bluuebunny/crossref_metadata_2025 huggingface dataset:
Scalar Gravitation
Authors: Wellner Marcel , Sandri Guido
Published: August 2005

Nordström's scalar theory of gravitation is discussed from a modern point of view, and compared with some aspects of general relativity. We discuss the equations of motion for test masses, the field equations in the presence of matter, and the extent to which the principle of equivalence, Mach's principle, and the expansion of the universe are contained in this model. The theory implies what amounts to a Riemannian metric, and features a positive energy density for the gravitational field.
A General Theory of Symmetry Coordinates
Authors: Wilde R. E.
Published: August 2005

Students of molecular dynamics are often confused by the somewhat arbitrary nature of symmetry coordinates. This paper presents a completely general theory of symmetry coordinates which allows every symmetry coordinate to be obtained for any molecule but which also requires a knowledge of the irreducible representations of the point groups. The molecules CH3Cl, CH4, and C6H6 are used as examples.
Redshift and Deflection of Photons by Gravitation: A Comparison of Relativistic and Newtonian Treatments
Authors: O'Leary Austin J.
Published: August 2005

Gravitational redshift of photons from a star and gravitational bending of the path of photons grazing the sun can be derived by using only Newton's laws and the idea of a photon as a particle of mass hv/c2. The difference between the relativistic and Newtonian equations for gravitational redshift is too small to be detected and, therefore, gravitational redshift does not provide experimental verification of the general theory of relativity. On the other hand, a Newtonian treatment of gravitational bending of the path of photons gives only half the true amount of total deflection derived by Einstein in 1915 using general relativity. The case of gravitational bending is treated in some detail.
Mössbauer-Effect Apparatus for an Advanced Undergraduate Teaching Laboratory
Authors: Bearden Alan J. , Mattern P. L. , Nobel P. S.
Published: August 2005

A Mössbauer-effect apparatus, suitable for either lecture demonstration or inclusion in an undergraduate teaching laboratory, is described. Use of a rotating tilted disk to provide linear motion between source and absorber simplifies the construction and calibration of the experimental equipment. Some features are as follows: calibration of velocity by timing rotations of the wheel with a stopwatch, provision of a large-scale motion which graphically illustrates the first-order relativistic Doppler shift and its effect on monochromatic radiation, and sufficient precision to measure the nuclear Zeeman splitting in iron of the Fe57m transition. Construction details, as well as instructions for the use of the equipment, are given.
Compton Effect: Historical Background
Authors: Bartlett Albert Allen
Published: August 2005

A review of the chain of experiments whose results were finally explained by Compton's discovery of the Compton effect shows that these experiments were not solely in the field of x rays. The studies of the scattering of high-energy gamma rays of radium had presented physicists with the puzzle that scattered gamma rays were distinctly less penetrating than were those that had not been scattered, and that the amount of this “softening” of the scattered gamma rays was dependent on both the initial “hardness” of the gamma rays and on the scattering angle. Many of the experimental facts of the Compton effect were well known from the studies of scattering of gamma rays some years before the effects were observed with x rays. Compton's interest in the problem was apparently greatly stimulated by his own experiments on the scattering of gamma rays.

However, since the first detailed and convincing experimental verification of several of the consequences of Compton's hypothesis came from experiments with x rays, one may not be aware of the important role played by gamma-ray experiments in the steps leading to the discovery.
Compton Effect: A Simple Laboratory Experiment
Authors: Bartlett Albert Allen
Published: August 2005

An experiment is described in which the magnitude and angle dependence of the wavelength shift of Compton scattered photons can be determined. The equipment necessary for the experiment is simple and inexpensive. The experiment is a modified version of the “absorption curve” type of study which as early as 1904 (nearly 20 years prior to Compton's discovery) showed the wavelength shift of scattered gamma-ray photons.
Compton Effect: an Experiment for the Advanced Laboratory
Authors: Bartlett A. A. , Wilson J. H. , Lyle O. W. , Wells C. V. , Kraushaar J. J.
Published: August 2005

A description is given of an advanced laboratory experiment in which the student is able to verify the Compton effect in detail. The experiment allows the student to examine the angular dependence of the energy of the Compton-scattered photon and of the Compton-scattered electron. The simultaneity of the two scattered “particles” is the key to the experimental observations. The results allow one to directly verify conservation of energy for single-photon scattering events. The agreement of experiment and theory then allow one to conclude that momentum is also conserved in these encounters.
Second-Order Electric Field due to a Conduction Current
Authors: Baker Don A.
Published: August 2005

Assuming that the fields of a moving-point charge as computed from the retarded Liénard-Wiechert potentials give valid descriptions for moving electrons, it is shown that no net second-order static electric field of the type discussed by Rosser appears on the axis of a charge-neutral circular loop carrying a steady current. An argument is given for the nonexistence of such “residual” electric fields around any closed, charge-neutral region in which the current flow is time independent.
Transition Probabilities for the Forced Quantum Oscillator
Authors: Scarfone Leonard M.
Published: August 2005

Transition probabilities for the forced, undamped quantum harmonic oscillator are obtained by expressing S-matrix elements entirely in terms of Heisenberg states and operators. The application of this method to this elementary-field theoretic model provides a simple example of the contraction technique of modern field theory whereby particles are converted into their corresponding currents. This problem was recently analyzed in the interaction picture from a pedagogical point of view and the treatment presented here is given in the same spirit.
Note on a Decomposition of the Lorentz Transformation
Authors: Davis William R. , Katzin Gerald H. , York James W.
Published: August 2005

A decomposition of the Lorentz transformation is considered which is thought to be more amenable to a simple physical interpretation than a similar type of decomposition given by Møller. While such decompositions are not unique, they can be of some value in considering the limiting processes by which one obtains the infinitesimal Lorentz and Galilean transformations.
Semipermeable Membrane and the Gibbs Paradox
Authors: Fong Peter
Published: August 2005

A number of problems connected with the use of semipermeable membrane in thermodynamics including the Gibbs paradox are discussed from logical and physical points of view.
Resource Letter Scy-1 on Superconductivity
Authors: Ginsberg D. M.
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 Arnold Arons, 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 freshman liberal arts through sophomore physics courses; 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 Scy-1 and enclose a stamped return envelope. A small booklet containing reprints of some of the fundamental references will soon be available for purchase from the American Institute of Physics.
Matrix Representation of Gaussian Optics
Authors: Halbach Klaus
Published: August 2005

The ray-tracing method is used to discuss Gaussian optics. After proving that Gaussian optics can be described by matrices, some often-used general formulas for telescopic and focusing systems are derived. This formalism is then used to solve several problems. They are selected to make the reader familiar with the application of the matrix representation of Gaussian optics and to acquaint him with some optical systems that are very useful but not well known among physicists who use optical methods only occasionally.
Galileo Pilgrimage
Authors: Seeger Raymond J.
Published: August 2005

What are the thoughts of a theoretical physicist when he visits places associated with the life of Galileo, namely, Vallombrosa, Pisa, Padua, Florence, Rome, and Siena? In particular, what did Galileo do scientifically at each of these places and what souvenirs of his activity now remain? His important works are reviewed briefly in this connection. The celebrated case of Galileo and the Roman Catholic Church is viewed in the light of Galileo's own personality and character.
Prediction of Success in Physics for High-Ability Students—A Small Sample Study
Authors: Dessel Norman F.
Published: August 2005

Fifteen commonly available measures of achievement and intelligence are analyzed for a test group of high-ability physics students in an attempt to establish their contributions to the variance of physics scores in a college physics course. Two regression equations are given for prediction of success in physics for this group. It is concluded that: (1) success in physics for this group is not significantly correlated with measured Otis I.Q., social studies subtest of ACT, high-school grade-point average, or rank in high-school class; (2) there is no advantage or disadvantage for the test group in having taken physics in high school; (3) better evaluation practice is needed at the college-physics level in order to extend the study; (4) better evaluation instruments are needed for testing high-ability students.
Incoming Waves in Final States in Matrix Elements for Scattering Problems
Authors: Adawi I.
Published: August 2005

The use of modified plane waves with the spherical incoming waves modification as final states in matrix elements used in calculating scattering cross sections is discussed from the standpoint of two techniques. The first method makes use of general properties of Green's functions for outgoing and incoming waves and their reciprocity relations. The second method is based on expanding Green's function in terms of modified plane waves with either incoming or outgoing spherical wave modification.
Physical Basis for Hund's Rule
Authors: Karayianis N. , Morrison C. A.
Published: August 2005

It is shown that a consideration of the Coulombic and spin-orbit interactions between the electrons of a given atomic configuration is sufficient to arrive at a lowest-energy state consistent with Hund's rule. The maximum-spin requirement of Hund's rule is a result of minimum Coulombic energy alone, whereas maximum orbital angular momentum consistent with maximum spin is a result of minimum spin-orbit energy. It is argued that, to first order, the spin-spin interaction is not a principal factor in determining the properties of this state. The simple notions used to obtain these results are extended to excited states of the nf6 configuration and are shown to give results consistent with calculations based on hydrogenic wavefunctions.
An Undergraduate Laboratory Experiment for Studying the Motion of Coupled Mechanical Systems
Authors: Bueche F. , Pavelka C.
Published: August 2005

The experiment described illustrates the principles of coupled mechanical oscillation, makes use of coupled simple pendulums and favorably lends itself to precise experimental measurements. In addition, the motion of the system in the range of small to moderate amplitudes of oscillation may be completely described in terms of measurable lengths and masses. The experiment appears to be valuable for the intermediate laboratory since it shows the physical significance of the theoretical concepts of normal modes and coordinates.
Newton's Laws of Motion and the 17th Century Laws of Impact
Authors: Arons A. B. , Bork Alfred M.
Published: August 2005

A number of writers on history of science have made it clear that in using the term “motive force” in the “Principia,” Newton referred to what we now call “impulse.” With this interpretation, there is a simple and plausible connection between the laws of impact as they were known and described in Newton's day and Newton's formulation of the Laws of Motion in the “Principia,” and we speculate that Newton might have been motivated by such a perception.
Resource Letter Scr-1 on Semiconductors
Authors: Handler Paul
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 in 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. Such communications should be sent to Professor Arnold Arons, 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 freshman liberal arts through sophomore physics courses; 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 Scr-1 and enclose a stamped return envelope.
Ambipolar Diffusion in Semiconductors
Authors: Geiger F. E. , Cunningham F. G.
Published: August 2005

Ter Haar has shown that simple kinetic theory arguments based on Drude's early work can be used to derive approximate expressions for the transport properties of semiconductors and metals. Using ter Haar's ideas, this paper derives an expression for the ambipolar diffusion contribution to the electron thermal conductivity. In the first part of the derivation a general expression is obtained for the heat conductivity, using the concepts of the kinetic theory of gases and assuming an electron mean free path. The expression obtained is in all respects similar to the diffusion equation from the kinetic theory of gases, except for a term taking the effect of an electric field into consideration. In the second part of the derivation the concepts of band theory and semiconductor statistics are introduced in the kinetic theory equations. The final expression for the ambipolar contribution, using Boltzmann statistics agrees, except for numerical constants, with the exact form derived from considerations based upon the Boltzmann transport equation. The application of Fermi-Dirac statistics to the problem yields no ambipolar diffusion term as a correction to the conductivity, if terms higher than the first order of the reciprocal of the reduced Fermi level are neglected. This is in agreement with the exact results based upon the Boltzmann transport equation from which it is seen that the ambipolar term contains only second and higher order terms of the reciprocal of the reduced Fermi-level.
Some Demonstration Experiments in Optics Using a Gas Laser
Authors: Dutton David , Givens M. Parker , Hopkins Robert E.
Published: August 2005

Some elementary experiments in geometrical and physical optics, usually limited to individual observations in the laboratory, can be adapted for presentation to larger groups as lecture or classroom demonstrations, by making use of the gas laser as light source. This paper describes several such experiments dealing with lens aberrations, interference and diffraction phenomena, and the Abbe theory of the microscope; together with some practical optical systems for performing them.
1964 Citations for Distinguished Service
Authors: Parker Vincent E.
Published: August 2005

The American Association of Physics Teachers annually cites some of its members for distinguished service to the teaching of physics. Four citations were presented at the Annual Meeting of the Association on 25 January 1964. These citations are quoted below.
Identical Motion in Quantum and Classical Mechanics
Authors: Rosen Nathan
Published: August 2005

The conditions are set down, under which the stationary-state motion of a particle in a static field of force is the same according to the Schrödinger equation as in classical mechanics. Some solutions are found. All the cases obtained correspond to unbound states.
Three-Dimensional Polar Coordinates
Authors: Grubin Carl
Published: August 2005

It is shown that conventional plane-polar coordinates can be extended to three dimensions. The result is that three-dimensional motion of a particle can be viewed as instantaneous planar motion plus a rotation of the plane of motion around the instantaneous radius vector from the origin to the particle. The kinematic and dynamic equations in this system are developed and applied to two examples, the spherical pendulum and a problem in orbit motion.
Study Programs for College Physics Teachers—An Analysis of Supply and Demand
Authors: Strassenburg Arnold A.
Published: August 2005

The influence of the rapid increase in scientific knowledge and the changing patterns of science education on college physics teaching is discussed. Training criteria for college physics teachers are suggested, and statistics are quoted on the number of teachers who presently fail to meet the criteria. A survey is presented of the study opportunities available for college physics teachers. It is recommended that more summer study opportunities be provided; some problems involved in implementation are outlined. An analysis is made of the present demand for summer institute programs; suggestions are offered on how to stimulate more participation in study programs among college teachers without advanced degrees. The contributions of the Commission on College Physics in providing summer study opportunities are mentioned, and the role of the physics community in coordinating the entire effort is assessed.
The Berkeley Physics Laboratory
Authors: Portis A. M.
Published: August 2005

A brief description of the development and present state of the Berkeley Physics Laboratory is given. Thirty-six experiments in all are planned. Twenty-eight of these experiments have been used with student groups ranging in size from forty to six-hundred and fifty. The first twenty-eight experiments are described with particular emphasis on the electron deflection and microwave experiments, which are innovations of this laboratory.
Undergraduate Curricula in Physics: A Report on the Princeton Conference on Curriculum S
Authors: Jossem E. Leonard
Published: August 2005

Starting with the recommendations of the Second Ann Arbor Conference for two distinct undergraduate physics major programs, R and S, the Princeton Conference on Curriculum S continued the consideration of the conceptual and practical problems of providing appropriate instruction in physics to undergraduate majors having a variety of educational goals. Major discussion was concerned with the nature of the S curriculum and its relation to R, with the desirability of providing more open curricular structures, and with the problems of obtaining an optimum mixture of the elements of analysis and synthesis in intellectually vigorous courses. Several sample skeleton outlines of possible major curricula were produced by Conference working groups, and it is expected that progress in developing the working materials for the S Curriculum will be continued.
Freedom, Responsibility, and Barriers
Authors: Michels Walter C.
Published: August 2005

Response of the Oersted Medalist to the American Association of Physics Teachers, January 23, 1964.
Thermodynamics of a Reacting Gas
Authors: Vardya M. S.
Published: August 2005

Thermodynamical properties of a gaseous mixture undergoing dissociation or ionization, or both, have been considered in a general way. As a special case, the behavior of ionizing hydrogen gas has been studied. It is found that a perfect gas behaves as an imperfect gas in many ways, when undergoing dissociation or ionization.
Some Aspects of the Splitting of Ionic Energy Levels in Crystals
Authors: Band Hans E.
Published: August 2005

Bethe's early group-theoretical treatment is supplemented by some physical arguments illustrating his method of semiquantitative evaluation of the term splitting. Up to date notations are introduced. The cases of weak, intermediate, and strong crystal-field splitting are discussed, with typical ions given as examples. For cubic and hexagonal site symmetry, the Bethe method is demonstrated step-by-step and the results applied to transition metal ions. Double-valued group representations, double groups and Kramers degeneracy are introduced, compared, and illustrated with physical examples. Certain mathematical analogies between formulas of representation theory and angular momentum theory are pointed out.
Low Cost Radio Telescope
Authors: Taylor Joseph H.
Published: August 2005

A radio interferometer has been constructed at Haverford College as an aid to learning the fundamentals of radio astronomy. Its cost, both in cash outlay and in construction time, make it a feasible year-long project for an undergraduate. Its simplicity does not prevent it from being a useful instrument for instruction at the college or high-school level; among its capabilities are the measurement of the positions of at least four of the strongest discrete cosmic-noise sources, and the diameter of the radio sun.
Particle Orbit Theory for an Ionized Gas
Authors: Mallozzi P.
Published: August 2005

The electrical and optical properties of an ionized gas are derived from a simple physical consideration, based on the average energy acquired by an electron between collisions. The correct formulas are obtained if a time-dependent collision frequency is employed.
Paradoxical Features of Uniformly Distributed Random Events
Authors: Kunz Kaiser S.
Published: August 2005

Some of the problems posed in this paper have been passed around the scientific community for several years and have served to jar a good many scientists regarding their intuition for statistical events. Since these problems are part of the scientific folklore, it seems worthwhile to write them down. The informal narrative style used reflects an attempt to capture a part of the spirit of the usual oral presentation. The author has added some additional questions and methods of solution that have arisen in presenting the problems to informal colloquiums.
Galileo and the Law of Inertia
Authors: Drake Stillman
Published: August 2005

In Aristotle's physics, any motion of a heavy body was either natural (toward the earth's center) or forced (away from the center). Every forced motion was required to have an external mover. For projectiles, the medium was invoked as mover. These rules precluded a true science of dynamics. Galileo, following some earlier critics, noted that rotatory motion of homogeneous spheres would be neither natural nor forced under Aristotle's definition. Investigating such “neutral” motions, he saw that they would include the motion of a heavy body over a frictionless surface concentric with the earth. Hence, motion once imparted to a body on a horizontal plane would be perpetual, and Galileo declared that a heavy body is indifferent to motion or rest in the horizontal plane and would forever remain in whichever state it was given. This restricted principle of inertia enabled Galileo and his followers to found the science of dynamics, by which physics was immeasurably advanced, though he neglected to state explicitly the general inertial principle as formulated two years after his death by Pierre Gassendi and René Descartes.
Canonical Quantization of the Schrödinger Equation
Authors: Tassie L. J.
Published: August 2005

In the usual treatment of the field theory of the nonrelativistic Schrödinger equation, there are more dynamical variables than is warranted by the number of degrees of freedom. This causes difficulties in the canonical quantization. Working in momentum space it is possible to eliminate the extra dynamical variables, leaving a number of independent dynamical variables appropriate to the number of degrees of freedom. The canonical commutation relations can then be applied in a straightforward manner.
On Teaching the History of Physics
Authors: Seeger Raymond J.
Published: August 2005

After reviewing trends in general courses in college physics, the author discusses potential objectives in teaching the history of physics, viz., cultural, pedagogical, research. He emphasizes the necessity for a cultural bridge that will include history, philosophy, and science (the basic course preferably given by a scientist, if an understanding of science is a primary goal). With respect to pedgagogy, he stresses the need for an approach that is immediately functional, but directed toward ultimate understanding. The author's particular concern here is the unique contribution of the history of physics to comprehensive understanding and research training (preferably in the senior year). In addition to the correlating review, a course along this line affords insights into important lessons of the past, the ensnaring involvment of the present and guiding directions for the future, as well as hereditary physics and its social matrix.
Generalization of the Abbe Sine Law in Geometric Optics
Authors: Rainwater James
Published: August 2005

This paper presents relatively unknown, though not new, theorems applicable to a real axially symmetrical optical system. It treats the situation where rays leaving a particular axial object point O in object space are assumed to image perfectly at axial image point O′. A ray through O at angle α with the axis passes through O′ at angle α′ with the axis. The Abbe and Herschel conditions state the required functional relationship between α and α′ to ensure that rays from P image perfectly into P′, when P is infinitesimally displaced from O perpendicular to, or parallel to the axis, respectively. The formulas derived here give the detailed variation of β1, β2, and γ in terms of the functional relation between α and α′, independent of the further specification of the system. They are derived using Fermat's theorem and the second law of thermodynamics. Here β1, β2, and γ represent, respectively, the meridional (primary) lateral magnification, the sagittal (secondary) lateral magnification, and the longitudinal magnification relative to small displacements from O. The variation of β1 and β2 with α specifies the coma figure, while the variation of γ gives the longitudinal spherical aberration for an axially displaced object point.
Henri Poincaré and the Principle of Relativity
Authors: Scribner Charles
Published: August 2005

A review is made of the historical background of the Special Theory of Relativity with particular attention to the theoretical contributions of Henri Poincaré. The primary aims are to show the synthetic aspects of Einstein's original paper on relativity and to clarify the logic of his fundamental innovations.
A Simple Furnace for Growing Metal Crystals
Authors: Clayton Glen T. , Hendrickson Charles
Published: August 2005

A simple furnace has been constructed for growing large metal crystals. Single crystals of aluminum which are conical in shape, 2 in. in diameter at the base and 5 in. in height have been produced.
The Temperature Variation of Gamma for Various Gases: A Student Experiment
Authors: Cronin David J.
Published: August 2005

This paper describes a method for determining γ for gases by measuring the velocity of sound in a closed resonance tube with fixed ends. Air, nitrogen, helium, carbon dioxide, normal hydrogen, and parahydrogen were studied at temperatures between 77°K and 373°K. Inexpensive ceramic transistor radio earphones were used as both exciter and detector. The exciter was driven by a variable frequency audio oscillator in the range 50–3000 cps and the output voltage of the detector was amplified and observed on an oscilloscope. The measured values of γ are accurate to about 1%. This accuracy, and the simplicity of the experiment, combine to offer a good experiment for the undergraduate laboratory.
Experimental Experiments in the Elementary Physics Laboratory
Authors: Landis Harry M.
Published: August 2005

The desirability of including an element of discovery in the laboratory work of beginning students is discussed, and two experiments on elementary mechanics which embody this characteristic are described.
Advanced Physics Laboratory Course at Cornell
Authors: Hartman Paul L.
Published: August 2005

For fifty years an advanced laboratory course has been one of the major course offerings of the Department of Physics at Cornell. It has been taken by all undergraduate physics majors and by almost all physics graduate students, potential theorists and experimentalists alike. During this period of time, the course has gone through many changes, both in “philosophy” and in facilities. Instead of the ten or a dozen students of forty years ago, the enrollment is now over 100 and requires the teaching time of eleven staff members and a full-time laboratory technician. The Department receives many requests for information about the course, requests for the list and description of the experiments offered, and about the general pedagogical format. Many other universities have established courses in its pattern. It is the purpose of this paper to provide a rather general description of the course, a description that might be of interest to a physics student, to a teacher, or to a person interested in the teaching of physics.
Physics of the Mössbauer Effect
Authors: Eyges Leonard
Published: August 2005

This paper considers from a simple physical point of view the Mössbauer effect, i.e., the “recoilless emission” of gamma rays from a nucleus bound in a crystal lattice. It begins with a discussion of the kinematics of gamma-ray emission from such a nucleus. The idealized case of a massive “lattice” characterized by a single frequency and the more realistic one and three-dimensional models are treated. We point up the fact that in the Mössbauer effect the lattice as a whole (the lattice center of mass) always recoils after photon emission, so that the term “recoilless emission” is in one sense misleading. We emphasize that the essence of the Mössbauer effect is not photon emission without recoil, but rather is photon emission without transfer of energy to internal degrees of freedom of the lattice. Using the basic ideas of quantum mechanics, namely, the rules for the manipulation of probability amplitudes (the so-called “transformation theory”), we calculate the probability for recoil without excitation of internal degrees of freedom, i.e., the Mössbauer f factor, on the assumption that the individual photon emissions, and consequent lattice recoil, are instantaneous. In Appendix A we discuss this question of instantaneous emission in some detail, and show how it is not in contradiction with the fact that the nuclear transition that leads to the gamma-ray emission has a finite half-width. In Appendix B those rules of transformation theory that are used in the body of the paper are summarized.
Experiments with a Thermoelectric Heat Pump
Authors: Mortlock A. J.
Published: August 2005

A teaching experiment based on a commercial thermoelectric heat pump which utilizes semiconductor materials is described. The measurements made yield the figure of merit for the thermocouple as well as its coefficient of performance as a pump.
Determination of Radii of Curvature of Spherical Surfaces using Newton's Rings
Authors: Sandhu H. S. , Friedmann G. B.
Published: August 2005

Newton's rings formed by an air film bounded by spherical surfaces are discussed. The physical and mathematical limitations involved in determining the radii of curvature of the bounding spherical surfaces are pointed out.
The Weight of Mass
Authors: Armstrong H. L.
Published: August 2005

It is argued that insistence on the use of the word “mass,” where one would ordinarily say “weight” is nothing but pedantry, and imposes a needless “weight,” i.e., burden, on students. Evidence is invoked from laws that the word “weight” expresses the notion of the measure of an object, which is supposed to be the peculiar meaning of “mass,” and has done so for a long time. Finally, an example shows how dropping this distinction (which, it is maintained, is nothing but a distinction without a difference) helps to clear up certain objections which have been proposed about the development of Newton's laws.
Resource Letter CM-1 on the Teaching of Angular Momentum and Rigid Body Motion
Authors: Shonle John I.
Published: August 2005

Prepared at the request of the AAPT Committee on Resource Letters and the AAPT Committee on Tests; 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 Arnold Arons, Chairman, Resource Letter Committee, Department of Physics, Amherst College, Amherst, Massachusetts.

Notation: The letter E after an item number indicates elementary reading level, the letter I indicates intermediate 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 CM-1 and enclose a stamped return envelope.
Photographic Storage of Pulse-Height Information in Scintillation Experiments
Authors: Work Richard N.
Published: August 2005

A simplified arrangement is described for making gray wedge and two-dimensional coincidence pulse-height analyses. Examples of different types of spectra are given and application is made to an experiment on the Compton effect.
Hamiltonian Operator in Generalized Coordinates
Authors: Dureau Lionel D.
Published: August 2005

The quantum mechanical, time-dependent wave equation in generalized coordinates is obtained by a slight modification of Schrödinger's original derivation. If the classical Hamiltonian for a system is known, the variational technique may be applied to the Hamilton-Jacobi equation to yield an Euler-Lagrange equation. This latter is then the wave equation for the system. The method, which is generally easy to apply, is illustrated by applications to a single particle in curvilinear coordinates and to a symmetric top molecule.
External dc Field of a Long Solenoid
Authors: Brick D. B. , Snyder A. W.
Published: August 2005

The external dc field of a long solenoid is investigated. An exact solution is obtained in the form of an infinite series. For three cases, the series reduces to simple analytical expressions amenable to slide-rule computation: (a) the infinitely long solenoid for which the external field is zero, (b) the field far from the ends of a long finite solenoid for radial distances close to the solenoid surface, and (c) the long solenoid at radii comparable to and greater than the solenoid half-length. The variations with radial distance of the approximate expressions derived for cases (b) and (c) are plotted parametrically over a large-range of radial distances. Exact results are also plotted for two typical solenoid length-to-radius values obtained by numerical integration. Agreement of the exact results with the approximate expression for case (c) over the entire range of radial distances is extremely good. Expression (b) is a good approximation only for small radial distances; however, for typical solenoid length-to-radius values, the two expressions (b) and (c) converge for small r.
Measuring the Wavelength of Light with a Ruler
Authors: Schawlow A. L.
Published: August 2005

A simple lecture demonstration is described, in which light from a gas-discharge laser is diffracted at grazing incidence by the rulings of a steel scale. The wavelength of light is obtained by measuring the pattern spacings and the distance from the ruler to the screen.
Energy Propagation in a Finite Lattice
Authors: Band William , Bhatti A. D.
Published: August 2005

The standing-wave normal modes and their frequencies are derived for a finite, one-dimensional harmonic lattice with force-free boundary conditions. The energy-current operator is derived in terms of excitation and deexcitation operators for the standing-wave energy states. The expectation value of the energy current in any such state is identically 0. External driving and load forces on the ends of the lattice are treated as time-dependent perturbations. The perturbed states of the lattice are found. The expectation values of the energy-current operator in such perturbed states coincide with the classical response of the lattice; the energy current is the linear energy density multiplied by the group velocity. This approach is more realistic than the conventional method using cyclic boundary conditions, describing the energy current in terms of running normal modes (momentum states) that can exist only in topologically unrealistic lattices without ends. It is hoped to generalize this work to finite lattices of 2 and 3 dimensions.
Relativistic Accelerated Systems
Authors: Marsh L. McL.
Published: August 2005

Conditions that must be satisfied by the transformation equations connecting inertial and accelerated systems are deduced for the case of rectilinear motion. Solutions are obtained and discussed for certain special cases, with reference to the “clock paradox”.
Operator Gauge Transformations
Authors: Corinaldesi E. , Roman P.
Published: August 2005

The Gupta-Bleuler formulation of the subsidiary condition of quantum electrodynamics in the interaction picture is reviewed. This formalism is used to construct a simple proof of the invariance of the S-matrix under q-number gauge transformations A′μ = Aμ+δμF(□)δνA or, equivalently, under certain well-known modifications of the photon propagator.
Complexions of an Assembly of Quasi-Independent Localized Systems
Authors: Offenbacher Elmer L.
Published: August 2005

The total number of complexions is computed exactly for an isolated assembly of N quasiindependent localized systems with equally-spaced energy levels. This number Ω(N), is equal to Σt{Nk} where each term depends on a particular set of energy-level occupation numbers, Nk, allowed by the energy and system-number conservation conditions. In thermodynamic calculations, the approximation is usually made of replacing Ω by the maximum term in this sum tmax. A procedure is proposed for obtaining the exact value of tmax for integral N. The error made in the approximation is then calculated, and χ = ln tmax/lnΩ is computed for N = 2r. For N = 212 = 4096 one finds that (χ−1) is less than 0.005. An approximate analytic form for χ valid for higher N is also given.
Quantitative Study of Linear Momentum in Two Dimensions by Means of Pucks Operated on a Rectangular Air Table
Authors: Webb Helen H.
Published: August 2005

The construction and operation of a two-dimensional air-table that yields quantitative linear momentum data are described. The air cushion is provided by running compressed air into a rectangular box whose top surface is perforated with many small holes on the intersections of an illustrated rectangular grid. The data are obtained by arranging that a trace of the motion of each puck is made on a sheet of paraffined paper by a 1/60-sec spark timer. The apparatus makes possible the quantitative study of the conservation of linear momentum in two dimensions. These air tables have been used in the elementary physics laboratories at The Pennsylvania State University since the fall of 1962.
Observation of the Precession of the Spin Axis Relative to the Body Axes of a Rotating Body
Authors: Retsky Michael W.
Published: August 2005

A method is described for observing the precession of the spin axis relative to the body axes of a rotating steel ball. The ball is magnetized and is made to spin at 2000 rps in a shaped air column. A sensing coil detects any change in the axis about which the ball spins. The observed precessional frequency must be analyzed statistically and the statistical variation is discussed. Several other related experiments are presented.
Rutherford Scattering Apparatus for Laboratory and Lecture Demonstration
Authors: Lindsay Richard H. , Ehlers David H. , McLeod Raymond R.
Published: August 2005

A relatively inexpensive scattering chamber and associated apparatus for performing the Rutherford scattering experiment in laboratory and lecture demonstrations is described. Typical data from a 30-min lecture demonstration is discussed. Features of the apparatus include a silicon surface barrier detector, externally controlled angle settings, and the applicability of the apparatus to a number of experiments for the undergraduate.
Faraday Effect in a Plasma
Authors: Porter W. S. , Bock E. M.
Published: August 2005

A treatment of the Faraday effect in an anisotropic plasma is presented. The plasma is treated as a fluid in which collisions may occur. Relations are derived for the rotation of the plane of polarization and the ellipticity of the electromagnetic wave in terms of parameters associated with the plasma.
Inverted Pendulum
Authors: Blitzer Leon
Published: August 2005

The equations of motion for the driven inverted compound pendulum are derived from elementary principles. Detailed attention is given to the steady-state motion of the pendulum driven horizontally in a sinusoidal fashion.
Pedestrian Covariant Phase-Space Integration
Authors: Williamson W.
Published: August 2005

Two- and three-body Lorentz invariant phase-space volumes are given in terms of covariant variables. Examples in the use of covariant variables for two- and three-body final-state problems are given and methods which may reduce the labor in the analytic integrations for involved problems are discussed. In the Appendix of this paper four-body phase-space procedures are summarized.
Energy Conservation as the Basis of Relativistic Mechanics. II
Authors: Ehlers J. , Rindler W. , Penrose R.
Published: August 2005

From the relativity principle and the conservation of energy in particle collisions we deduce the form of the energy function, and the conservation of inertial mass and three-momentum. We show that the arguments are parallel under Einsteinian and Galilean kinematics.
Scattering of Wave Packets
Authors: Wichmann Eyvind H.
Published: August 2005

The elastic scattering of spinless particles from a spherically symmetric stationary target is considered. The main idea is to describe the incident beam of particles as a certain statistical ensemble of one-particle wave packets, and to define the differential cross section in terms of the average scattering of the particles in this ensemble. The physical significance of this mode of description is discussed, and arguments are presented as to why it should be regarded as a realistic description of typical scattering experiments. The discussion is general, and not restricted to potential scattering. It is based on the notion of the S matrix, and the most basic ideas of the S matrix are discussed. A simple derivation of the partial wave expansion is given within the framework of S matrix theory.

The aim of this paper is mainly pedagogical, and the final results obtained are old and well established.
Factorization of the Radial Equation for the Hydrogen Atom
Authors: Salsburg Zevi W.
Published: August 2005

The radial equation for the hydrogen atom problem is factored to yield raising and lowering operators for the oribtal angular momentum quantum number l. This procedure, which is a direct analog for the usual treatment of the angular momentum operators, is considered to offer many pedagogical advantages for an introductory course in quantum mechanics over the usual series method of solution. The raising process is terminated by establishing the existence of an upper bound for l. The use of the hypervirial relations is advocated for displaying such an a priori upper bound.
Fermat's Principle and Geometrical Optics
Authors: Shaw J. H.
Published: August 2005

The paths of light rays reflected or refracted at spherical surfaces are obtained by application of Fermat's principle. The first-order Gaussian equations describing the image-forming properties of such surfaces are derived and the criteria for image formation are discussed.
Magnetic Monopoles, Weak Interactions, and Angular Momentum
Authors: Strax N.
Published: August 2005

If magnetic monopoles were to engage in processes fully analogous to the parity nonconserving weak interaction processes engaged in by electrically charged particles, then the sign of angular momentum vectors would acquire an absolute significance. This is a consequence of (a) the symmetry properties of electromagnetism, (b) the symmetry properties of weak interactions, and (c) the inequality between the numerical value of the quantum of electric charge and the numerical value of the quantum of magnetic pole strength.
Cosmology and Newtonian Mechanics
Authors: Callan C. , Dicke R. H. , Peebles P. J. E.
Published: August 2005

The general relativistic solution to the cosmological problem is often considered to be one of its most beautiful results. It is shown that Newtonian mechanics is quite sufficient to discuss the dynamics of the expanding universe. Furthermore, this is not a cleverly contrived classical model, or a crude nonrelativistic approximation, but a completely correct discussion of the dynamics of the expansion in a region where both general relativity and Newtonian mechanics are equally valid.
Ball Lightning and Self-Containing Electromagnetic Fields
Authors: Johnson Philip O.
Published: August 2005

A model for ball lightning is developed in which most of its energy is accounted for by a toroidal magnetic field. The poloidal motion of its electrons, which maintains the magnetic field, is stabilized by a seaparation of charges which produces the required electric field. Loss of electrons and ions by recombination is made up by an interaction of the magnetic field with the current which replaces the lost charges. Order of magnitude computations are made for three phenomena reported in the literature: (1) a large ball lightning, (2) a plasmoid observed in a submarine, and (3) a granule on the surface of the sun. The principal justification for this model is its mechanism for extended lifetimes.