bluuebunny/crossref_metadata_2025 huggingface dataset:
Connection between conserved quantities and degeneracies in quantum systems
Authors: Fallieros S. , Hadjimichael E.
Published: March 2005

In the framework of quantum theory, we present one theorem and three corollaries regarding the direct connection between constants of motion of a physical system and degeneracies of its energy eigenvalues. It is shown that this connection emerges when there exist quantum operators which commute with the Hamiltonian, but not with each other. Further it is shown that if the commutator of these operators is a nonvanishing constant number then (a) all the eigenvalues of the system are degenerate, and (b) the degree of degeneracy is infinite. A number of examples are discussed including the parity degeneracy of the hydrogen atom and the infinite degeneracy of the Landau levels of a charged particle in a constant magnetic field.
Which variational wave function is the best?
Authors: ten Hoor Marten J.
Published: March 2005

Using known properties of the exact wave function, a number of one-parameter variational wave functions for the ground states of atomic two-electron systems have been constructed. The best energies found compare favorably with those obtained in other work.
Heat, light, and videotapes: Experiments in heat conduction using liquid crystal film
Authors: Bacon Michael E. , Wick R. M. , Hecking P.
Published: March 2005

A range of experiments in heat conduction suitable for upper level undergraduate laboratories are described. The experiments progressively cover situations of increasing theoretical complexity. The experiments are relatively easy to perform and make use of heat sensitive liquid crystal film to measure temperature contours. The initial experiments cover examples of situations where Laplace’s equation is applicable and can be used to complement experiments in electrostatics using resistive paper. The remaining experiments extend the investigations to situations where Poisson’s equation and the diffusion equation are applicable. In these latter two cases the liquid crystal film serves as the heat conduction medium in addition to its function as a temperature sensor. For the diffusion equation situation a video camera is used in conjunction with the liquid crystal film.
Nonlinear coupled oscillators and Fourier transforms: An advanced undergraduate laboratory
Authors: DeYoung P. A. , LaPointe D. , Levy J. , Lorenz W.
Published: March 2005

As part of an upper-level laboratory course, the oscillations of one and two mass systems on an airtrack were measured in real time. Both linear oscillations with spring forces and nonlinear oscillations with magnetic forces were analyzed with fast Fourier transforms and compared to theoretical predictions. The results for the coupled linear oscillator agree with the theoretical values to within 0.5%. The coupled nonlinear oscillator results were modeled numerically.
Teaching Fourier analysis in a microcomputer based laboratory
Authors: Büll Ingo , Lincke Reimer
Published: March 2005

Using a sequence of suitably chosen signals and interesting physical examples, Fourier analysis can be taught in an microcomputer based laboratory (MBL) with a minimum of mathematics. Thus, even nontrivial applications like the response of resonance circuits to δ-function inputs can be treated on a very elementary level.
Throwing nature’s dice
Authors: Aguayo Ricardo , Simms Geoff , Siegel P. B.
Published: March 2005

A simple experimental setup to produce true random numbers is described. The experiment involves measuring successive times between decays of a radioactive source. We discuss two different ways of comparing these times: one that generates a string of random zeros and ones, and another that produces numbers derivable from the permutation group. It is shown that the methods used in the experiment produce the same results for any random process and can therefore be used as a test for randomness in other physical systems.
Thermally excited liquid surface waves and their study through the quasielastic scattering of light
Authors: Klipstein W. M. , Radnich J. S. , Lamoreaux S. K.
Published: March 2005

A simple apparatus employing a semiconductor diode laser and PIN photodiode has been used to investigate thermal capillary waves on liquid surfaces. These waves act as a weak, time-varying diffraction grating for the incident laser light; the diffracted light can be heterodyned with the light directly reflected from the liquid surface to extract fluid properties (surface tension and viscosity). In this paper we present a discussion of the phenomenon of surface waves and describe the construction of an apparatus to observe them. Results of measurements with this apparatus for the surface tension and viscosity of water with and without oil films and of benzyl alcohol at different temperatures demonstrate the effectiveness of the technique as well as environmental effects on liquid properties. This problem provides rich ground for a study of wave and thermal phenomena as well as an introduction to a variety of experimental techniques.
Computers in the general physics laboratory
Authors: Preston Daryl W. , Good R. H.
Published: March 2005

Nine of the 30 experiments performed by students in our 1-year general physics laboratory involve computer-assisted experimentation. Experiments are interfaced to the computer via conditioning circuits and an inexpensive 8 bit ADC/DAC card. Software is written for each experiment.
Degeneracies of the spherical well, harmonic oscillator and hydrogen atom in arbitrary dimensions
Authors: Shea Richard W. , Aravind P. K.
Published: March 2005

A simple prescription is given for determining the degeneracy of any energy level of the spherical well, harmonic oscillator, or hydrogen atom in arbitrary spatial dimension.
Heat engines in finite time governed by master equations
Authors: Feldmann Tova , Geva Eitan , Kosloff Ronnie , Salamon Peter
Published: March 2005

A simple example of a four-stroke engine operated in finite-time is analyzed. The working medium consists of noninteracting two-level systems or harmonic oscillators. The cycle of operation is analogous to a four-stroke Otto cycle. The only source of irreversibility is due to the finite rate of heat transfer between the working medium and the cold and hot baths. The dynamics of the working medium is governed by a master equation. The engine is shown to settle to a stable limit cycle for given contact periods with the hot and cold baths. The operation of the engine is analyzed subject to a fixed cycle time. The time allocation between the hot and cold branches that maximizes the work output is considered. Analytical results are obtained when the relaxation is very slow, very fast, or when the relaxation rates along the hot and cold branches are equal. Numerical results are presented for the general case. A maximization of the power with respect to the cycle time leads to a finite optimal cycling frequency provided the adiabatic branches are allotted finite durations.
The mathematics of Brownian motion and Johnson noise
Authors: Gillespie Daniel T.
Published: March 2005

One reason why Brownian motion and Johnson noise are difficult subjects to teach is that their mathematical requirements transcend the capabilities of ordinary differential calculus. Presented here is an exposition of the needed generalization of calculus, namely continuous Markov process theory, in a form that should be accessible to advanced physics undergraduates. It is shown how this mathematical framework enables one to give clear, concise derivations of all the principal results of Brownian motion and Johnson noise, including fluctuation–dissipation formulas, auto-covariance transport formulas, spectral density formulas, Nyquist’s formula, the notions of white and 1/f2 noise, and an accurate numerical simulation algorithm. An added benefit of this exposition is a clearer view of the mathematical connection between the two very different approaches to Brownian motion taken by Einstein and Langevin in their pioneering papers of 1905 and 1908.
Photon counting statistics—Undergraduate experiment
Authors: Koczyk P. , Wiewiór P. , Radzewicz C.
Published: March 2005

A photon counting experiment for student physics laboratory is described. It is designed to illustrate the probabilistic nature of the photodetection process itself as well as statistical fluctuations of light. The setup enables the student to measure photon count distributions for both coherent and pseudothermal light sources yielding Poisson and Bose–Einstein distributions, respectively.
Linear, one-dimensional models of the surface and internal standing waves for a long and narrow lake
Authors: Prigo Robert B. , Manley T. O. , Connell Benjamin S. H.
Published: March 2005

Linear, one-dimensional, analytical, and numerical models for seiches (standing waves) existing at the surface and on the internal interface between the upper warm and bottom cold layers for a long, narrow lake are developed. Using the specific bathymetric and thermal structures of a lake, Lake Champlain, these models predict the periods, nodal locations, vertical displacements, and current velocities associated with the fundamental and higher-order modes. Modeled results are compared with historical limnological data obtained from Lake Champlain. Agreement is good for the periods of the first few modes of the surface and internal seiches; however, predicted current velocities associated with the internal seiche are about half as large as those actually observed.
Use of pressure transducers in laboratory experiments. II. Experimental verification of the Hagen–Poiseuille law. Application to viscosity measurement. Electrical analogy
Authors: Victoria L. , Molina C. , Arenas A. , Ibáñez J. A.
Published: March 2005

As a continuation of part I of this work, further experiments were designed for the physics class using pressure sensors. An experimental setup using a pressure sensor and two optical fiber sensors makes it possible to verify the Hagen–Poiseuille equation, to measure the viscosity of several gases and, by analogy with an electric current circuit, to verify that the parallel and series association of flow resistance may be solved as if they were electrical resistances.
The reciprocal lattice as the Fourier transform of the direct lattice
Authors: Thompson D.
Published: March 2005

We argue that introducing the reciprocal lattice as the Fourier transform of the Bravais lattice provides not only a concise definition for the reciprocal lattice, but also makes it a concept easy to grasp. To illustrate the power of the concept we derive the reciprocal lattices of the bcc and fcc structures directly from their conventional unit cells, rather than from the primitive unit cells.
Resource Letter CP-1: Computational Physics
Authors: DeVries Paul L.
Published: March 2005

This Resource Letter provides a guide to the literature on the emerging field of computational physics. While traditional textbooks, expositions, and conference proceedings are cited, we also cite URLs on the World Wide Web to guide the reader to current information.
Efficiency and efficacy of incandescent lamps
Authors: Agrawal D. C. , Leff Harvey S. , Menon V. J.
Published: March 2005

Planck’s radiation formula is used to estimate the dimensionless efficiency of incandescent lamps as a function of filament temperature, with typical values of 2%–13%. Similarly, using the known spectral luminous efficiency of the eye, the efficacy of incandescent light bulbs is estimated as a function of temperature, showing values of 8–24 L W−1 for bulbs of 10–1000 W. The efficiency and efficacy results compare favorably with published data and enable estimation of the filament temperature for any lamp of known efficacy.
Random-exchange Ising model with spatially correlated disorder
Authors: Hobbie Erik K.
Published: March 2005

The pair correlation function g(r,r′) is derived in the mean-field approximation for a ‘‘random-exchange’’ Ising ferromagnet with long-range spatial correlations in the disorder. The static structure factor S(q) describing the intensity of scattered electromagnetic radiation or neutrons is then calculated. The inadequacy of a mean-field treatment is demonstrated, and the physical aspects of renormalization are discussed. From a pedagogical perspective, this problem offers a contemporary application of a number of techniques typically encountered in an advanced undergraduate or first-year graduate course in mathematical physics and can be used at that level to introduce the concept of renormalization
Classical theory of the chaotic ionization of highly excited hydrogen atoms
Authors: Sanders M. M. , Jensen R. V.
Published: March 2005

Over the past decade, classical mechanics has been transformed from an historical relic into a contemporary model for certain problems in atomic and molecular physics. This transformation has been brought about by recent interest in the study of chaotic dynamics in nonlinear classical systems. A good example is the behavior of highly excited atoms in microwave fields. In the language of classical mechanics a hydrogen atom in a microwave field is a periodically perturbed nonlinear oscillator. Depending on the strength of the perturbing microwave field, the equations of motion can become chaotic. The chaotic electron dynamics results in rapid ionization above a threshold microwave field strength. This paper presents the basic components of the classical models that we have introduced to describe this chaotic ionization of highly excited hydrogen atoms.
The ambiguity of random choices: Probability paradoxes in some physical processes
Authors: Basano Lorenzo , Ottonello Pasquale
Published: March 2005

Intriguing problems whose solutions seem to run counter to intuition are sometimes discussed theoretically in probability textbooks; under close scrutiny, they often appear to originate from an incomplete specification of the sampling procedures. Interest in these oddities is not purely academic; the world of real point processes (with its multitude of applications in science and engineering) exhibits its own ‘‘paradoxes’’ that follow from certain ambiguities in the random choice of an event. The paper discusses some probabilistic subtleties that can be easily illustrated by ordinary demonstration experiments in the physics laboratory.
On a simple experiment on the free rotation of a ruler and other laminas
Authors: Amengual A.
Published: March 2005

The torque-free rotation of a solid body is unstable about the axis with the intermediate principal moment of inertia. Such an instability can be shown with a simple experiment using a ruler. In this work, the equations of Euler are integrated and the orientation of the ruler, referred to the laboratory reference frame, determined as a function of time. This allows a beautiful comparison between the observed rotation of the ruler and the theory behind it.
Approximate evaluation of capacitances by means of Green’s reciprocal theorem
Authors: Donolato C.
Published: March 2005

The application of Green’s reciprocal theorem to a system of two conductors forming a capacitor leads to an analytical expression for the capacitance that involves the equilibrium charge density on the surface of one conductor. This unknown density can be approximated on the basis of physical arguments (in the simplest case, with a constant) or with the aid of Thomson’s theorem. The method is applied to the evaluation of the capacitance of the sphere-plane system and the parallel disk capacitor, and is shown to yield fairly accurate results. For the latter capacitor, the constant density approximation yields a maximum deviation of about 7% from recently published numerical values; an improved density is also proposed that yields agreement within 1.5%.
Models of power plants that generate minimum entropy while operating at maximum power
Authors: Bejan Adrian
Published: March 2005

Chambadal, Novikov, Curzon and Ahlborn have shown that the efficiency of an irreversible heat engine at maximum power output is 1−(TL/TH)1/2. This article describes several heat engine models in which the same efficiency formula can be derived by minimizing the rate of entropy generation. Included in the entropy generation is the usually overlooked contribution made by the components that provide a freely varying heat input to the power cycle.
Understanding alpha decay
Authors: Holstein Barry R.
Published: March 2005

The subject of alpha decay is an important part of a course in modern physics, as it provides a clear experimental manifestation of the phenomenon of barrier penetration. The traditional approach, based on Gamow’s complex eigenvalue method, raises a number of questions which can be answered by employing the older but less well-known procedure of summing over scattering states. Additional insights are gained by examination of the alpha decay system via more contemporary path integral based techniques.
Classical theory of the chaotic ionization of highly excited helium atoms
Authors: Sanders M. M. , Jensen R. V.
Published: March 2005

In this paper, we introduce a classical model for the behavior of the outer electron of a Rydberg helium atom in both static and time-dependent electric fields; we contrast the behavior of this dynamical system with the behavior of the classical model for highly excited hydrogen atoms in similar fields; and we show that these classical models recover many features of the system that would seem to be purely quantal in origin. Perhaps the most surprising of these is the apparent presence of ‘‘classical avoided crossings’’ in the Stark energy level structure of the classical helium model. Finally, we compare the behavior of our helium model to experimental data obtained by Koch, Mariani, and co-workers in their investigations of the ionization of highly excited helium atoms in a microwave field, and we note the agreement between experiment and theory.
Duality transformation properties of quantities quadratic in the electromagnetic field
Authors: Brownstein K. R.
Published: March 2005

Transformation properties of those quantities linear and quadratic in the electromagnetic field (E,B) are compared and contrasted for the case of (i) ordinary spatial rotations and (ii) duality transformations (which ‘‘rotate’’ E and B in E–B space). Of the 21 independent quadratic quantities, we point out that (15,3,3) of them exhibit (tensor, vector, scalar) like behavior under spatial rotations, whereas (12,0,9) of them do so for duality transformations.
The explanation of the Trouton–Noble experiment revisited
Authors: Teukolsky Saul A.
Published: March 2005

One class of explanations of the null result of the Trouton–Noble experiment uses the ‘‘standard’’ definitions of electromagnetic energy and momentum but is quite complicated. Another class is much simpler but appears to require new definitions of electromagnetic energy and momentum. We reconcile the two sets of explanations and show that they are both physically correct. We use the same arguments that have been used in discussions of the famous ‘‘4/3’’ factor in the electromagnetic mass of the classical electron.
Development of a computer-based tutorial on the photoelectric effect
Authors: Steinberg Richard N. , Oberem Graham E. , McDermott Lillian C.
Published: March 2005

An investigation conducted after standard lecture instruction in a sophomore-level modern physics course revealed that many students were unable to interpret the photoelectric experiment in terms of the photon model for light. Findings from this research were used to guide the development of an interactive computer-based tutorial to address the conceptual and reasoning difficulties that were identified. The primary instructional strategy used in the tutorial is the drawing and interpretation of graphs of current versus voltage for the circuit in the experiment. The program has been used both as an aid to instruction and as a probe to obtain additional information about the nature, prevalence, and persistence of specific difficulties. Analysis of student performance on examination problems on the photoelectric experiment indicates that those who have worked through the tutorial make fewer errors and give better explanations than those who have not had this experience. This result suggests that the intellectual engagement required by the program helps students improve their understanding of the photoelectric effect.
Direct calculation of radiation resistance in simple radiating systems
Authors: Templin Jacques D.
Published: March 2005

It is shown that the radiation resistance for sinusoidal sources can be calculated directly from the retarded potentials by evaluating the electric field at points on the source and that for electric and magnetic dipoles in the long wavelength limit the calculation is fairly simple. The problem is also examined from the point of view of Maxwell’s equations and their solutions, and it is shown that there is a significant portion of the electric and magnetic field which is finite everywhere, even for points on the source.
Using music to teach physics
Authors: Hoffman G. Lyle , Jouny Ismail
Published: March 2005

The analysis and synthesis of tones produced by acoustic musical instruments is used as a tool for teaching physics to students majoring in disciplines other than the sciences. A series of laboratory exercises, based on sound analysis and synthesis software running on microcomputer-based workstations, is described and placed in context with more traditional physics laboratory experiences and written assignments in a one-semester course in the physics of musical sound taught without advanced mathematics. Student reaction to the exercises is discussed.
Thermodynamic entropy: The spreading and sharing of energy
Authors: Leff Harvey S.
Published: March 2005

A new approach to thermodynamic entropy is proposed to supplement traditional coverage at the junior–senior level. It entails a model for which: (i) energy spreads throughout macroscopic matter and is shared among microscopic storage modes; (ii) the amount and/or nature of energy spreading and sharing changes in a thermodynamic process; and (iii) the degree of energy spreading and sharing is maximal at thermodynamic equilibrium. A function S that represents the degree of energy spreading and sharing is defined through a set of reasonable properties. These imply that S is identical with Clausius’ thermodynamic entropy, and the principle of entropy increase is interpreted as nature’s tendency toward maximal spreading and sharing of energy. Microscopic considerations help clarify these ideas and, reciprocally, these ideas shed light on statistical entropy.
Rigorous Newtonian cosmology
Authors: Tipler Frank J.
Published: March 2005

It is generally believed that it is not possible to rigorously analyze a homogeneous and isotropic cosmological model in Newtonian mechanics. I show on the contrary that if Newtonian gravity theory is rewritten in geometrical language in the manner outlined in 1923–1924 by Élie Cartan [Ann. Ecole Norm. Sup. 40, 325–412 (1923); 41, 1–25 (1924)], then Newtonian cosmology is as rigorous as Friedmann cosmology. In particular, I show that the equation of geodesic deviation in Newtonian cosmology is exactly the same as equation of geodesic deviation in the Friedmann universe, and that this equation can be integrated to yield a constraint equation formally identical to the Friedmann equation. However, Newtonian cosmology is more general than Friedmann cosmology: Ever-expanding and recollapsing universes are allowed in any noncompact homogeneous and isotropic spatial topology. I shall give a brief history of attempts to do cosmology in the framework of Newtonian mechanics.
Restoration of interference and the fallacy of delayed choice: Concerning an experiment proposed by Englert, Scully, and Walther
Authors: Mohrhoff Ulrich
Published: March 2005

A two-slit experiment with atoms, proposed by Englert, Scully, and Walther, appears to permit experimenters to choose, after each atom has made its mark on the screen, whether the atom has passed through a particular slit or has, in some sense, passed through both of them. Through a misleading wording these authors even appear to endorse this interpretation. In actual fact, this choice exists only until the atom hits the screen. The said experiment thus is a ‘‘delayed-choice’’ experiment only in the semantically contingent sense of Wheeler.
Reflections on the pedagogic motive power of unconventional thermodynamic cycles
Authors: Kaufman Richard , Marcella Thomas V. , Sheldon Eric
Published: March 2005

Pedagogic niceties in the treatment of unconventional thermodynamic cycles, especially those involving (negatively sloping) diagonal linear transitions in a P/V state diagram and/or those implying supposedly superefficient heat-engine operation, are discussed as a means of stimulating student interest and comprehension, as well as promoting fresh insights, correcting erroneous notions, and provoking further enquiry. In particular, a novel (ostensibly all-adiabatic) engine using two ideal gases of mutually differing atomicities as working substance is analyzed qualitatively and quantitatively. Emphasis is placed on the crucial role of the second law of thermodynamics in a determination of heat-engine operation.
A pedagogical model of primordial helium synthesis
Authors: Eskridge Brent , Neuenschwander Dwight E.
Published: March 2005

The calculation of the primordial hydrogen and helium abundances in the big-bang cosmology is presented in an oversimplified model accessible to university physics students who have had no physics beyond an elementary modern physics course.
Answer to Question ♯21 [‘‘Snell’s law in quantum mechanics,’’ Steve Blau and Brad Halfpap, Am. J. Phys. 63 (7), 583 (1995)]
Authors: Milonni Peter W.
Published: March 2005

The quantum mechanical description of reflection and refraction in terms of photons is further extrapolated. The probability amplitude for a photon to be found inside or outside the medium is derived.
Spin stabilized magnetic levitation
Authors: Simon Martin D. , Heflinger Lee O. , Ridgway S. L.
Published: March 2005

The stability of the Levitron® cannot be explained if the top’s axis has a fixed direction in space. Stability against flipping is not enough. Gyroscopic precession around the local magnetic field direction is necessary. An analysis and numerical integration of the equations of motion for an experimental stemless top that includes gyroscopic precession around the local magnetic field lines predict that the top will be supported stably up to spin speeds of about 3065 rpm. An upper spin limit of 2779 rpm for this top is observed experimentally and explained as an adiabatic condition. Spin stabilized magnetic levitation is a macroscopic analog of magnetic gradient traps used to confine particles with a quantum magnetic moment.
Millikan Lecture 1996: Promoting active learning based on physics education research in introductory physics courses
Authors: Laws P. W.
Published: March 2005

Early in his career Robert Millikan experimented with a laboratory-based method of teaching introductory physics that bears close resemblance to Workshop Physics.® In this talk, key elements of Workshop Physics are summarized. Some Workshop Physics activities are described which involve apparati that are used for rapid observations of conceptual aspects of physical phenomena as well as for equation verification experiments. Challenges are discussed that must be faced if recently developed activity-based approaches to teaching based on the outcomes of physics education research are to provide a foundation for a major paradigm shift in physics teaching.
Electromagnetic waves in space: Visualization of E and B, and pedagogical approaches using superposition
Authors: Heller Peter
Published: March 2005

A beam of electromagnetic waves, produced by a “ham” transmitter at a frequency just below 450 MHz, is studied using a pair of antennas, one an electric and the other a magnetic “dipole,” each coupled to subminiature lamp bulb. These bulbs become very brightly lit in response to the local time average values of |E|2 and |B|2, respectively. Most strikingly, the interleaving of the electric and magnetic oscillation maxima in a standing wave is seen. This and other aspects of the phenomena are described using an accompanying pedagogical approach which emphasizes the primary idea of wave superposition.
Hanging shapes of nonuniform cables
Authors: Fallis M. C.
Published: March 2005

Using a variational approach, I derive the equation governing the equilibrium shape of an inelastic cable with an arbitrary mass distribution hanging freely under uniform gravity except for being supported at both ends. I then develop a parametric solution to this shape equation, giving the coordinates of points on the curve assumed by the cable in terms of the distance along the cable. Using numerical integration to determine values, I plot several examples of the cable’s shape for linearly and exponentially increasing density. I also consider the inverse problem of determining the mass distribution which gives rise to a specified shape. I compare the distributions yielding a semicircle, a parabola, and a catenary.
Resource Letter: CQO-1: Coherence in Quantum Optics
Authors: Slosser John J. , Meystre Pierre
Published: March 2005

This Resource Letter provides a brief introduction and an annotated guide to the literature about the roles of quantum coherence in quantum optics. Books, conference proceedings, and selected journal articles are listed for the following topics: Early history, lasers, in particular novel systems such as lasers without inversion, nonclassical states of light including squeezed states, cavity quantum electrodynamics, cooling and trapping of atomic samples, atom optics, and quantum optical tests of the foundations of quantum mechanics.
A very simple and inexpensive apparatus for detecting superconducting transitions via magnetic screening
Authors: Lukefahr H. G. , Priest V. , St. Jean K. B. , Worley J. S. R. , Yeager C. S. , Gajewski D. A. , Maple M. B.
Published: March 2005

We report a very simple and inexpensive technique for detecting the screening of the B field by high temperature superconductors via the change in the inductance of a coil containing the sample. While related to previously reported techniques for measurement magnetic susceptibility via changes in inductance, the apparatus we report does not require lock-in amplification and is suitable for general physics labs.
The quasilinear generator and ∫B⋅
d
S=0
Authors: Valverde Jorge Guala , Mazzoni P. , Blas Ro.
Published: March 2005

At the undergraduate level, it is often easier to measure electrical magnitudes than magnetic ones. Working within the framework of classical electromagnetism (i.e., without referring to massive photons or to hypothetical magnetic monopoles) we develop an inexpensive and easy-to-use device capable of verifying a fundamental property of the magnetic flux density as applied to free space, ∫B⋅dS=0, to better than 5 parts per million accuracy. In order to achieve the above purpose, we make a slight variant of our former quasilinear generator. Gauss’s theorem ensures that div B=0 for empty space to the same accuracy as above.
The fraction of “all different” combinations: Justifying the semiclassical partition function
Authors: Baierlein Ralph
Published: March 2005

Modern statistical mechanics directly acknowledges the indistinguishability of identical particles, a characteristically quantum property. Under laboratory conditions such that classical physics ought to suffice for most purposes, the indistinguishability is often incorporated by a judicious division by N!. This paper explores a common justification for that procedure—and finds it wanting. Nonetheless, the procedure is valid, but for a different reason.
Extending the application of the relativity principle: Some pedagogical advantages
Authors: Galili Igal , Kaplan Dov
Published: March 2005

Although textbooks usually present the conservation laws of energy and momentum only in the laboratory frame of reference, it is important that an introductory physics course show that they are valid in any inertial frame. It can be useful to apply the conservation laws in more than one frame of reference so as to highlight that they are precise only in closed systems. This is of particular note if one of the interacting partners is of near-infinite mass, whose share of the redistributed energy cannot always be neglected. In this sense, the notion of “infinitely large mass” is frame dependent. Balancing the energy and momentum in more than one frame of reference can help resolve some common difficulties with regard to energy conservation. We show also that the energy-work theorem holds in noninertial frames where inertial forces are treated as external.
The Thomas–Reiche–Kuhn sum rule and the rigid rotator
Authors: Hadjimichael E. , Currie William , Fallieros S.
Published: March 2005

It is shown that the Thomas–Reiche–Kuhn sum rule, associated with the photoabsorption cross section from quantum systems, appears to be violated in the case of the quantized rigid rotator. The origin of the apparent violation is investigated, and its resolution is presented on the basis of a related system, i.e., a particle in a spherical δ-function potential whose energy spectrum approaches that of the rigid rotator when the strength of the potential becomes large.
An alternative classical approach to the quantum-mechanical definition of the scattering cross section
Authors: Fiol J. , Pregliasco R. G. , Samengo I. , Barrachina R. O.
Published: March 2005

We discuss an alternative classical description of the nonrelativistic scattering process that is completely analogous to the time-independent formalism employed in quantum-mechanics textbooks. This approach provides an elementary introduction to the standard stationary scattering theory, embodying many of its essential concepts.
A simple experimental demonstration of the principle of equivalence
Authors: Klein W. , Mittelstaedt P.
Published: March 2005

According to the principle of equivalence, local experiments, in all freely falling frames of reference, are independent of the gravitational field surrounding this frame. A simple experiment, in which Einstein’s freely falling elevator is replaced by a pendulum system sliding down an inclined plane, serves as a demonstration for this principle. The pendulum experiences a force orthogonal to the inclined plane. With an eddy current damping mechanism, the oscillation of the pendulum can be damped, and the pendulum will move into its equilibrium position orthogonal to the inclined plane shortly after being released from rest.
Sub-Poissonian photocurrent statistics: Theory and undergraduate experiment
Authors: Funk A. C. , Beck M.
Published: March 2005

We present the results of an experiment in which we observe a sub-Poissonian photocurrent. This photocurrent is generated by detecting the light emitted from a high-quantum-efficiency light-emitting diode driven by a high-impedance current source. We also present classical, semi-classical and quantum mechanical theories of photoelectric detection. The observed sub-Poissonian statistics are in agreement with quantum mechanical predictions, but are unexplainable using the classical and semi-classical theories. The experiment uses only equipment already found in most undergraduate laboratories, making this a nice experiment to demonstrate a purely quantum mechanical effect.
Transverse bending waves and the breaking broomstick demonstration
Authors: Vandegrift Guy
Published: March 2005

When a broomstick is supported at both ends by two wine glasses, a strong downward blow to the center will break the stick, leaving the wine glasses undisturbed, provided care is taken to cushion the wine glasses against an initial and brief downward motion of the ends of the broomstick. This downward motion is analyzed and estimated to be about 1 mm in magnitude. Qualitative experimental evidence of this motion is easily obtained using a force probe to monitor a light and nondestructive tap to a 2-m measuring stick. The method of analysis developed here leads to a simple derivation of the dispersion relation for transverse bending waves on a long rod.
Diagonalization of the Dirac equation: An alternative approach
Authors: Holstein Barry R.
Published: March 2005

The reduction of a relativistic Hamiltonian to its effective nonrelativistic form, usually accomplished via a Foldy–Wouthuysen transformation, is derived via Lagrangian methods. This technique provides a pedagogically interesting introduction to the so-called heavy baryon field theory.
Phase space integration method for bound states
Authors: Nagabhushana Sharada , Kagali B. A. , Vijay Sivramkrishna
Published: March 2005

We present here an alternate method that may be called the phase space integration method for finding energies of bound states. This new method is applied to anharmonic oscillators, square well potentials, and logarithmic potentials. The numerical values are found to agree very well with those from other elaborate calculations.
Can an ideal gas feel the shape of its container?
Authors: Gutiérrez Gonzalo , Yáñez Julio M.
Published: March 2005

Thermodynamic quantities of an ideal gas enclosed in a finite container are examined. We use an asymptotic expansion for high temperatures to obtain the partition function of an ideal gas, both in two and three dimensions, showing the leading corrections to the internal energy due to a finite container. In the three-dimensional case, the first correction term depends only on the area–volume ratio, but higher order terms depend also on other geometric properties of the container. However, according to recent results, we show that the answer to the question posed in the title is negative.
The dead spot of a tennis racket
Authors: Cross Rod
Published: March 2005

It is shown that a tennis racket has a dead spot, but it does not have a well-defined sweet spot, when measured in terms of the rebound of a tennis ball. A ball dropped onto the center of the strings bounces to about 30% its original height. The bounce is much weaker near the tip of the racket, being almost zero at the dead spot. These effects are explained in terms of the effective mass and rotational inertia of the racket, and by reference to the behavior of other cantilevered beams. It is concluded, somewhat paradoxically, that the best place to hit a serve or smash is at the dead spot.
Logarithmic perturbation expansion for the Dirac equation in one dimension: Application to the polarizability calculation
Authors: Coutinho F. A. B. , Nogami Y. , Toyama F. M.
Published: March 2005

The method of logarithmic perturbation expansion which was developed by Aharonov and Au for the Schrödinger equation is extended to the Dirac equation in one dimension. The method enables us to calculate the perturbed energy and wave function of a bound state without involving summation over intermediate states. The method is illustrated by applying it to the calculation of the polarizability of a bound system which is subject to a linear perturbation. The notion of anti-polarization, which is peculiar to relativistic bound systems, is discussed.
Paul Langevin’s 1908 paper “On the Theory of Brownian Motion” [“Sur la théorie du mouvement brownien,” C. R. Acad. Sci. (Paris) 146, 530–533 (1908)]
Authors: Lemons Don S. , Gythiel Anthony
Published: March 2005

We present a translation of Paul Langevin’s landmark paper. In it Langevin successfully applied Newtonian dynamics to a Brownian particle and so invented an analytical approach to random processes which has remained useful to this day.
Scaling in model aircraft
Authors: Waltham Chris
Published: March 2005

The aerodynamic principles of flight are described from the point of view of the way they scale from the largest full-size aircraft to the smallest flying models. Particular attention is paid to the difficulties encountered by small, slow flying machines.
On water, steam, and string theory
Authors: Schmidhuber Christof
Published: March 2005

At a pressure of 220 atm and a temperature of 374 °C there is a second-order phase transition between water and steam. Understanding it requires a key concept of both condensed matter and elementary particle physics: the renormalization group. Its basic ideas are explained with images from computer simulations of the lattice gas model. Then I briefly review how the renormalization group is used to compute critical coefficients for the water–steam phase transition. The results of this calculation are in good agreement with experiment. Finally, some applications in particle physics and string theory are mentioned.
Friction forces on charges moving outside of a conductor due to Ohm’s law heating inside of a conductor
Authors: Tomassone M. S. , Widom A.
Published: March 2005

It is very well known and taught to undergraduate students of electromagnetic theory that a charge e sitting at a height h above a conductor feels a force Fstatic=−(e2/4h2)N, where N is a unit normal vector to the conductor surface. The static force is due to an induced conductor charge density. Suppose (i) that the charged particle has a small velocity V parallel to the conductor surface, and (ii) that the induced conductor currents obey Ohm’s law with conductivity σ. Ohm’s law induced heating in the conductor then gives rise to a friction force (over and above the static force) Ffriction=−(e2/16πσh3)V. A simple derivation of this friction provides the undergraduate student with an interesting physical example of an induced friction force acting at a distance, i.e., a charged particle moving in the vacuum can feel a friction force due to a neighboring conductor.
Abundance of Cellular Material and Proteins in the Atmosphere
Authors: Jaenicke Ruprecht
Published: March 2005

Suspended atmospheric particles play a crucial role in any global climate scenario: They can both enforce and suppress radiative forcing. In developing climate modeling further, a deeper understanding of atmospheric aerosol is needed. Because of extreme local and temporal variations, proper incorporation of aerosols into models requires modeling of the aerosol itself. It turns out that cellular material and proteins compose up to 25% of the atmospheric aerosol. Consequently, the source strength of the biogenic aerosol in general must be corrected and should be estimated on the order of other major aerosol sources.
Spin-Charge Separation and Localization in One Dimension
Authors: Auslaender O. M. , Steinberg H. , Yacoby A. , Tserkovnyak Y. , Halperin B. I. , Baldwin K. W. , Pfeiffer L. N. , West K. W.
Published: March 2005

We report on measurements of quantum many-body modes in ballistic wires and their dependence on Coulomb interactions, obtained by tunneling between two parallel wires in an GaAs/AlGaAs heterostructure while varying electron density. We observed two spin modes and one charge mode of the coupled wires and mapped the dispersion velocities of the modes down to a critical density, at which spontaneous localization was observed. Theoretical calculations of the charge velocity agree well with the data, although they also predict an additional charge mode that was not observed. The measured spin velocity was smaller than theoretically predicted.
Getting to Know You: Reputation and Trust in a Two-Person Economic Exchange
Authors: King-Casas Brooks , Tomlin Damon , Anen Cedric , Camerer Colin F. , Quartz Steven R. , Montague P. Read
Published: March 2005

Using a multiround version of an economic exchange (trust game), we report that reciprocity expressed by one player strongly predicts future trust expressed by their partner—a behavioral finding mirrored by neural responses in the dorsal striatum. Here, analyses within and between brains revealed two signals—one encoded by response magnitude, and the other by response timing. Response magnitude correlated with the “intention to trust” on the next play of the game, and the peak of these “intention to trust” responses shifted its time of occurrence by 14 seconds as player reputations developed. This temporal transfer resembles a similar shift of reward prediction errors common to reinforcement learning models, but in the context of a social exchange. These data extend previous model-based functional magnetic resonance imaging studies into the social domain and broaden our view of the spectrum of functions implemented by the dorsal striatum.
Crustacean zooplankton in lakes and reservoirs of temperate and tropical regions: variation with trophic status
Authors: Pinto-Coelho Ricardo , Pinel-Alloul Bernadette , Méthot Ginette , Havens Karl E
Published: March 2005

The influence of trophic status on the crustacean zooplankton community was investigated in lakes and reservoirs in temperate and subtropical-tropical regions. We tested if there is a consistent relationship between crustacean species richness, assemblages, and abundance and trophic indices such as total phosphorus and chlorophyll a. We also examined if these patterns differ between regions. Cumulative species richness and assemblages varied among regions. The greatest number of crustacean species was found in the temperate oligotrophic region with the largest number of lakes sampled. However, cumulative species richness was similar in temperate and subtropicaltropical regions when comparing subsets with a similar number of lakes and reservoirs. The relationships between species richness and latitude or trophic status were difficult to assess owing to imbalance among regions in number of lakes and reservoirs sampled and to biogeography and fish predation potential influences. Trophic status was associated with changes in abundance of all major crustacean zooplankton groups. Eutrophic ecosystems supported greater crustacean abundances at all latitudes. However, cladocerans and cyclopoids were more abundant in eutrophic lakes and reservoirs, whereas calanoids were more abundant in temperate oligotrophic lakes. Total phosphorus was found to be a better predictor of the biomass of major crustacean groups than chlorophyll a in all regions.
A synthetic, structural, and113Cd NMR study of cadmium complexes of 1,3-thiazolidine-2-thionate, including the structures of Cd(C3H4NS2)2, (Cd(C3H4NS2)2(C5H5N)3·C5H5N, and (Ph4P)2[I2Cd(µ-C3H4NS2)2CdI2]
Authors: Craig Donald C , Dance Ian G , Dean Philip AW , Hook James M , Jenkins Hilary A , Kirby Christopher W , Scudder Marcia L , Rajalingam Umarani
Published: March 2005

The crystallization of cadmium bis(1,3-thiazolidine-2-thionate), Cd(C3H4NS2)2(1), is reported. Freshly prepared 1 reacts with Ph4P+Xin a 1:2 ratio to give (Ph4P)2[Cd2(C3H4NS2)2X4] (X = I (4) or Br (5)). Crystallization of 1 from pyridine produces a solvate 7, which loses pyridine readily. X-ray analyses show that 1 has a polymeric sheet structure in which the C3H4NS2ligands act as bidentate bridges through N and the exocyclic S and the Cd has a CdN2S2kernel; 5 is isomorphous with 4, which contains a dimeric anion again with bridging through the N and exocyclic S of the heterocyclic ligands; and 7 is Cd(C3H4NS2)2(C5H5N)3·C5H5N, containing trigonal bipyramidal Cd(C3H4NS2)2(C5H5N)3molecules, in which the C3H4NS2ligands, both of which are monodentate and in equatorial positions, occur as a unique combination of S- and N-bound. Cadmium-113 NMR data for 1 in pyridine solution and solid-state CP-MAS113Cd data for 1, 7, bis(pyridinium-4-thiolate)cadmium, and tetrakis(pyridinium-2-thiolate)cadmium nitrate are reported and discussed. The compound 1 has chemical and NMR spectroscopic properties that make it a useful standard for solid-state CP-MAS113Cd NMR spectroscopy. Key words: cadmium, 1,3-thiazolidine-2-thionate, X-ray analysis, solid-state113Cd NMR,113Cd NMR standard compound.