bluuebunny/crossref_metadata_2025 huggingface dataset:
Covariant formulation of Hooke’s law
Authors: Gro/n O/.
Published: March 2005

Introducing a four-vector strain and a four-force stress, Hooke’s law is written as a four-vector equation. This formulation is shown to clarify seemingly paradoxical results in connection with uniformly accelerated motion, and rotational motion with angular acceleration.
Experiment on impulsive excitation, resonance, and Fourier analysis of a harmonic oscillator
Authors: Macomber Hilliard K.
Published: March 2005

It is shown how a simple electrical circuit may be made to operate as an impulsively excited damped harmonic oscillator having independently variable natural frequency and damping. The oscillator’s response is developed in a particularly transparent way through impulse analysis, a technique that is wholly within the time domain and provides an alternative to Fourier analysis in the frequency domain. Resonance is exhibited and interpreted using impulse analysis, and through resonance, contact is made with Fourier analysis.
Constants of motion and Hamiltonians
Authors: Yan C. C.
Published: March 2005

It is shown that for one-dimensional motion a canonical momentum can be defined based on the first integral of the equation of motion. By substituting the so defined canonical momentum into the first integral, one obtains a Hamiltonian.
Computer symbolic math in physics education
Authors: Stoutemyer David R.
Published: March 2005

The author discusses the role of computer symbolic mathematics to join numerical computation in support of physics education, the the symbolic math system can perform non-numeric analytical operations.(AIP)
Geometrical treatment of force: A static example
Authors: Bender Robert K.
Published: March 2005

An example of the geometric treatment of a classical force is presented as a concrete illustration of the principle of covariance, an idea that is basic to general relativity. The manner in which the force components are accounted for by the Christoffel symbols associated with the model geometry is easily seen because of the familiar nature of the three-dimensional, classical, example. We then briefy indicate how this three-dimensional case can be extended to the four-dimensional geometries of general relativity. Making contact between classical examples and general relativity is usually done via the principle of equivalence, which involves coordinate systems in relative motion. Our example involves the geometric model that represents a single coordinate system.
A new look at stimulated transition rates
Authors: Doughty Glenn R.
Published: March 2005

A general expression for stimulated transition rates between two levels of an atomic system is developed. This expression not only applies for an arbitrary radiation field, but it also includes the effects of line broadening on transition rates. The general expression is used to obtain the rate equation for the spectral photon number density per steradian for a given pair of atomic energy levels. The result is applied to two special cases by integrating over the spectral and angular ranges of interest.
The world’s evolving energy system
Authors: Hubbert M. King
Published: March 2005

Human history can be divided into three distinct successive phases. The first, comprising all history prior to about 1800, was characterized by a small human population, a low level of energy consumption per capita, and very slow rates of change. The second, based upon the exploitation of the fossil fuels and the industrial metals, has been a period of continuous and spectacular exponential growth. However, because of the finite resources of the Earth’s fossil fuels and metallic ores, the second phase can only be transitory. Most of the ores of the industrial metals will have been mined within the next century. The third phase, therefore, must again become one of the slow rates of growth, but initially at least with a large population and a high rate of energy consumption. Perhaps the foremost problem facing mankind at present is that of how to make the transition from the present exponential-growth phase to the near steady state of the future by as noncatastrophic a progression as possible.
Dimension of a quantum-mechanical path
Authors: Abbott L. F. , Wise Mark B.
Published: March 2005

We show that the observed path of a particle in quantum mechanics is a fractal curve with Hausdorff dimension two.
Microscope resolution
Authors: Higbie J.
Published: March 2005

When dealing with the topic of finite conjugate, point-source resolution in elementary discussions, we generally take one of two courses. Either we adopt the (somewhat unmotivated) standard Jenkins and White approach or else we try to derive the result on the basis of standard diffraction theory using the known result for the diffraction by a circular aperture. However, the Jenkins and White approach, while giving a believable resolution formula, implies a magnification formula which appears to be wrong. On the other hand, the diffraction approach gives the ’’correct’’ magnification formula but its resolution formula implies that infinite resolution is possible for finite wavelength light since the diffraction angle goes to zero for large apertures. It is shown that the key to a coherent presentation of this topic and the resolution of these difficulties is provided by the relatively obscure Abbe’s sine theorem.
Experiments in special relativity using Compton scattering of gamma rays
Authors: Egelstaff P. A. , Jackman J. A. , Schultz P. J. , Nickel B. G. , MacKenzie I. K.
Published: March 2005

Some simple undergraduate laboratory experiments are described, which verify the energy–momentum relationship of special relativity. These experiments have been designed either to be used as classroom demonstrations or to be carried out by second-year students.
Methods of resolution of resistance and some simple applications
Authors: Nan-xian Chen
Published: March 2005

This paper presents a extension of traditional circuit theory in analogy to the resolution of forces. In mechanics, for solving various problems we use the composition of force and also the resolution of a force as well, the latter being the inverse operation of the former. In electricity, we indeed use only the connection of resistances in series and in parallel. In this article, it is intended to related the inverse operation of resistances in series and in parallel—the method of resolution and its simple applications. In solving some of the circuit problems it may be found convenient and adoptable even if the circuit includes inductance and capacity.
Spherical pendulum revisited
Authors: Olsson M. G.
Published: March 2005

A simplified calculation of spherical pendulum precession is given at an introductory or intermediate level. An apparatus is described to verify the theoretical result.
Cognition of learning physics
Authors: Larkin Jill
Published: March 2005

Experienced physicists solve even simple textbook problems in ways that are very different form the solutions produced by beginning students. This paper describes these differences using a computer-implemented model that ’’learns.’’ This research is set in the context of modern information-processing psychology, and is related to other work relevant to how people know and learn in quantitative domains.
Kinematics of the free throw in basketball
Authors: Tan A. , Miller G.
Published: March 2005

The kinematics of the two basic styles of free throw in basketball are discussed. It is shown that from a purely kinematic and trajectory point of view, the overhand push shot is preferable to the underhand loop shot. The advantages of the underhand shot lie in the actual execution of the shot.
Two-body three-dimensional collisions leading to orthogonal final velocities
Authors: Draper James E.
Published: March 2005

The general conditions of two-body (arbitrary mass ratio), three-dimensional, elastic or inelastic collisions leading to mutually perpendicular outgoing velocities are given simply in terms of vector diagrams.
An exactly soluble quantum model of an atom in an arbitrarily strong uniform magnetic field
Authors: Silverman Mark P.
Published: March 2005

The isotropic oscillator in a uniform magnetic field is an exactly soluble quantum problem which can serve as a useful model of an atom in a magnetic field of arbitrary strength. The exact eigenvalue spectrum is derived, compared with perturbation theory for low field strengths, and shown to yield a quasi-Landau spectrum for high field strengths. The frequency, polarization, and relative intensity of the spectral lines of the Zeeman effect are determined as a function of the field strength. The effect of the field on atomic size and on the atomic wave functions is discussed; the three-dimensional system is shown to collapse into a needlelike one-dimensional system for a sufficiently intense field.
Moment expansion representation of probability density functions
Authors: Gillespie Daniel T.
Published: March 2005

A discussion is given of a formal way of representing probability density functions in terms of their central moments and the derivatives of the Dirac delta function. This generalized function representation is then used (a) to obtain an expression giving the value of density function at any point and (b) to exhibit an alternative way of deriving the Kramers–Moyal expansion from the Smoluchowski equation.
Scientific presentation of project results: Role playing in a course for nonscientists
Authors: Jewett John W.
Published: March 2005

One of the goals of a science course for nonscientists is to introduce the student to the thought processes and experiences of being a scientist. This article discusses a role-playing technique used in a physics of music course that addresses this goal. The students choose a research project to work on, and present their results as a journal article or an oral presentation at a scientific ’’meeting.’’ The journal articles are refereed and those accepted, along with a program of the meeting, are formed into a journal which is distributed to all the students. Student response has been positive, both in terms of enjoyment of the project and of improvement in writing skills.
Fourier integral treatment yielding insight into the control of Gibb’s phenomenon
Authors: Harvey James E.
Published: March 2005

The phenonmenon of overshoot and the associated oscillation (Gibb’s phenomenon) that occur in the Fourier series approximation to a discontinuous function are investigated by considering the Fourier sum to be a special case of the Fourier integral transform. It is then shown that Gibb’s phenomenon can be reduced or eliminated by multiplying the Fourier transform of the desired function by an appropriate filter function; however, this also reduces the steep slopes representing the points of discontinuity. Two separate parameterized filter functions are presented that can be used in trade-off studies to optimize the magnitude of the resulting oscillations and reduction in slope associated with the discontinuity.
Physical approach to the theory of constrained motion
Authors: Liu Shu-Ping
Published: March 2005

A mathematically elementary approach based entirely on Newton’s laws of motion and physical arguments to the problem of constrained motion subjected to general velocity-dependent constraints is presented. Natures of constraint forces are extracted from constraint relations and, consequently, the equations of motion in Newton’s, Lagrange’s, and Appell’s form are obtained. D’Alembert’s principle is proved to be true for and only for holonomic constraints and constraints homogeneous in velocity dependence.
Quantum operators in generalized coordinates
Authors: Villaseñor-González Pedro , Cisneros-Parra Joel
Published: March 2005

It will be shown in this paper how to build quantum operators in generalized coordinates. A direct substitution of momentum operators in the classical expression suffices; the only condition being that this expression must be written in matrix form before the substitution. Specifically, we are then able to show that the two operators −ih/(∂/∂Q) and −ih/g−1/2 (∂/∂Q)g1/2, and only these, are to be associated with generalized momenta.
Comparative reasoning abilities of college students
Authors: Maloney David P.
Published: March 2005

Comparative reasoning abilities of college students, based on an application of Piagetian theories, are discussed with to different populations of students.(AIP)
Computing the moment of inertia
Authors: Patera Russell
Published: March 2005

The author presents a method for computing the moment of inertia of an extended body without the use of calculus for a specific class of geometrical shapes. (AIP)
Computer projects in physics: A course
Authors: Patterson J. D.
Published: March 2005

The development of a physics course that makes use of computer facilities is discussed. (AIP)
Comments on Fourier analysis of the simple pendulum
Authors: Hall Donald E.
Published: March 2005

The author offers observations on comments recently made by Simon and Riesz concerning a simple pendulum. (AIP)
Resource letter BH-1: Black holes
Authors: Detweiler Steven
Published: March 2005

The author has selected resource material that focusses on black holes.
An elementary formalism for general relativity
Authors: diSessa Andrea A.
Published: March 2005

An elementary formalism for representing curved space-time is developed which allows transparent qualitative explanation of such general relativistic effects as gravitational redshift, deflection of starlight, and precession of a gyroscope in orbit. The formalism is based on a method of surveying and subsequent mapmaking and does not rely on the usual tensor machinery, connection coefficients, etc. Yet metric (survey) information can be quantitatively specified and subsequently used to calculate the magnitudes of those relativistic effects and even to build a simple computer simulation. In addition, the formalism is used to make a conceptual analysis of Einstein’s principle of equivalence which explains the famous factor of two missing from his first calculation of the deflection of starlight using only the equivalence principle. A final section outlines a number of student activities.
Acceleration of a static observer near the event horizon of a static isolated black hole
Authors: Doughty Noel A.
Published: March 2005

The magnitude of the proper acceleration of a static observer (or test particle) in a static, isolated, spherically symmetric space-time region is compared with the Newtonian result including the situation in the interior of a perfect-fluid star. The calculation shows that the proper acceleration diverges on the event horizon of a spherically symmetric black hole. The ’surface gravity’ of a spherically symmetric black hole, as used in descriptions of the Hawking radiation, is then explicitly related to the accelerations of such static observers, thus providing a simple physical interpretation of the surface gravity and illustrating the global (nonlocal) nature of the event horizon. The calculations are presented in the SI physical equations used almost exclusively by many students and teachers of physics.
Evolution of the Two Cultures controversy
Authors: Bieniek Ronald J.
Published: March 2005

The Two Cultures schism is a persistent problem in our society. For over a century, scientific spokesmen and literary critics, from T. H. Huxley and M. Arnold to C. P. Snow and F. R. Leavis, have been involved in the Two Cultures issue. This article examines the evolution of the controversy between the ’’scientific’’ and ’’humanistic’’ elements of Western culture and its relation to educational policies. The division and antagonism between these two cultures appears to have arisen from differences in the human attitudes that they are preceived to engender. ’’Scientific’’ professionalism has been associated with a progressive optimism and self-assurance that nurture a broad humanitarianism, while the ’’literary’’ tradition is characterized by restraint, acceptance, and a more selective humanism.
Falsification by space charge of electron beam energy measurements
Authors: Varney Robert N.
Published: March 2005

When the energy of the electrons in a beam is determined by noting the value of a stopping potential that cuts off the beam, the current density of the beam must be below a limiting value determined by space charge considerations. Above this limit, cutoff occurs sharply at a voltage that may be far below the potential that accelerates the beam. At stopping potentials above cutoff, a weak tail of current does persist all the way up to the full potential of the beam.
Modified Bohr quantization of charmonium
Authors: Sheehy Brian , von Baeyer Hans C.
Published: March 2005

Bohr quantization of circular orbits is modified by the addition of radial excitations treated in the harmonic approximation, and by the use of half-interger angular momentum quantum numbers. Applied to the hydrogen spectrum, the modification leads to a correct assignment of angular momenta, but fails to reproduce the ground state. Applied to charmonium this simple method yields a spectrum in fairly good agreement with the results of other more complicated calculations.
Maxwell’s relations for a van der Waals gas and a nuclear paramagnetic system
Authors: Herlihy James , Michelson Carol , Prieto Mercedes , Ruth Jonathan , Barker William A.
Published: March 2005

Appropriate partition functions for the van der Waals gas and the nuclear paramagnetic system are used to obtain the entropy expressions and the equations of state. The particular form for each of the four Maxwell’s relations is evaluated for these two systems, establishing internal consistency with the first two laws of thermodynamics. The well-known limiting expressions for the ideal gas and Curie law paramagnetism readily follow. Maxwell’s relations are important in analyzing the throttling process for a nonideal gas and adiabatic demagnetization for a nuclear spin system. The van der Waals equations are of classical orgin, they have a limited temperature range of validity, and they do not describe real gases at low temperature after they have condensed. The low-temperature predictions of the equations describing the nuclear paramagnetic system are consistent with the third law of thermodynamics because the partition function takes quantum effects into account.
Inexpensive photovoltaic solar radiometer
Authors: Kissner Fritz
Published: March 2005

Using a solar cell as a sensor, a low-cost instrument can be constructed which measures both the instantaneous and integrated value of solar flux. The process of constructing and calibrating the instrument constitutes an excellent undergraduate experimental project, affording the student an opportunity to examine a variety of aspects associated with solar energy measurements.
Electric fields and charge distributions associated with steady currents
Authors: Coombes C. A. , Laue H.
Published: March 2005

By means of the example of a very long straight wire, we investigate the question of what determines the electric field outside current-carrying conductors.
Intelligent light bulb: A negative feedback demonstration
Authors: Wolfson R. L. T.
Published: March 2005

The author demonstrates the Intelligent Light Bulb, an optoelectronic feedback circuit. The circuit is extremely simple and may be understood easily in dc terms. (AIP)
Buoyant force analog: A demonstration for the vertical stage overhead projector
Authors: Spagna George
Published: March 2005

A bouyant force analog is used with a vertical stage overhead projector.(AII )
Walsh transforms
Authors: Beer Tom
Published: March 2005

Walsh functions are an orthogonal set of square-wave functions that arise when dealing with digitized data. The Walsh transform and inverse Walsh transform are easy to calculate by hand, and can be very quickly done by digital computers. Examples of the uses of Walsh transform include real-time image processing of noisy data, and the rapid solution of nonlinear differential equations.
Flexible, mastery-oriented astrophysics sequence
Authors: Zeilik Michael
Published: March 2005

This paper reports on the implementation and impact of a two-semester mastery-oriented astrophysics sequence for upper-level physics–astrophysics majors designed to handle flexibly a wide range of student backgrounds. A Personalized System of Instruction (PSI) format was used, which facilitated frequent student–instructor interaction and role-modeling behavior in class. Compared to students’ reactions to the same content in a lecture format, students reported the mastery-oriented courses as helping them better to develop professional skills, competencies, and points of view; learn how professionals gain new knowledge in astrophysics; develop skills in oral and written expression; and learn fundamental principles and theories. These attitudes held up over three years of course development and evaluation.
Determination of the acceleration due to gravity with the Cenco–Behr free-fall apparatus
Authors: Nelson Robert A.
Published: March 2005

Spark-recorded speed and distance data for a freely falling body are analyzed by the method of least squares to obtain the acceleration due to gravity g. It is found that the resistance and buoyancy of the air produce systematic errors that are not negligible. These factors are taken into account both by an approximate correction and by an exact nonlinear least-squares analysis of the data. From a wind tunnel measurement the drag coefficient of the falling body is found to be CD = 0.63±0.03. Then from the distance data for ten trials we obtain g = 9.8012 ±0.0035 m/sec2. This value agrees with the nominal value of g for our location, 9.8026 m/sec2, within one standard deviation.
Spiral-syllabus course in wave phenomena to introduce majors and nonmajors to physics
Authors: Touger Jerold S.
Published: March 2005

A single course to introduce physics to both nonscience and physics majors has been developed, dealing with light, sound, and signal, transmission and reception, and emphasizing wave aspects of these phenomena. Themes such as the observational basis of physics, the progression from qualitative observation to measurement, physical models, mathematical modeling, and the utility of models in developing technology are stressed. Modes of presentation, consistent with the notion of a spiral syllabus, are explained with reference to the cognitive and educational theories of Bruner and Piaget. Reasons are discussed for choosing this subject matter in preference to Newtonian mechanics as a starting point for physics majors.
Path integral solution to the infinite square well
Authors: Goodman Mark
Published: March 2005

The infinite square-well potential in one dimension is solved using Feynman path integration. This solution uses an image point method equivalent to a sum over classical paths.
Critique of conventional relativistic quantum mechanics
Authors: Fanchi John R.
Published: March 2005

Relativistic quantum-mechanical theories presently taught in upper-division undergraduate and graduate programs are critically examined. Following an historical sketch of the development of relativistic quantum mechanics, a discussion of the still unresolved difficulties of the presently accepted theories is presented. This review is designed to complement and update the discussion of relativistic quantum mechanics presented in many widely used texts.
Poincaré gauge in electrodynamics
Authors: Brittin Wesley E. , Smythe W. Rodman , Wyss Walter
Published: March 2005

The gauge presented here, which we call the Poincaré gauge, is a generalization of the well-known expressions φ = −r⋅E0 and A = 1/2 B0×r for the scalar and vector potentials which describe static, uniform electric and magnetic fields. This gauge provides a direct method for calculating a vector potential for any given static or dynamic magnetic field. After we establish the validity and generality of this gauge, we use it to produce a simple and unambiguous method of computing the flux linking an arbitrary knotted and twisted closed circuit. The magnetic flux linking the curve bounding a Möbius band is computed as a simple example. Arguments are then presented that physics students should have the opportunity of learning early in their curriculum modern geometric approaches to physics. (The language of exterior calculus may be as important to future physics as vector calculus was to the past.) Finally, an appendix illustrates how the Poincaré gauge (and others) may be derived from Poincaré’s lemma relating exact and closed exterior differential forms.
Hyperfine splitting in the ground state of hydrogen
Authors: Griffiths David J.
Published: March 2005

The hyperfine structure of atomic hydrogen is derived in a simple and self-contained way that makes the theory accessible to advanced undergraduates in a first course on quantum mechanics.
Local-field effects and effective-medium theory: A microscopic perspective
Authors: Aspnes D. E.
Published: March 2005

Standard textbook derivations of the Clausius–Mossotti (Lorentz–Lorenz) relation tend to obscure the physical origin of local-field effects by proceeding from the macroscopic dielectric function of the equivalent homogeneous system to the microscopic parameters of the model. The microscopic and macroscopic aspects can be made clearer by reversing the order, that is, by first obtaining the microscopic solution and then implementing the definition of macroscopic quantities as averages of their microscopic counterparts. This approach also leads naturally into a treatment of effective-medium theory and the description of the dielectric response of heterogeneous materials.
Science and society test VII: Energy and environment
Authors: Hafemeister David W.
Published: March 2005

Approximate numerical estimates are developed in order to quantify a variety of environmental effects that result from energy production. The results of these calculations are consistent with either direct observations or with more complex calculations. This paper will cover some of the possible environmental effects of the following: (1) the greenhouse effect caused by increased CO2 in the atmosphere; (2) loss of coolant accidents in nuclear reactors; (3) increased radon concentrations in buildings with very low air infiltration rates; (4) acid rain from the combustion of fossil fuels; (5) expolosions of liquified natural gas (LNG); and (6) ozone in the stratosphere.
Dirac’s light-cone coordinate system
Authors: Kim Y. S. , Noz Marilyn E.
Published: March 2005

It is shown that Dirac’s light-cone coordinate system provides an effective method for treating the geometry of Lorentz transformation in a rectangular coordinate system. Transformation properties of the coordinate variables and those of the derivatives are discussed in detail. The Lorentz boost along a given direction is shown to be a coordinate transformation in which ’’cross products’’ are preserved. It is pointed out that the Lorentz boost is a symplectic transformation.
Teaching problem-solving in physics: A course in electromagnetism
Authors: van Weeren J. H. P. , de Mul F. F. M. , Peters M. J. , Kramers-Pals H. , Roossink H.J.
Published: March 2005

In order to improve the teaching and learning situation in the course Electromagnetism for first-year students at the Twente University of Technology, this course has been reconstructed. The main activity in the reconstruction has been directed towards developing means and instructional procedures helpful to the students in learning how to tackle problems in electromagnetism. Therefore a model of the process of solving such problems has been developed and a system of actions and methods appropriate to this problem solving has been derived from the model. On the basis of the learning and instruction theory of Gal’perin this system has been incorporated in the instructional procedures of the course. The results of the reconstructed course as shown in the examination scores have improved compared to previous courses.
Sudden loss of mass from a binary gravitating system
Authors: Noerdlinger Peter D.
Published: March 2005

A recent discussion by Mitalas is generalized to treat sudden mass loss from a binary system in an originally elliptical orbit. Emphasis is placed on characterizing the orbits by angular momentum and energy, and it is shown that none of the changes in the relative orbit depends on which object loses part of its mass; indeed, in principle, each could lose a different fraction. Time averages are introduced so that the orbital changes, which depend on where in orbit the mass loss occurs, can be suitably averaged over a statistical ensemble of initial systems. Although I present several results that appear to be new (such as a unique relation between the increase in the semimajor axis and the change in eccentricity, independent of the orbital phase at the moment of mass loss), the main thrust is to choose and manipulate variables yielding the greatest economy of description and the greatest power of computation. (All calculations were easily done on a pocket calculator.) Graphs are presented showing the fraction of systems that on the average will be disrupted, the mean orbital changes for the survivors (which can easily turn out to have smaller mean eccentricity than the progenitors), and the extreme limits for the change in eccentricity.
Actions at a distance, four-dimensionality, and the problem of ’’where is the energy?’’
Authors: Sánchez-Ron José M.
Published: March 2005

An argument traditionally used against action-at-a-distance theories is that for such theories one cannot find a ’’reasonable’’ statement of conservation of energy because ’’where is the energy?’’Using as an example Fokker’s electrodynamics, we argue against such an objection, showing that it is possible to construct a model in which the question ’’where is the energy?’’ is answered. We also relate this problem to the question of the formal character of conservation laws.
Propagation of an electromagnetic wave in a slowly moving conducting dielectric
Authors: Wangsness Roald K.
Published: March 2005

The effect of conductivity on the propagation of an electromagnetic wave in a moving medium is considered and a modified form of the Fresnel formula is obtained. The effect is shown to be negligible for light waves for the usual experimental situations. Some relative properties of the fields and briefly considered.
Isospin relations by counting
Authors: Wohl Charles G.
Published: March 2005

A method is given for finding the relations between reaction cross sections or decay branching fractions that result from isospin conservation. The method was discovered long ago by Shmushkevich but is not widely known. It makes no call on the usual machinery of amplitude expansions and Clebsch–Gordan coefficients, but works instead by apportioning certain populations of particles according to a simple counting rule, the charge-uniformity rule. A number of examples, including several that require lengthy calculation to solve using Clebsch–Gordan coefficients, are here solved by inspection, usually without any equations at all.
Standing and traveling waves on lumped component lines
Authors: Blair J. Morris
Published: March 2005

The use of electrical transmission lines constructed from lumped components provides an opportunity for students to make detailed measurements of standing and traveling waves which would not be possible with the mechanical spring–mass–pendulum systems commonly used in lecture demonstrations. Four simple electrical lines are described which provide two examples of waves which travel with dispersion and two examples of waves which do not travel.
Relativistic acoustic Doppler effect
Authors: Bachman R. A.
Published: March 2005

The formulation of the relativistic acoustic Doppler effect is considered in detail. Two approaches were developed, both leading to the same result. The first method parallels the derivation of the classical formula, using Lorentz velocity transformation and time dilation effects when required. The second method is an intuitive approach done in the frame of the medium, clearly showing that the relativistic correction terms arise solely from time dilation effects; the rest of the derivation is entirely classical. It is demonstrated that the relativistic deviation is exactly zero when the source and observer speeds are equal, even if the two motions are oppositely directed. Finally, a numerical estimate reveals that the correction terms amount to only a few parts in 1015 for ordinary acoustic velocities.
A covariant four-dimensional expression for Lorentz transformations
Authors: Fahnline Donald E.
Published: March 2005

References on special relativity, despite denoting Lorentz transformations abstractly in covariant four-dimensional notation, express the explicit formulas for these transformations only in the three-vector form which treats space and time separately. Rewriting the explicit formulas covariantly yields an expression more natural for the four-dimensional context where space and time are unified. A slight generalization valid in any inertial frame transforms any proper velocity four-vector into any other. The direct decomposition of the product of two pure Lorentz transformations into the product of a pure spatial rotation and a pure Lorentz transformation illustrates how the covariant expression can simplify difficult problems.
Physicists and the doctoral dissertation
Authors: Rossini Frederick A. , Porter Alan L.
Published: March 2005

This article is based on a recent study of 645 1969–1970 Ph.D. recipients from the disciplines of physics, electrical engineering, biochemistry, zoology, psychology, and sociology. It focuses on the 97 physicists in the sample, studying their personal characteristics, work histories, dissertation experiences and assessment of their worth, and early career productivity including publications and citations. In the process of analyzing the physicists’ careers, it compares them as a group with the other disciplinary groups and the sample as a whole. There is general satisfaction with the dissertation experience and little inclination to change its structure. However, the data suggest certain areas where improvement is possible in the dissertation process. These include beginning the dissertation during course work, increasing the relevance and originality of the dissertation, and using the dissertation experience as an opportunity to begin learning research management.
Path integrals and the WKB approximation
Authors: Holstein Barry R. , Swift Arthur R.
Published: March 2005

The WKB approximation is demonstrated to be formally identical to the semiclassical limit of the Feynman path integral propagator. In the limit that the path integral propagator is dominated by the classical particle trajectory, it is identical to the propagator calculated directly from WKB wave functions in the stationary phase approximation.
Barrier penetration via path integrals
Authors: Holstein Barry R. , Swift Arthur R.
Published: March 2005

Path integral methods are applied to the problem of barrier penetration. By an excursion into complex time it is shown how the ideal of a ’’classical’’ path may be generalized to give a simple geometrical derivation of the usual WKB formulas.
Resonances and analyticity of scattering wave function for square-well-type potentials
Authors: Weber T. A. , Hammer C. L. , Zidell V. S.
Published: March 2005

In this paper we extend our previous analysis of the scattering of wave packets in one dimension to the case of the square-well potential. The analytic properties of the general scattering solution are emphasized thereby making the analysis useful as introductory material for a more sophisticated S-matrix treatment. The square-well model is particularly interesting because of its application to the deuteron problem. Resonance scattering, barrier penetration, time delay, and line shape are discussed at the level of the first-year graduate student.
Electromagnetic waves in a plasma containing both electric charges and magnetic monopoles
Authors: Meyer-Vernet N.
Published: March 2005

We study electromagnetic wave propagation in a hypothetical cold plasma containing both electric and magnetic charges. The waves exhibit rather unusual properties. In particular, they can propagate below the characteristic frequencies. Reflection on a half-space and electric dipolar radiation are discussed.
Effect of boundary conditions on the behavior of Bloch electrons
Authors: Churchill J. N. , Holmstrom F. E.
Published: March 2005

The behavior of Bloch electrons in a uniform electric field is considered from first principles with the result that the crucial significance of certain mathematical and conceptual difficulties, which have been the source of considerable debate in the literature, becomes apparent. For several typical configurations, it is shown that the choice of boundary conditions has a drastic effect on the density-of-states function D(ε). For certain configurations, D(ε) will execute an unacceptable and discontinuous behavior as the electric field is varied. Conversely, when compatible boundary conditions are used, D(ε) varies smoothly over all electric field values, converging uniformly as the field becomes vanishingly small. Special problems concerning the order of taking the limits ℰ→0, L→∞ are brought out. The energy eigenstates will not generally converge to the zero-field Bloch-type states in the limit as ℰ→0 (unless special precautions are taken).
Einstein’s first derivation of mass–energy equivalence
Authors: Stachel John , Torretti Roberto
Published: March 2005

It is shown that, contrary to what several authors have claimed, Einstein’s first derivation of the mass–energy equivalence was logically sound, the alleged fallacy lying merely in the fact that Einstein’s conclusion is entailed by, and is therefore a necessary condition of his premises. (AIP)
An investigation of CAI teaching methods in an electronics course
Authors: Wood Kenneth W.
Published: March 2005

Computers are increasingly being used in the classroom. An investigation of several educational techniques in a computer-based version of an electronics course is reported. We found that, with a lesson for teaching virtual equality, students learned faster when using a general to specific approach. Students using a simulation of a Schmitt trigger before a qualitative analysis of the circuit performed the analysis faster and with less difficulty than the group performing the analysis first and then exploring the circuit with the simulation. Given a sizable amount of optional material in a computer lesson, most of the electronics students used all of the optional material.
Density matrix and energy–time uncertainty
Authors: Blanchard C. H.
Published: March 2005

The statistical operator of von Neumann and its use by Eberly and Singh to give a natural formulation of energy–time uncertainty are explained in elementary detail.
Solution of space charge problems by conservation of momentum
Authors: Forrester A.Theodore
Published: March 2005

The use of conservation of momentum makes it possible to solve space charge problems usually attacked by means of Poisson’s equation. The proposed method can be shown to be equivalent to Poisson’s equation but, in some types of problems, it appears easier to set up and the resulting equation is a first-order differential equation, rather than second order. Three problems are solved for which solutions have been previously found by Poisson’s equation. The solutions are more simply arrived at and are identical to those obtained via Poisson’s equation.
Coordination radii in diamond, zinc blende, and CaF2 structures
Authors: Hall George L.
Published: March 2005

The radii of all ’’shells’’ of atoms about any lattice point are given for these three structures, and for the zinc blende (AB) and CaF2 (AB2) structures it is shown that all shells about an A origin and all shells about a B origin are of pure type, i.e., contain only A’s or only B’s. The initial sequence (small radii) of shell types does not continue indefinitely and is broken according to rules completely specified. These results are analogous to those reported by Hall and Christy earlier for the NaCl and CsCl structures in which the ABABAB⋅⋅⋅ sequence for NaCl and the ABAABAABAA⋅⋅⋅ for CsCl, both taken about an A origin, do not continue indefinitely. It is shown that Ferris-Prabhu’s results for diamond violate theorem 1 of Hall and Christy.
Nuclear explosions
Authors: Broyles A. A.
Published: March 2005

A summary of the physics of a nuclear bomb explosion and its effects on human beings is presented at the level of a sophomore general physics course without calculus. It is designed to supplement a standard text for such a course and problems are included.
Inadequacy of the usual Newtonian formulation for certain problems in particle mechanics
Authors: Stadler W.
Published: March 2005

The problem of the rigid double pendulum is used to show that the Newtonian axioms are inadequate to obtain a solution. It is further shown that an additional independent axiom, such as the law of moment of momentum, must be introduced to make the solution possible.
Work–energy theorem for variable mass systems
Authors: Copeland Jack
Published: March 2005

It is shown that the classical work–energy theorem can be generalized so as to be applicable to open systems, i.e., systems for which there exists an influx or efflux of mass. Some instructive examples are given.
Nonadiabatic compression of a cold gas
Authors: Lemons Don S.
Published: March 2005

I derive the P–V relation of an initially cold gas during a one-dimensional nonadiabatic compression. Here P is the gas pressure on a moving piston and V is the gas volume.
Dismantling a centuries-old myth: Newton’s P
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i
n
c
i
p
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a and inverse-square orbits
Authors: Weinstock Robert
Published: March 2005

Examination of Newton’s Principia reveals a fallacy in its purported proof of the otherwise well established fact that an inverse-square central force acting on a particle requires that the particle move in a conic-section orbit. The great difficulty of reading through the Principia material antecedent to the fallacy is offered as a major reason for the centuries-long delay in its detection and general acknowledgment. It was Johann Bernoulli, evidently, who in 1710 first proved that the inverse-square force implies a conic-section orbit.
Bohr orbit model and Ruedenberg’s theory of the origin of the binding energy for H2
Authors: Harcourt Richard D. , Solomon Helen , Bechworth John , Chislett Leigh
Published: March 2005

Bohr theory is employed to compute the ’’crucial depression’’ in kinetic energy for H2 when bonding occurs.
Resource Letter GI-1: Gravity and inertia
Authors: Worden P. W. , Everitt C. W. F.
Published: March 2005

This Resource Letter provides a guide to the literature on gravity and inertia. The letter E after an item indicates elementary level or material of general interest to persons becoming informed in the field. The letter I, for intermediate level, indicates material of somewhat more specialized nature; and the letter A indicates rather specialized or advanced material. An asterisk (*) indicates articles that we feel are especially useful or interesting; a double asterisk (**) indicates those articles to be included in an accompanying reprint book.
Elementary derivation of the magnetic flux quantum
Authors: Crawford Frank S.
Published: March 2005

Starting with the well-known de Broglie relation mv = h/λ that holds for a particle in zero magnetic field we give an elementary derivation of the generalized de Broglie relation that holds for a charged particle in a circular orbit in a cylindrically symmetric magnetic field. We make no use of ’’div, grad, curl, and all that’’ and do not introduce canonical momentum, the vector potential, or the Schrödinger equation. This generalized de Broglie relation is then assumed to hold for each of the Cooper pairs in a superconducting hollow cylinder. With the further assumption of the Meissner effect we find the well-known result φ = nh/q for the flux φ trapped by the circulating Cooper pairs of charge q = 2e. We then use the generalized de Broglie relation to show that the Cooper pairs have velocities about 10−6 times too small for them to be in equilibrium ’’cyclotron orbits’’ in the magnetic field they experience. We also show that this de Broglie relation gives the correct value (i.e., the Schrödinger theory value) for the London penetration distance.
Mirage in the laboratory
Authors: Fabri E. , Fiorio G. , Lazzeri F. , Violino P.
Published: March 2005

The theory of the mirage is reviewed at several levels of complexity, in order to show that the phenomenon can usefully be discussed in teaching. In addition, an experimental device has been set up to obtain the mirage in the laboratory under controlled conditions, with the possibility of observing the finer details discussed in the theory.
One-dimensional hydrogen atom in an infinite square well
Authors: Lapidus I. Richard
Published: March 2005

The effect of boundary conditions on solutions to the Schrödinger Equation is demonstrated.
Another look at the uniform rope sliding over the edge of a smooth table
Authors: Prato Domingo , Gleiser Reinaldo J.
Published: March 2005

The motion of a uniform rope sliding over the edge of a table has been repeatedly used to exemplify systems with variable mass. This usually involves a division of the system into two parts, which are considered separately. As a result, some physical information is lost and the motion of the rope looks somewhat awkward. The problem is re-examined by properly considering the rope as a fixed-mass two-dimensional system. Several questions, including under what conditions will the rope keep the ’’inverted L shape,’’ are also studied.
Zitterbewegung and the Klein paradox for spin-zero particles
Authors: Fuda Michael G. , Furlani Edward
Published: March 2005

The Hamiltonian form of the Klein–Gordon equation is used to study the Zitterbewegung of spin- zero particles. It is shown that the time dependence of the velocity and position operators in the Heisenberg picture is formally the same as that of a spin- 1/2 particle. It is also shown that the Zitterbewegung is the result of the interference between positive and negative energy states. A representation-free expression is found for the mean position operator. This operator is free from Zitterbewegung. The Klein–Gordon equation is solved with an electrostatic potential originally used by Sauter in his investigation of the Klein paradox for spin- 1/2 particles. It is shown that the transmission to states with negative kinetic energy is very small when the electric field is weak.
Quark confining potential in relativistic equations
Authors: Ram Budh
Published: March 2005

A linear potential, when used in the Schrödinger equation, confines a quark. In this paper, we discuss what happens when this potential is used in the relativistic Klein–Gordon and Dirac equations.
Measurement of spectral line splittings with a scanning, student-grade, Fabry–Perot interferometer
Authors: Zajonc Arthur G.
Published: March 2005

A simple method allowing precise measurement of spectral line splittings with a scanning, student-grade, Fabry–Perot interferometer is described. The isotope split between hydrogen and deuterium emission lines is taken as a characteristic experiment. Typical data are presented and analyzed. The experiment is suitable for a junior–senior-level laboratory.
Fluctuations in light beams: A simple student experiment
Authors: Wolf R. P. , Crooker P. P.
Published: March 2005

Light emitted from a thermal source has a fluctuating intensity; these fluctuations are a direct illustration of the elementary principles of statistical and quantum physics. We describe here a student experiment demonstrating these ideas. First the probability density for the intensity of thermal light inhabiting s coherence volumes is derived, using the Bose–Einstein distribution for photons in phase space. Then a simple method is shown for measuring this probability density using a quasithermal light source and a multichannel analyzer. Data are presented and a scheme for fitting the data to the theory is outlined.