bluuebunny/crossref_metadata_2025 huggingface dataset:
Resource Letter SP-1 on Symmetry in Physics
Authors: Park David
Published: August 2005

Prepared at the request of the AAPT Committee on Resource Letters; supported by a grant from the National Science Foundation.

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.

Notation: The letter E after the item number means that the reference should be mainly useful for elementary courses. In view of the complexity of the subject elementary will normally imply junior courses. The letter I indicates intermediate (senior and first-year graduates) and A indicates advanced (second-year graduates and students beginning research in Physics). An asterisk indicates items particularly recommended for introductory study.

Additional copies: Available from American Institute of Physics, 335 East 45 Street, New York, New York 10017. When ordering, request Resource Letter SP-1 and enclose a stamped return envelope.
Difference-Equation Solutions for the Linear Ising Model and Nearest-Neighbor Fluid
Authors: Leff Harvey S. , Flicker Michael
Published: August 2005

The one-dimensional nearest-neighbor Ising model, in the presence of a uniform external magnetic field, is solved using a difference equation technique. The approach involves neither combinatorial analyses nor matrix methods, and can be understood with a minimal knowledge of difference equations. The cases with periodic boundary conditions and with no boundary constraints are treated with equal ease. Similarly, the one-dimensional nearest-neighbor fluid is solved with the aid of difference equation techniques. Some difference-equation theory and the conventional matrix Ising model solutions are outlined in appendixes.
Fourier Analysis of a Square Wave Using a Simple Tuned Circuit Amplifier
Authors: Alpert Seymour S.
Published: August 2005

A simple tuned circuit amplifier which can be readily constructed by advanced undergraduate physics students is used as a spectrum analyzer. A repetitive square voltage waveform is analyzed using this device. The main motivation for the development of the simple spectrum analyzer is to demonstrate physically the reality of the existance of the Fourier components of a repetitive waveform.
Physical Oceanography for the Nonscience Major
Authors: Warsh K. L.
Published: August 2005

A physical science course centered around physical oceanography, which was taught to nonscience majors, is described. A very high level of interest was shown by the students. Most of the topics covered in conventional physical science courses can be covered in such a course but in a manner more enjoyable to the student.
Relativistic Dressing of a Free Particle
Authors: Smith Charles Ray
Published: August 2005

An application of Feynman-type diagrams in a simple one-particle problem is offered as a pedagogical prop for setting the stage for the diagrammatic representation of serious perturbation calculations. This example is useful to the student, since it brings out several features that will be involved in the applications of diagrams to more sophisticated problems. Important aspects of this application are: (1) It is shown how the rules for combining probability amplitudes can be used; (2) a technique for introducing an external field (which can cause transition among states) is described; and (3) some of the language used in diagrammatic representations is introduced. The concept of dressing a particle is only partially developed.
Forces, Uncertainty, and the Gibbs Entropy
Authors: Baierlein Ralph
Published: August 2005

A physicist's educated intuition indicates that the presence of some readily analyzed forces in a gas reduces one's uncertainty about the actual state of affairs at the molecular level below the corresponding uncertainty in the absence of such forces. There ought to be a connection with at least one of the entropylike expressions appearing in statistical mechanics. A simple proof is given that, in the classical limit, the presence of any forces (represented by potentials dependent on particle positions only) does reduce the Gibbs entropy below its value, at the same temperature, in the absence of such forces. This may be taken as support for an interpretation of the Gibbs entropy as a measure of one's uncertainty about the actual microscopic situation, given the information typically available.
Laboratory Exercises in Classical Electromagnetic Field Theory
Authors: Atwater H. A.
Published: August 2005

A description is given of laboratory experiments that have been developed to accompany a course of instruction in the static and time-varying electromagnetic field. These comprise nine exercises in which the principal concern is with the study of field phenomena rather than of circuits and electronic devices.
Some Experiments with a Radioisotope X-Ray Source for the Undergraduate Laboratory
Authors: Robinson W. K. , Adams W. D. , Duggan J. L.
Published: August 2005

Until recently x-ray experiments were done mainly in laboratories which had x-ray machines. With radioisotope x-ray sources now readily available, many experiments can now be performed in small universities with a minimum investment in equipment. In this paper such a source is used to excite fluorescent x rays in the 0–30-keV range in various metals. These x rays are studied with a conventional proportional counter and with one of the newly developed lithium-drifted silicon, Si(Li), surface barrier detectors. With this latter device resolutions as good as 450 eV are obtained for some of the x-ray measurements. The interaction of x rays with matter is studied by making half-value thickness measurements on aluminum, cobalt, and nickel, using Co57 and Zn65 sources.
Quantitative Field Mapping Experiments
Authors: Grossberg Alan B.
Published: August 2005

Computer programming is used in conjunction with experiments in electric field mapping in the general physics laboratory. Experimental data are superimposed on the computed equipotential curves. Required modifications of the Overbeck mapping apparatus are described.
Quantum Mechanics of Individual Systems
Authors: Hartle J. B.
Published: August 2005

A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for individual systems. A discussion of the meaning of the “state” of an individual quantum mechanical system is given, and an application is made to the clarification of some of the paradoxical features of the theory.
The Description of Polarization in Classical Physics
Authors: Collett Edward
Published: August 2005

An alternate derivation of the Stokes polarization parameters is presented; the parameters are obtained from the elliptic equation of polarization rather than the plane wave equations. As a result of deriving the parameters in this manner, the relationship between the polarization ellipse and the Stokes parameters is clarified. The Stokes parameters for various states of polarized light are briefly reviewed. The remainder of this article is then devoted to obtaining the Stokes parameters for a number of important physical phenomena such as the classical Zeeman effect, synchrotron radiation, Thomson scattering, reflection of electromagnetic waves by dielectric surfaces, and wave propagation in a plasma.
Crystal Symmetry and Macroscopic Laws
Authors: Callen Herbert
Published: August 2005

The macroscopic response of a system is often expressible by linear or bilinear laws, of the form X = χ·F or X = F·χ·F′. The “forces” F and “responses” X may be scalars, polar or axial vectors, or tensors. Crystal symmetry then imposes severe restrictions on the form of χ. Tables of basis functions for crystallographic point groups are provided in a form which directly dictates the form of χ (and which requires no knowledge or application of group theory). Various special cases, such as that presented by a complex representation, are illustrated by concrete examples. If X and F are conjugate thermodynamic variables, the crystal symmetry is augmented by thermodynamic symmetry relations. If X and F are thermodynamically conjugate dynamical variables, crystal symmetry is augmented by Onsager reciprocity. These thermodynamic cases are most conveniently treated by applying symmetry considerations to the free energy or the dissipation function respectively, as is illustrated by specific applications.
A Simplified Derivation of the Irreducible Representations of SU(3)
Authors: Nelson T. J.
Published: August 2005

A simple solution to the eigenvalue problem posed by a set of operators which have the commutation rules of SU(3) is developed. The analogy with the more familiar problem for SU(2), i.e., angular momentum, is used as a guide. The set of labels used to describe the states in an irreducible representation admits of a folded-ladder interpretation that is particularly transparent. Finally the dimensionality formula and the effect of complex conjugation are derived.
Spin Hamiltonian Derivation of Paramagnetic Susceptibility in Axial Crystal Systems
Authors: Veigele Wm. J. , Henry E. M.
Published: August 2005

The spin Ilamiltonian of EPR is used in the trace formalism to derive the paramagnetic susceptibility of a salt, containing paramagnetic ions in sites of axial crystal symmetry. The resulting equation holds for all values of electron spin and angle between the crystalline field axis and the external magnetic field.
Bernoulli Effect and Kinetic Theory
Authors: Glover Francisco
Published: August 2005

Certain conceptual pitfalls for the unwary student first meeting Bernoulli's principle are considered. An alternate derivation is presented, based on a kinetic theory picture of a gas, assuming that a moderate wind causes no appreciable increase of gas temperature. The advantages and disadvantages of this alternate derivation are discussed.
Intersecting Adiabatic Surfaces and the Second Law of Thermodynamics
Authors: Curry S. M. , Henry G. R.
Published: August 2005

In elementary presentations of thermodynamics, it is sometimes stated that the second law implies that adiabatic surfaces never intersect. A simple counterexample to this statement is constructed, and some remarks are made on the sufficient conditions for the nonintersection of adiabatic surfaces.
Analog Simulation of the Bouncing-Ball Problem
Authors: Pfaltzgraff David J.
Published: August 2005

This paper endeavors to show, by means of an example, the usefulness of the analog computer as a demonstration tool for undergraduate students. The treatment of the problem is basically theoretical, using laws developed early in physics courses. The results of the computations may be observed graphically or on an oscilloscope, depending upon the circumstances of the demonstration. Also discussed are the distortions of the ball due to impact and possibilities of expanding the problem to include more complex approximations to the real situation.
Radioactivity Calculations
Authors: Onega Ronald J.
Published: August 2005

Three problems in radioactive buildup and decay are presented and solved. Matrices are introduced for the solution of the second problem, and the third example deals in a simple way with flux depression.
Compressivity Tensor and Dispersion Relation for a Plasma
Authors: Chen Hollis C.
Published: August 2005

By the introduction of the compressivity and the permittivity tensors, the governing equations for a lossy, compressible, and anisotropic electron plasma are reformulated. The compressivity tensor takes into account the thermal motions of the electrons, while the permittivity tensor characterizes the anisotropy of the medium due to an external static magnetic field. A general dispersion relation with the coefficients in terms of the components of the compressivity and the permittivity tensors is obtained. The nature of the small oscillations in the plasma is thus determined completely by the two tensors. In the general case, the dispersion relation cannot be factorized into products which show the coupling between electromagnetic and plasma waves. Various simplifying assumptions which give some insight into the complex structure of the dispersion relation are examined. Some numerical results are also included.
A Simple Measurement of the Relative Permittivity of an Insulating Liquid
Authors: Secker P. E.
Published: August 2005

A simple test cell has been devised in which the charge on one plate of a parallel-plate capacitor is repeatedly transferred to a capacitor—electrostatic voltmeter combination. From the voltmeter readings as the system is operated first in air and then in an insulating liquid, the relative permittivity of the latter can be evaluated with an error of less than 2%.
Notes on the Thermodynamics of Paramagnets
Authors: Leupold Herbert A.
Published: August 2005

An attempt is made to clarify some of the concepts concerning the interaction of magnetic fields with material bodies. The various ways of writing the equation of the first law of thermodynamics for paramagnets are derived, and apparent contradictions between them are resolved. These different expressions are also compared as to relative utility and esthetic appeal.
The Quadrupole Mass Spectrometer
Authors: Mathieson E. , Harris T. J.
Published: August 2005

The quadrupole mass spectrometer is recommended as an instrument for experimentation in the advanced teaching laboratory. An outline is given of the theory of operation of the spectrometer, and factors affecting the resolution are discussed. A laboratory instrument is briefly described, and examples of mass spectra obtained with this instrument are shown.
Is there an Azimuthal Angle Observable?
Authors: Perlman H. S. , Troup G. J.
Published: August 2005

The concept of an azimuthal-angle operator canonically conjugate to the z component of angular-momentum operator is known to present certain difficulties in quantum mechanics. These difficulties are resolved rigorously for the first time, and their implications are discussed.
Resource Letter EP-1 on Educational Psychology
Authors: Ivany J. W. George
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.

Notation: The letter E after an item number indicates elementary level; the letter I indicates intermediate level; and the letter A indicates advanced material. An asterisk (*) indicates items particularly recommended for introductory study.

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 EP-1 and enclose 25 cents per copy (not in stamps), together with a self-addressed stamped envelope.
Designing an “Acoustic Suspension” Speaker System in the General Physics Laboratory: A “Divergent” Experiment
Authors: Horton Philip B.
Published: August 2005

Student design of an “acoustic suspension” speaker system as a laboratory project is reported. The characteristics of the loudspeaker employed are measured as an extension of the inertia-balance experiment. The experiment may be diverged to a study of Helmholtz resonators, coupled oscillators, electromagnetic forces, thermodynamics, and ac-circuit theory.
Elementary Analysis of Translunar Apollo Orbit
Authors: Christy R. W. , Mayhugh M. R.
Published: August 2005

Geometrical parameters of the translunar Apollo orbit are derived from elementary equations relating to elliptical and hyperbolic orbits in an inverse-square force field. The simplification is to divide the problem into an elliptical orbit in the region where the earth's attraction dominates and a hyperbolic orbit (referred to a moving coordinate system attached to the moon) in the region where the moon dominates. The result shows that the orbit will return the spacecraft to earth (unless the propulsion system is fired), provided the spacecraft is properly incident on the leading side of the moon. The elementary results are compared with those of a computer simulation of the orbit.
Introductory Modern Physics: A Course for Freshmen
Authors: Mikkelson R. C.
Published: August 2005

A pre-calculus, freshman-level modern physics course for prospective physics majors is described. The problems and goals which led to the course are discussed, a description of the course after three years of development is given, and its contributions to the physics curriculum are presented.
Dirac and Photon Interference
Authors: Sciamanda Robert J.
Published: August 2005

Students' difficulties in applying a statement of Dirac to two-laser interference should have been brought up in connection with many of the traditional beam-splitting experiments, which also involve more than one source. The temptation to add intensities rather than wavefunctions is a throw-back to the classical concept of distinguishable particles, and the intuitive feeling that one can divide radiating matter into distinct sources, each emitting distinct photons.
Lorentz Transformation Derived from First-Order Experiments
Authors: Pfleiderer J.
Published: August 2005

The electric field that is created in a moving magnetic field can be used to establish the Lorentz transformation without considering the constancy of light velocity or the full set of Maxwell's equations.
Kepler's Laws: Demonstration and Derivation without Calculus
Authors: Chapman Seville
Published: August 2005

A demonstration apparatus for Kepler's three laws of planetary motion consists of an air-supported “satellite” whose orbit on a 1.2×1.5-m level-table surface is determined by an inverse-square force generated by a Peaucellier linkage and long spring. The equipment is a feasibility model which works—not an ultimate design. Cost of the equipment is about $25 for parts, plus considerable labor. Several comments are made regarding tricky aspects of the design. The apparatus can be analyzed by using high-school algebra and geometry. From the principles of conservation of energy, conservation of momentum, and static equilibrium, Kepler's laws can be deduced that: (1) the oribt is an ellipse with center of force at one focus, (2) the time rate of area swept out by the radius vector is constant, and (3) the square of the period is proportional to the cube of the semimajor axis. This analysis (believed to be new) in essence integrates the force, 1/r2, to obtain the energy, −1/r, without using calculus.
A Pedagogical Measurement of the Velocity of Light
Authors: Tyler Charles E.
Published: August 2005

An inexpensive, simple, easily constructed and convincing technique is described both for demonstrating that the speed of light is finite, and for measuring its value. All that is required is about $40 and a good oscilloscope. Detailed instructions and experimental results are given, and it is found that c = (29.8±0.6) cm/nsec.
Some More Simple Laser Experiments for the Undergraduate Laboratory
Authors: Yap F. Y.
Published: August 2005

Certain elementary optics experiments can be performed with considerably greater ease using a laser instead of conventional light sources. This paper describes three such experiments which illustrate the Fresnel-Arago law, elliptical polarization, double refraction and polarization in calcite, and interference by a Fresnel biprism. Because of the high intensity of the laser beam, these experiments lend themselves very well to demonstrations in front of large groups.
On the Interpretation of Measurement within the Quantum Theory
Authors: Cooper Leon N. , Van Vechten Deborah
Published: August 2005

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 Schrödinger 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.
Measurement and Interference
Authors: Schulman L. S.
Published: August 2005

We use the density matrix formalism to discuss the often encountered question: When do final states due to various initial states add coherently (interfere)?
Equivalence of the δ′ and the Hard Core Potentials
Authors: Schenter R. E. , Zwibel H. S. , Cassola R. L.
Published: August 2005

The introduction of the hard core potential into the two-body problem forces the system wave function to vanish, if the interacting particles approach each other more closely than the hard core radius. In this paper it is shown that this “hard core effect” can also be obtained in the two-body problem by replacing the hard core potential with a δ′ interaction of suitable strength.
The Reflection and Transmission of Electromagnetic Waves by a Moving Dielectric Slab. I. Solution in the Moving Frame
Authors: Noble William J. , Ross Carl K.
Published: August 2005

The Darwin scattering method is used to calculate the amplitudes, frequencies and propagation directions of the free space electromagnetic waves reflected and transmitted by a plane-parallel, non-dissipative, isotropic, homogeneous, dielectric slab. The laws of reflection and refraction and the conservation of energy flux follow naturally. Explicit formulas are given for perpendicular polarization but the method is equally applicable to polarization parallel to the plane of incidence. The results of Part I for the reference frame of the moving slab are in a form to be transformed in Part II to the reference frame of a “fixed” observer.
Heat Capacity of an Ideal Free-Electron Gas: A Rigorous Derivation
Authors: Weinstock Robert
Published: August 2005

It is shown that a standard derivation found in the literature for the heat capacity of an ideal free-electron gas is vitiated by the use of divergent series. A plausible argument is offered to indicate that these series are actually asymptotic expansions that provide good approximations through their first few terms—a provable fact acknowledged by a few writers, but the proof of which has nowhere been seen in print by the present author. The invalid standard procedure is modified through replacement of an infinite series by its first two terms plus a remainder whose bounds are easily estimated as being negligible to the accuracy required; a rigorous derivation of the well-known temperature dependence of the electronic heat capacity of a metal results.
On L1L2 ≥ M2
Authors: Power Edwin A.
Published: August 2005

The well-known inequality L1L2 ≥ M2 connecting the coefficients of self- and mutual inductances for a pair of coupled circuits is derived by analytical methods, and a discussion is given concerning their connection with the physical arguments found in elementary textbooks.
Wave Mechanics and the Concept of Force
Authors: Taylor P. L.
Published: August 2005

The concept of the force exerted by a quantum-mechanical particle is examined. Two expressions for this force, one local and one nonlocal, are derived, and shown to be equivalent. These results are applied to a discussion of the transmission of force by a single electron and to an elementary derivation of the Fermi-Segrè formula.
Anniversaries in 1969 of Interest to Physicists
Authors: Barr E. Scott
Published: August 2005

During the year 1969 there are major anniversaries of the birth or death of six men whose accomplishments and influence have been of importance to the development of physics. They are: Armand Hippolyte Louis Fizeau, Thomas Graham, Ernest Fox Nichols, George Gabriel Stokes, James Watt, and Charles Thomson Rees Wilson. Brief accounts of their achievements and lives are given here.
Force, Momentum Change, and Motion
Authors: Tiersten Martin S.
Published: August 2005

Classical equations of motion for open systems are discussed and the equation of motion for fixed volume systems is shown to be F = Ṗ+Φ, where Φ is the momentum flux. Numerous examples are given.
Resource Letter XR-1 on X Rays
Authors: Muldawer Leonard
Published: August 2005

Prepared at the request of the AAPT Committee on Resource Letters; supported by a grant from the National Science Foundation.

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

Notation: The letter E after an item number indicates elementary level, useful principally for high school and introductory college use; the letter I indicates intermediate (junior, senior) level; and the letter A indicates advanced material, principally suited for senior, graduate study. An asterisk (*) indicates items particularly recommended for introductory study.

Additional copies: Available from American Institute of Physics, 335 East 45 Street, New York, New York 10017. When ordering, request Resource Letter XR-1 and enclose a stamped return envelope.
Helicon Waves in Solids
Authors: Maxfield B. W.
Published: August 2005

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 compared. A review of both local and nonlocal experimental studies involving the helicon is given. In the local regime, these include measurements of the Hall coefficient and magnetoresistance in metals (including superconductors) while in the nonlocal regime such phenomena as helicon-phonon coupling and Landau damping are described.
An Advanced Laboratory Experiment on Tunneling in Semiconductor Diodes
Authors: Merrill J. R.
Published: August 2005

This paper deals with an advanced laboratory experiment on tunneling mechanisms in tunnel diodes. The experiment measures phonon-assisted tunneling in silicon tunnel diodes. Student data are shown; the results agree nicely with previous data in the literature and with band structure calculations for Si. The student learns about band structure, phonons, tunneling techniques, and differentiation, techniques.
The Part II Physics Laboratory at Flinders University
Authors: Murray E. L. , Westwood W. D.
Published: August 2005

The experiments comprising an undergraduate laboratory for physics majors in their second year of study at an Australian university are described. The experiments are in the field of electricity, magnetism, and optics. In addition to the normal experiments carried out by the students, demonstration experiments on Fourier spectroscopy and holography are described.
Holography and Coherent Imaging
Authors: Young M.
Published: August 2005

A number of aspects of holography is discussed at a level suitable for the undergraduate who is familar with interference and diffraction. As byproducts, we obtain an elementary understanding of coherent imaging and several results that may be of use to the do-it-yourself holographer. Finally, we mention integral photography as an interesting competitor with holography.
Measurement of Photoelectric, Compton, and Pair-Production Cross Sections in Germanium
Authors: French W. R. , Wehrbein W. M. , Moore S. E.
Published: August 2005

The lithium-drifted germanium detector's high resolution provides an opportunity to measure the photoelectric, Compton, and pair-production cross sections as a function of photon energy in the range of 100 to 2750 keV. This conceptually simple experiment can be readily performed in an undergraduate laboratory equipped with a small Ge(Li) detector and pulse-height analysis equipment. Results compare very favorably with theoretical calculations.
The Kinematics of Two-Particle Collisions in Special Relativity
Authors: Chow Yutze
Published: August 2005

The kinematics of elastic two-particle collisions may be summarized by the convenient four-vector equation q = Rθp, where p and q are four-momenta of the same particle before and after collision in the laboratory frame, and Rθ is the rotation induced in the laboratory frame by a two-dimensional rotation of angle θ in the center-of-mass frame. It is shown that this form has the advantage of being conceptually clear and computationally convenient.
The Flinders University Part I Physics Laboratory
Authors: Brennan M. H. , Fletcher J.
Published: August 2005

A freshman physics laboratory is described which represents a marked departure from the pattern previously accepted in Australian universities. The student is encouraged to treat the experiments as small research projects rather than demonstrations of lecture material. This objective is achieved by the timing of the experiments and their duration, by the use of modern equipment, and by requiring end-of-term reports. The experiments have been grouped in three sets—dynamics, waves and oscillations, and quantum physics—one set being studied per term, such that each set of experiments presents a series of similar phenomena for investigation.
Experimental Thermodynamics with a Stretched Wire
Authors: Wintle H. J.
Published: August 2005

Temperature scales and the evaluation of thermodynamic temperature for a nongaseous system are discussed, and a simple practical arrangement using a stretched wire is described. Measured thermal quantities can be compared directly with theoretical predictions based on tabulated material constants, and the phenomenon of adiabatic cooling on stretching is readily observed.
Cosmology for Everyphysicist
Authors: Peebles P. J. E.
Published: August 2005

The Friedman-Lemaître cosmological models are based on a very simple world picture, and it is unfortunate that the standard approach to the models brings to bear theoretical machinery much more complicated than this world picture. The purpose of this paper is to give an alternative and perhaps more illuminating approach to the model results from a discussion of how a local observer would describe the expansion of the universe. This treatment of the models is rigorous, according to the theory of general relativity, but hopefully simpler than the standard one, because it deals with quantities that are in principle directly observable.
Resonance-Sustained Radio Frequency Discharges
Authors: Taillet J.
Published: August 2005

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.
Holography in the Undergraduate Optics Course
Authors: Brown Judith C. , Harte Judith A.
Published: August 2005

The theory of holography is presented with special emphasis on the reconstruction process. The directions of the reconstructed beams and the nature of the two images are examined in detail by choosing particularly simple object beams. An interpretation in terms of phase shifts is also included.
Origin of Counting Statistics in Simple Nucleonic Instruments
Authors: Joyce W. B.
Published: August 2005

The variance of the (Poisson) counting statistics of a typical nucleonic instrument is shown to be expressible as the sum of contributions from a variety of distinct random processes. The utility of this decomposition is illustrated in an example where the effect of the random decay rate of the isotope is removed. Contradicting numerous articles and texts, it is also shown that the random decay rate of the isotope and the random detector counting statistics do not participate in a cause-effect relationship, but are nearly independent phenomena in most instruments.
The Lorentz Electron Theory of Relativity
Authors: Schaffner Kenneth F.
Published: August 2005

This paper traces H. A. Lorentz's work on the electrodynamics of moving bodies from 1887 to 1909. His initial rejection of Michelson's 1881 interferometer experiment and the development of the “electron theory” as a modification and extension of Maxwell's ideas are discussed. The 1892 article in which Lorentz proposes the contraction hypothesis (Lorentz-Fitzgerald contraction) is analyzed, and the manner in which the hypothesis is integrated into the electron theory then, and later in the 1895 Versuch, is presented. A discussion of the Versuch's introduction of “local time” and the “theorem of corresponding states” follows, and it is then shown that Lorentz introduced second-order Lorentz transformations in an 1899 paper. The well-known 1904 paper is analyzed, and is shown to be presenting the latest modifications in transformation equations designed to prove a theorem of corresponding states for many electromagnetic phenomena to all orders of v/c. Using Lorentz's 1909 Theory of Electrons, it is argued that the Lorentz transformations as understood by Lorentz prior to Einstein's work possessed inverse transformations which entailed length dilations, time contractions, etc., and which were nonrelativistic and inconsistent with the Lorentz electron theory. Finally a brief discussion of a reason for Einstein's difference of approach is outlined.
Expanding Wavefronts in Special Relativity: A Computer-Generated Film
Authors: Schey Harry M.
Published: August 2005

We describe a computer-generated film which shows an expanding wavefront as seen from a coordinate frame relative to which the source moves with constant velocity. An expression for the wavefront as a function of time is derived, and features of it are discussed in terms of the relativistic laws for the addition of velocities. Sample stills from the film are presented and used in discussing the shape of the wavefront, the velocity of the center of the wavefront, and the headlight effect, all as functions of the signal velocity and the velocity of the source.
Forced Oscillations and Magnetic Resonance in the Introductory Laboratory
Authors: Hageseth Gaylord T.
Published: August 2005

A compass is placed in a uniform magnetic field produced by Helmholtz coils. An oscillator produces a perturbing field perpendicular to the uniform field causing a forced oscillation. A plot of the square of the resonant frequency versus the Helmholtz coil current yields a straight line. The slope gives the magnetic-dipole moment-moment of inertia ratio, and the intercept yields the damping constant.
Rotation Operators
Authors: Wolf A. A.
Published: August 2005

The wide variety of conventions in use concerning rotation operators can be confusing to the student who is beginning a serious study of the quantum theory of angular momentum. These conventions are discussed and compared, and the relation between active and passive rotations is examined. Using these results, a useful formula is derived which connects the reduced matrix element of a tensor operator with quantities that are measured relative to a rotating reference frame.
Spatial Filtering Experiments for Undergraduate Laboratories
Authors: Phillips Richard A.
Published: August 2005

Experiments in the spatial filtering of optical images, which are suitable for an upper division undergraduate laboratory, are presented. These experiments exploit the spatial coherence of laser radiation for their success. It is shown that the field distribution across the aperture of a lens, and the field distribution across the focal plane are a Fourier transform pair. Since a lens resolves an image into its Fourier components, filtering operations can be performed at the transform plane which enhance or eliminate selected components of the image. A second lens performs another transformation that recreates the original image, plus the effects of whatever filtering operation which has been performed. Three examples of experiments that use this principle are described. The irregularities across the wavefront of a laser output beam are eliminated. A two-dimensional pattern is filtered so only the information in one dimension is transmitted. The squares which make up a self-portrait are subtracted, leaving a continuous rendition.
Quantum Fact and Fiction III
Authors: Landé Alfred
Published: August 2005

Part III of this series [A. Landé, Amer. J. Phys. 33, 123 (1965), and 34, 160 (1966), quoted as Parts I and II] continues the critique of the customary interpretation of quantum mechanics. It is directed against the idea that electrons, in opposition to the Born statistical particle interpretation of the wave function, are “wavicles.” Serious conceptual and elementary mathematical defects in Bohr's famous “Discussion with Einstein” are pointed out. The doctrine that position q and momentum p of a particle are blurred over an uncertainty range because both allegedly cannot be measured simultaneously, that q and p do not exist simultaneously, is due to a confusion of analogy with identity of qualities. In its second part, the paper offers a nonquantal derivation of the probability interference law as a necessity under the postulate that the general interdependence between probabilities is to become the ordinary probability addition law in the average. The wave picture of matter violates the postulate of relativity.
Discussion on the Criterion for Conservative Fields
Authors: Feng Shih-yu
Published: August 2005

The usual criterion for a conservative field is that the curl should be zero. However, this criterion meets difficulty when the field contains a singularity. It is shown that the requirement for a conservative field is, besides the vanishing of the curl, that Fx must be continuous in y and z, Fy must be continuous in z and x, and Fz must be continuous in x and y. The word “continuous” implies a limiting process at the singular point as explained in the text.
The Rayleigh-Ritz Method: A Graphical Proof
Authors: Flores J. , Mello P. A.
Published: August 2005

We give a simple graphical proof for the Rayleigh-Ritz variational method for simultaneously obtaining upper bounds to the n lowest eigenvalues of a Hermitean operator.
Measurement of Neutron-Induced, Fission-Fragment Energy Spectra in the Advanced Laboratory
Authors: French W. R. , Bunting R. L.
Published: August 2005

Fission experiments can be profitably performed in the Advanced Laboratory. Measurement of the fragment energy spectrum from a fissile source using a surface barrier detector demonstrates several characteristics of the fission process. Experimental difficulties in such measurements are discussed, and typical results are presented for neutron-induced fission with sources of natural uranium and those enriched in U235. Also shown are the results with the spontaneous fissile source Cf252.
Undergraduate Experiment to Find Nuclear Sizes by Measuring Total Cross Sections for Fast Neutrons
Authors: Minor T. C. , Martin F. D. , Montgomery H. E. , Okun L. M. , Fowler J. L.
Published: August 2005

Pu-α-Be neutron sources, now available in many college laboratories, used with stilbene crystal detectors and proper circuits for neutron-gamma discrimination, permit students to measure fast-neutron total cross sections for a number of easily obtained samples. From these measurements they may calculate the size of nuclei and, using elements covering a wide range of the periodic table, demonstrate the constant density of nuclear matter.
Least Squares Made Easy
Authors: Heald Mark A.
Published: August 2005

A very practical method for hand calculation of least-squares-adjusted slopes, acceleration coefficients, etc., is presented and compared with better known but less-satisfactory algorithms. Particular attention is given to easy methods for estimating the precision of the adjusted constants. The method, based on weighted successive differences, applies to the special case of equal increments in the independent variable.
A Critique of the Definitions of Heat
Authors: Canagaratna S. G.
Published: August 2005

A review is given of three methods of defining heat, viz., the definition using the first law of thermodynamics, the definition through heat capacities, and the definition using the ice-calorimeter. It is shown that the concept of heat and a measure for the heat absorbed by a body can be defined in all its generality only through the use of the first law.
The Infinite Tilted-Well: An Example of Elementary Quantum Mechanics with Applications toward Current Research
Authors: Churchill John N. , Arntz Floyd O.
Published: August 2005

The quantum-mechanical problem of a particle under the simultaneous influence of a linear potential and one-dimensional infinite square-well is considered. A graphical technique is described whereby approximate solutions are obtained for the general case, and some analytical methods are discussed by which exact solutions may be obtained for various special cases. The results should provide insight into a problem of current theoretical and experimental interest: the behavior of electrons in solids under the influence of an applied electric field.
Musical Combination Tones and Oscillations of the Ear Mechanism
Authors: Olson Don
Published: August 2005

Musical combination tones and related phenomena are described and explained by the theory of nonlinear oscillations, as applied to the motion of the structures of the ear. A simple lecture presentation is described which uses combination tones to demonstrate the physical reality and significance of Fourier series solutions to oscillatory problems.
Application of Sommerfeld-Watson Transformation to an Electrostatics Problem
Authors: Pumplin Jon
Published: August 2005

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.
Theory of Quantum Crystals
Authors: Werthamer N. R.
Published: August 2005

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.
Symmetry and Properties of Crystals: Theorem of Group Intersection
Authors: McMillan J. A.
Published: August 2005

Polarized crystals exhibit the symmetry of the intersection of the polarizing-field and the crystal-point groups, thus imposing conditions on spontaneous polarization. Introduction of time reversal and charge conjugation in magnetic and electric configurations leads, through the intersection theorem, to Shubnikov's groups. Intersection with the symmetry point groups of second-rank tensor fields imposes conditions on these latter. Tables of group intersections are given and some instructional examples are discussed.
Particle Motion in a Force-Free Field
Authors: Hughes William T.
Published: August 2005

Particle motion perpendicular to the axis of symmetry of a simple, force-free, magnetic field is shown to be described by an equation whose solution is well known.
A Determination of the Speed of Light by the Phase-Shift Method
Authors: Rogers John , McMillan Ronnie , Pickett Robert , Anderson Richard
Published: August 2005

A low-frequency, phase-shift method for the measurement of the speed of light has been developed. This technique gives results commensurate with other advanced laboratory methods. One advantage of this technique is that the apparatus is of reasonable size and most of the circuitry involves widely known amateur radio techniques. Furthermore, our use of a low modulating frequency permits use of the solid-state, electro-optical light shutter. This eliminates the rather dangerous liquid Kerr cell, thus making our apparatus more acceptable to application in the undergraduate advanced laboratory. From a pedagogical point of view, the student is allowed to use and become acquainted with the lock-in amplifier which is so commonly found in the modern research laboratory. Two rather novel techniques were employed in this apparatus. These were phase multiplication and mixing of the rf signal in the last stages of the photomultiplier. Our value for the speed of light in air was 2.937 × 108 m /sec. The accepted value of the speed of light in air to the same number of significant figures is 2.997 × 108 m /sec.
Born-Oppenheimer Treatment of the Hydrogen Atom
Authors: Deshpande V. K. , Mahanty J.
Published: August 2005

The main features of the treatment of the molecular problem by separation of electronic and nuclear motion, and of the higher-order corrections to this procedure are brought out by the treatment of the exactly solvable two-body problem of the hydrogen atom.
The Virial Equation of State: Its Inversion and Other Manipulations
Authors: Kilpatrick John E. , Ford Douglas Ike
Published: August 2005

The general solution of the problem of expressing the density virial coefficients as polynomials in the pressure virial coefficients (and vice versa) is deduced by a very simple argument. The expressions for both kinds of virial coefficients are deduced as polynomials in the reducible cluster integrals. Some applications are made to the ideal Bosé-Einstein and Fermi-Dirac gases.