freshman Laboratory
Authors: Anger C. D. , Prescott J. R.
Published: August 2005

An experiment for the freshman laboratory is described, in which the essential features of the Brownian motion are given by a simplified model based on momentum-conservation principles, using the Monte Carlo technique. Calculations are carried out by a computation scheme based on computer language.
Electrostatics and Current Flow
Authors: Parker Sherwood
Published: August 2005

The relation between electrostatics and current flow in conductors is discussed, and a demonstration suitable for lecture classes is described.
An Elementary Experiment on the Energy Straggling of α Particles in Air
Authors: Cochran J. , Payne M. G.
Published: August 2005

The α particles from a covered Po210 source (full width at half-maximum without an absorber ≈0.232 MeV and mean energy ≈4.71 MeV) were allowed to penetrate a fixed thickness of air and their energy spectrum was measured as a function of the pressure. The energy spectra were also calculated from the zero pressure spectrum on the assumption that statistical fluctuations in the energy loss process could be neglected. It was found that even though the full width at half-maximum increased considerably (by a factor of 1.6 in one case) the measured and calculated spectra were in good agreement. The results obtained here are in agreement with theory which predicts that once the dispersion in energy becomes large, changes in the energy distribution function due to statistical fluctuations become small compared with the changes which occur because particles with different energies lose energy at different average rates. The surprising thing is that statistical fluctuations become unimportant for an α spectrum while the full width at half-maximum is still relatively small.
A Course in Modern Physics for Colombia
Authors: Fogel Alan
Published: August 2005

A modern physics course oriented to the specific educational needs of the Colombian student is discussed. Emphasizing independent thinking and original work, the course reinforces the efforts of the student through a strong correlation between the homework, the lectures, and a laboratory, which takes the form of a research project. Flexibility and a relatively inexpensive laboratory make it ideal for many Latin American universities.
Balmer's Manuscripts and the Construction of His Series
Authors: Banet Leo
Published: August 2005

An earlier regeneration of the Balmer series was difficult, because Balmer's publications omitted some of his steps and only presented fragments of others. After a search, the author located a collection of Balmer's papers which include two preliminary manuscripts and traced Balmer's steps on the basis of his own statements. It was found that initially Balmer used three coefficients of cubic integers and a basic wavelength of 30.38 Å; he then related a fourth, visible line in a similar manner as the first three. Subsequently, he rejected these unpublished equations and developed his final formula on the basis of an unrecorded geometrical construction. The origin and nature of this construction, which served as a model for the series, is documented and analyzed. Balmer's verification of his formula and his conclusions are described. In addition, it is shown that the Balmer series played a direct role in the formation of the Rydberg constant and the atomic theory of Bohr.
On Kepler Ellipses Starting from a Point in Space
Authors: Laporte Otto
Published: August 2005

The one-parameter family of Kepler ellipses is considered, which originates when mass points are released with the same initial velocity but in all directions at a point which has a finite distance from the attractive center. It is found that (a) the locus of the second foci is a circle whose center is the point of release, (b) the directrices of the ellipses have as envelope a conic which can be an ellipse or a hyperbola, (c) the envelope of the orbital ellipses is itself an ellipse, whose two foci are the attractive center and the point of release, and (d) that, if the particles are released at the same instant, they will return to the point of release simultaneously.