bluuebunny/crossref_metadata_2025 huggingface dataset:
Hannay angle study of the Foucault pendulum in action-angle variables
Authors: Khein Alexander , Nelson D. F.
Published: September 2005

The Hamiltonian is derived for the Foucault pendulum in polar coordinates in terms of the action variables of the system. The complete solution to the Foucault pendulum is found in the small oscillation limit from the action-angle approach. During a cycle of adiabatic change (one revolution of the earth), the polar angle change can be divided into a dynamic phase and a geometric phase, called the Hannay angle, which is independent of the duration of the adiabatic change. It is shown that the Hannay angle is equal to the solid angle swept out by the pendulum axis. Four special solutions arising from different initial conditions are considered and serve to clarify the meaning of the action variables. Other coordinate systems for which separation of variables is possible are discussed. In these doubly rotating systems, the Hannay angle is shown to vanish.
Canonical transformation to energy and ‘‘tempus’’ in classical mechanics
Authors: Kobe Donald H.
Published: September 2005

In classical Hamiltonian dynamics for a system with a single degree of freedom a canonical transformation is made to new canonical variables in which the new canonical momentum is energy and its conjugate coordinate is called tempus. This canonical coordinate tempus conjugate to the energy is not necessarily the time t in which the system evolves, but is a function of the original generalized coordinate, the energy, and time t. For conservative systems tempus reduces to the time t, and the equations reduce to the Hamilton–Jacobi equation for Hamilton’s characteristic function. For periodic or almost periodic systems, the energy and tempus canonical variables act as a bridge to the action and angle canonical variables. Hamilton’s equations for the action and angle variables in the adiabatic limit involve a generalized Hannay (or geometrical) angle. A pendulum with a length varying in time is treated as an example.
Double pendulum: An experiment in chaos
Authors: Levien R. B. , Tan S. M.
Published: September 2005

We describe an experiment which takes advantage of the surprising complexity of one of the simplest physical systems, the passive double pendulum. For large angle swings sensitive dependence on initial conditions, the signature of chaos, may be demonstrated and quantified in a very direct way. Small angle experiments and zero gravity experiments (with the pendulum swinging in a horizontal plane) may also be performed. The angles are measured very precisely and reliably using optical encoder wheels, and data are acquired and displayed using a personal computer. The experiment is suitable for the undergraduate laboratory.
Standing waves in air columns: Will computers reshape physics courses?
Authors: Johnston I. D.
Published: September 2005

It is often argued that the introduction of computational physics into undergraduate courses will, in time, change what is taught. This paper presents a supporting example, taken from the field of musical acoustics. The vibration of the air columns inside wind instruments, of any but the most idealized shapes, is a sufficiently difficult analytic problem that the subject is rarely treated in ordinary undergraduate courses. A simple computational treatment of the problem is presented that demonstrates many features of importance to real musicians: the effect of mouthpieces and bells, the positioning and sizing of fingerholes, and the production of multiphonics. The ability to treat previously intractable problems like this may enable acoustics to regain a place in the ordinary curriculum and allow its potential as an intuitive model for related systems to be usefully exploited.
A quantitative magnetic braking experiment
Authors: MacLatchy Cyrus S. , Backman Philip , Bogan Larry
Published: September 2005

A popular demonstration which often accompanies the introduction of magnetic induction is that in which a strong button-shaped magnet is dropped through a long copper or aluminum tube. The induced currents cause a retarding force which dramatically slows the descent of the falling magnet. Here, we describe methods of calculating and measuring the terminal velocity and magnetic forces in the magnetic braking experiment. The techniques are quite accurate, inexpensive to perform, and are suitable for introductory courses in electricity and magnetism.
Simple and inexpensive teaching apparatus for absolute measurement of voltage
Authors: Fulbright H. W.
Published: September 2005

Equipment designed for the absolute measurement of voltage is described, suitable for lecture demonstrations or for student laboratory experiments. Although simple and inexpensive it can give results accurate to 1% or 2%. A key element incorporated is a soft drink can.
Cosmological models
Authors: Harvey Alex
Published: September 2005

Two of the most common terms employed in discussing cosmological models are open and closed. They are occasionally misused either by not recognizing or by not making it clear that each term may be used to characterize, independently and simultaneously, both the dynamic behavior and spatial geometric structure of the model under discussion. In addition, the spatial geometric structure implied by the terms open and closed is itself often either misunderstood or misused. Lastly, the role played by the cosmological constant is often improperly slighted. This paper is intended to give several examples of the abuse of terminology and clarify the distinction by means of a brief, elementary overview of Friedmann–Robertson–Walker cosmological models.
A polytropic model of the Sun
Authors: Hendry Archibald W.
Published: September 2005

We show that the presently accepted standard model of the Sun exhibits polytropic power-law behavior P=Kργ over certain regions of the Sun’s interior. We then develop a three-polytype model that gives a good representation of this standard solar model. The model is easily computable.
Carnot-like processes in finite time. I. Theoretical limits
Authors: Nulton James D. , Salamon Peter , Pathria Raj K.
Published: September 2005

The set of feasible operations of a finite-time heat engine subject only to thermal losses is described in terms of a new inequality, which sets a lower bound for the time required by a Carnot-like process in terms of the entropy changes of the reservoirs. This leads to an analogue of the second law of thermodynamics and to a general notion of time efficiency for the class of processes considered.
Heisenberg’s uncertainty relation and thermal vibrations in crystals
Authors: Jauch W.
Published: September 2005

It is shown how results obtained from crystal structure analysis may provide a practical illustration of Heisenberg’s uncertainty relation. To this end lower limits for the vibrational amplitudes of atoms in crystals are derived and compared with experimental values.
Quantum mechanical squeezed state
Authors: Muñoz-Tapia Ramon
Published: September 2005

The squeezed states appear in different fields under different forms. Compact operator expressions are given and some of their properties reviewed with the connections between different contexts clarified.
Magnetic monopoles and hyperfine structure
Authors: Kocher Carl A.
Published: September 2005

The hyperfine contact interaction is examined for a nuclear magnetic dipole moment of polar origin, due to separated monopoles of opposite sign. In the ground state of hydrogen, where the electron distribution overlaps the nucleus, an electron-nucleus interaction of the form −μN⋅Be leads to hyperfine level shifts in agreement with experiment and in disagreement (by a factor of −2) with calculations based on −μe⋅BN. The latter are brought into accord with experiment by a ‘‘monopole threading’’ contribution arising from the passage of a monopole through the surface bounded by a circulating electric current. Measurements of the 1 s hyperfine splitting in hydrogen apparently do not test for monopole-pair contributions to nuclear magnetism.
Does the spherical step-potential well exhibit the Ramsauer–Townsend effect?
Authors: Greenhow R. C.
Published: September 2005

The ability of the spherical step potential well to model the Ramsauer–Townsend effect, the near disappearance of low-energy electron scattering in the noble gases argon, krypton, and xenon, is discussed. It is shown that conditions can be found for which the cross section vanishes as the energy approaches zero, but that the noble gas phenomenon, where the cross sections show sharp minima at finite energies, cannot be modeled. The low-energy s-wave cross section can be made to vanish, but the p-wave cross section rises too rapidly with energy to permit a minimum in the total cross section. In addition it is shown that the condition for the vanishing of the s-wave cross section at zero or low energy also implies the occurrence of a d-wave resonance at zero or low energy. In the noble gases, the polarization term appears to be the essential feature of the atomic potential which gives rise to the effect.
On the momentum representation of hydrogenic wave functions: Some properties and an application
Authors: Hey J. D.
Published: September 2005

The wave functions in momentum space for discrete states of hydrogenlike atoms are discussed in terms of both the early contributions to the subject and their present usefulness in atomic physics. The derivation of some of their important properties is outlined, in particular the expectation values of various powers of momentum and kinetic energy, and the kinetic energy distribution. As an application, the cross section for ionization of hydrogen in the metastable 2S state by electron impact is calculated with the aid of the binary-encounter approximation, which requires the use of momentum-space wave functions.
The Fibonacci ruler
Authors: McIrvin Matthew J.
Published: September 2005

The sharp peaks present in the diffraction pattern of a one-dimensional Fibonacci quasicrystal are explained physically. The explanation rests upon the discovery of periodically positioned spatial regions, with mutually incommensurable spacings, which completely or partially exclude the atoms of the quasicrystal. These sets of periodic exclusion zones act individually as gratings. A ruler-like optical analog of a 1-D quasicrystal, in which grating lines replace the hypothetical atoms of the quasicrystal, provides an opportunity to observe quasicrystal diffraction directly. Such a grating can be produced by hand with simple equipment.
Coupled-amplitude equations via a Green’s-function technique
Authors: Hall Dennis G.
Published: September 2005

Coupled-amplitude equations are used widely to analyze problems involving wave propagation. The free-space Green’s function can be used to advantage to show that these equations emerge naturally from the wave equation. The procedure for obtaining the coupled-amplitude equations is an instructive one that will likely prove a useful addition to the list of examples of the practical utility of Green’s functions.
Nonuniqueness in the solutions of Newton’s equation of motion
Authors: Dhar Abhishek
Published: September 2005

In the case of singular forces, for which some of the higher derivatives do not exist at a given point, it is not generally true that Newton’s equations of motion will give unique solutions for given initial conditions. In this paper, the motion of a particle in a one-dimensional conservative force field is considered. The necessary and sufficient conditions that ensure unique solutions are determined.
Frame grabbing techniques in undergraduate physics education
Authors: Benenson W. , Bauer W.
Published: September 2005

The availability of video and frame grabbing technology for desktop computers permits a new form of visualization and measurement in mechanics experiments. Simple systems such as bouncing balls can be studied in detail and with enough precision to determine important aspects of the motion. For example, the system can be used for introductory students to measure the acceleration of gravity, g, and it also can be coupled with advanced mathematical techniques to find the drag coefficient and elasticity of the bounce. Conventional spreadsheet programs can be used to carry out all but the most mathematical treatments of the data. Examples of analyses which were carried out by high school students through senior physics majors at college are given.
A simple derivation of work and efficiency limits for blackbody radiation converters
Authors: Gordon J. M.
Published: September 2005

The upper bounds on the work production and efficiency of energy conversion from blackbody radiation are derived by viewing the photon gas as a finite-capacity reservoir with a temperature-dependent heat capacity.
Derivation and implications of the symmetry property of the permittivity tensor
Authors: Tsao Pei-Hsi
Published: September 2005

The simplest way to establish the symmetry of the permittivity tensor is found to be based on the first law of thermodynamics. Expressions of energy density and the interpretation of Poynting’s theorem were found as deductions of this symmetry. It has also been shown that ideal dielectrics possess Hermitian complex permittivity tensors, while ohmic conduction leads to symmetric but non-Hermitian generalized permittivity.
Accretion onto a rotating compact object in general relativity
Authors: Karas Vladimír , Mucha Rastislav
Published: September 2005

Accretion of a perfect fluid is discussed within the framework of an exact relativistic solution. [Loren I. Petrich et al., Phys. Rev. Lett. 60, 1781–1784 (1988)] Flow lines of matter accreted onto a rotating black hole are constructed graphically. Asymptotically aligned and asymptotically perpendicular flows (with respect to the rotation axis) are both considered. The mass accretion rate across the hemisphere located on the horizon is evaluated and its dependence on the asymptotic flow direction is discussed.
Extending the quantal adiabatic theorem: Geometry of noncyclic motion
Authors: Garcı́a de Polavieja Gonzalo , Sjöqvist Erik
Published: September 2005

We show that a noncyclic phase of geometric origin has to be included in the approximate adiabatic wave function. The adiabatic noncyclic geometric phase for systems exhibiting a conical intersection as well as for an Aharonov–Bohm situation is worked out in detail. A spin-12 experiment to measure the adiabatic noncyclic geometric phase is discussed. We also analyze some misconceptions in the literature and textbooks concerning noncyclic geometric phases.
Aim high and go far—Optimal projectile launch angles greater than 45°
Authors: Price Richard H. , Romano Joseph D.
Published: September 2005

For ideal projectile motion, which starts and ends at the same height, maximum range is achieved when the firing angle is 45°. If air resistance is taken into account, the optimal angle is somewhat less than 45° and this is often considered obvious. We show here that it is not obvious by considering drag forces with different dependence on projectile speed. In some cases maximum range is achieved for launch angles greater than 45°. Simple physical arguments are given which help explain results that were found by computing trajectories and ranges.
The nature of particle–wave complementarity
Authors: Holladay Wendell G.
Published: September 2005

To resolve the challenges (paradoxes) attending the genesis of quantum theory, Niels Bohr in 1927 proposed a generalization of the conceptual framework of classical physics, termed complementarity, which posited pairs of classical concepts that could be manifested only in mutually exclusive experimental arrangements with both needed to embrace the full range of physical experience. In this context particle–wave complementarity has encountered two major obstacles; (1) No formulation of it has commanded a general consensus; and (2) empirical evidence abounds that contradicts the claim of mutual exclusivity of particle and wave properties of quantum objects in a single experiment. These problems are rooted in the unrestricted scope of this claim. It is shown that a restricted version of particle–wave complementarity, here called “which value–interference” complementarity, is consistent with observations, is naturally contained in the mathematical formalism of quantum theory and, in fact, holds in any representation of quantum theory defined by the eigenvectors of a complete set of commuting observables, such as the configuration space position (kinematic) variables or the complementary linear momentum (dynamic) variables. Thus, the which value–interference form of particle–wave complementarity exists within kinematic–dynamic complementarity, a “layered” complementarity, so to speak. It is hoped that a consistent and valid exposition of particle–wave complementarity will be helpful to those who find the framework of complementarity useful and appropriate for some purpose.
The Fréedericksz transition in liquid crystals: An undergraduate experiment for the advanced laboratory
Authors: Moses Thomas , Jensen Brian
Published: September 2005

The Fréedericksz transition is a magnetically induced reorientation of the molecules of a liquid crystal. We describe here an experimental investigation of the Fréedericksz effect in liquid crystals for the advanced undergraduate laboratory. Besides introducing students to the novel and fascinating liquid-crystalline state of matter, the experiment serves as a valuable introduction to light propagation in an optically anisotropic medium and to the use of the calculus of variations in a somewhat unusual context. All components for the experiments are readily available and inexpensive.
Visualizing motion in potential wells
Authors: Jolly Pratibha , Zollman Dean , Rebello N. Sanjay , Dimitrova Albena
Published: September 2005

The concept of potential-energy diagrams is of fundamental importance in the study of quantum physics. Yet, students are rarely exposed to this powerful alternative description in introductory classes and thus have difficulty comprehending its significance when they encounter it in beginning-level quantum courses. We describe a learning unit that incorporates a sequence of computer-interfaced experiments using dynamics or air-track systems. This unit is designed to make the learning of potential-energy diagrams less abstract. Students begin by constructing the harmonic or square-well potential diagrams using either the velocity data and assuming conservation of energy or the force-displacement graph for the elastic interaction of an object constrained by springs or bouncing off springy blocks. Then, they investigate the motion of a rider magnet interacting with a configuration of field magnets and plot directly the potential-energy diagrams using a magnetic field sensor. The ease of measurement allows exploring the motion in a large variety of potential shapes in a short duration class.
The Introductory University Physics Project 1987–1995: What has it accomplished?
Authors: Coleman Lawrence A. , Holcomb Donald F. , Rigden John S.
Published: September 2005

In 1987, one of us (JSR) challenged the physics teaching community to examine the content of the typical introductory, calculus-based, university physics course, with an eye to meshing that content with the contemporary knowledge, level of understanding, and relative importance of the various topics in the field, and to draw upon results of the many efforts to improve that course which have been carried out over the previous 30 years. The consequence of that call to arms was the Introductory University Physics Project (IUPP). This Project, supported by the National Science Foundation over the period 1987–1995, convened several conferences during the years 1987–90 to study how to bring about the desirable changes it envisioned. The Project Steering Committee then organized the conduct and evaluation of classroom trials of four alternate course models during the academic years 1991–92 and 1992–93, at nine different colleges or universities. This report is directed to the question, “What has the IUPP accomplished?” As we shall report, the accomplishments fall into two categories. (1) As a result of the Project conferences, of frequent reports at appropriate national meetings, and reports of the course trials, many individual physics teachers have instituted small or large changes in the content and style of their courses. (2) Evaluation results from the 1991–93 trials demonstrated the importance and effectiveness of giving thematic coherence to a course structure (one of the IUPP goals), and demonstrated the feasibility of a substantial exposure to quantum physics in the introductory course. We expect textbooks based on several of the IUPP course models to be published within the next several years. In addition to studying ways to further the central goals of the Project (more contemporary physics, a less-packed list of topics, a visible theme or “story line”), study of the evaluation materials from the 1991–93 trials yielded a substantial amount of information relevant to all physics instruction at the introductory level. This information came in areas such as effective use of the introductory laboratory, strengths and pitfalls of computer use in introductory courses, and the importance of helping students most usefully allocate the time they have available for physics.
Spectrum analysis for introductory musical acoustics
Authors: Smedley John E.
Published: September 2005

A “real time” fast Fourier transform spectrum analyzer facilitates several experiments for an introductory course in musical acoustics. With its rapidly updated display, the time-dependent vibrations of an aluminum bar are easily studied. Using longer time acquisitions and correspondingly higher resolution facilitates the study of string inharmonicities, resonant energy transfer, and sound radiation patterns in guitar acoustics.
The challenge of matching learning assessments to teaching goals: An example from the work-energy and impulse-momentum theorems
Authors: Pride Tara O’Brien , Vokos Stamatis , McDermott Lillian C.
Published: September 2005

The issue of how to assess learning is addressed in the context of an investigation of student understanding of the work-energy and impulse-momentum theorems. Evidence is presented that conceptual and reasoning difficulties with this material extend from the introductory to the graduate level and beyond. A description is given of the development of an instructional sequence designed to help students improve their ability to apply the theorems to real motions. Two types of assessment are compared. The results demonstrate that responses to multiple-choice questions often do not give an accurate indication of the level of understanding and that questions that require students to explain their reasoning are necessary. Implications for the preparation of teaching assistants are discussed.
Copernicus and Martin Luther: An encounter between science and religion
Authors: Kobe Donald H.
Published: September 2005

Martin Luther has been severely criticized by some scholars for a remark he made about Copernicus and his heliocentric theory. When this offhand remark, made at the dinner table four years before the publication of On the Revolutions of the Heavenly Spheres, is considered in its historical context, it is shown to be in keeping with the generally accepted scholarly opinion of the time. Luther’s view of science in general and astronomy in particular is examined.
The quotient function and its applications
Authors: Lindell I. V. , Sihvola A. H.
Published: September 2005

The Q function or the quotient function is frequently encountered in electromagnetics research without knowledge of its basic properties. However, the simple rules given in the present paper can speed up the algebraic work and reduce possible errors. Scalar, vector, and dyadic-valued Q functions are discussed together with some applications in physics.
On scale invariance and anomalies in quantum mechanics
Authors: Cabo A. , Lucio J. L. , Mercado H.
Published: September 2005

We reconsider the quantum mechanics of scale-invariant potentials in two dimensions. The breaking of scale invariance by quantum effects is analyzed by the explicit evaluation of the phase shift and the self-adjoint extension method. We argue that the breaking of scale invariance reported in the literature for the δ(r) potential is an example of explicit symmetry breaking and not an anomaly or quantum mechanical symmetry breaking.
Transformations between Schrödinger equations
Authors: Mavromatis Harry A.
Published: September 2005

It is shown how an N-dimensional Schrödinger equation, involving a particular central potential, may be related to seemingly unrelated Schrödinger equations involving other central potentials and spaces of different dimension. Two illustrative cases are given where analytically soluble Schrödinger equations are involved.
Holographic study of a vibrating bell: An undergraduate laboratory experiment
Authors: Menou Kristen , Audit Benjamin , Boutillon Xavier , Vach Holger
Published: September 2005

An experiment combining holography and musical acoustics is described. Structures of vibration modes of a bell are visualized by time-average holography under either acoustical or mechanical excitation. The vibration amplitude as measured by an accelerometer shows very good quantitative agreement with that determined from our holograms by fringe counting. An effect of degenerate level separation is shown in the mechanical case. It is argued that this experiment is not only very inexpensive for a physics laboratory already equipped for holography, but that it also strongly stimulates students to deepen their insight into a variety of different topics in applied physics.
The experiments of Biot and Savart concerning the force exerted by a current on a magnetic needle
Authors: Erlichson Herman
Published: September 2005

Francois Arago brought the news of Oersted’s discovery of the effect of a current-carrying wire on a magnet to Paris on September 4, 1820. André-Marie Ampère and the team of Jean-Baptiste Biot and Félix Savart quickly set to work to establish a quantitative law for this effect. Their approaches were quite different. This paper describes the experiments of Biot and Savart and their results. It also briefly discusses the approach of André-Marie Ampère, who coined the name “electrodynamics” and whose fundamental formula gave the force between two infinitesimal current elements. Ampere’s formula fell into disuse after the advent of Maxwell’s field approach. Biot and Savart’s experimental law, in the modern form of the differential magnetic field due to a current element, became the standard starting point for calculating the magnetic field due to steady currents.
The uncertainty principle for energy and time. II
Authors: Hilgevoord Jan
Published: September 2005

The meaning and scope of a recent type of uncertainty relation of a very general character are elucidated using the notions of time-indicating dynamical variables (clock variables) and place-indicating dynamical variables (position variables). It is shown that if the total energy (momentum) of a system is certain, all time-indicating (place-indicating) dynamical variables are completely uncertain. The quantum clock is discussed as an illustration of the energy–time uncertainty relation. The relations can be successfully applied to the thought experiments that Einstein introduced into his debate with Bohr about the uncertainty principle(s) and, in particular, to the famous photon-box experiment. It is shown that due to this general relation the photon box can never serve its purpose, independent of the details of the experiment.
Physics lecturing with audience paced feedback
Authors: Poulis J. , Massen C. , Robens E. , Gilbert M.
Published: September 2005

For some time we have experimented at the Eindhoven University of Technology with a system which provides students with an electronic feedback path to the lecturer, audience paced feedback (APF). In this paper we describe this APF system, and give indications of its effectiveness.
Evolution of a vibrational wave packet on a disordered chain
Authors: Allen Philip B. , Kelner Jonathan
Published: September 2005

A linear chain of point masses coupled by harmonic springs is a standard model used to introduce concepts of solid state physics. The well-ordered chain has sinusoidal standing wave normal modes (if the ends are fixed) or traveling wave normal modes (if the ends are connected in a ring). Ballistically propagating wave packets can be built from these normal modes, and illustrate the mechanism of heat propagation in insulating crystals. When the chain is disordered, new effects arise. Ballistic propagation is replaced by diffusive propagation on length scales larger than the mean free path for ballistic motion. However, a new length scale, the localization length, also enters. On length scales longer than the localization length, neither ballistic nor diffusive propagation occurs, and energy is trapped unless there are anharmonic forces. These ideas are illustrated by a computer experiment.
Klein’s paradox
Authors: Holstein Barry R.
Published: September 2005

Klein’s paradox is shown to be resolved by a careful consideration of Feynman’s picture of antiparticles as negative energy solutions traveling backward in time. Implications associated with the spin-statistics theorem are pointed out.
Schwinger’s method and the computation of determinants
Authors: de Albuquerque Luiz C. , Farina C. , Rabello S.
Published: September 2005

We show how to use Schwinger’s method to evaluate determinants of differential operators that appear quite often in ordinary quantum mechanics. Although this method was introduced by Schwinger in the early fifties to compute effective actions for quantum electrodynamics and was recently applied by him in the Casimir effect, it has never been used in nonrelativistic problems. As explicit examples we compute the partition functions for both the bosonic and the fermionic harmonic oscillator.
An undergraduate experiment on the propagation of thermal waves
Authors: Bodas A. , Gandı́a V. , López-Baeza E.
Published: September 2005

When a long thin bar of a material is subject to periodic heating, a temperature wave propagates along the sample, and its propagation properties can be used to determine the thermal diffusivity of the material. In this paper, we present a simple experiment that can be used by undergraduate students to better understand thermal waves and their propagation and to measure thermal diffusivity. In spite of its simplicity, the experiment provides acceptable results for a copper sample.
Vibrating soap films: An analog for quantum chaos on billiards
Authors: Arcos E. , Báez G. , Cuatláyol P. A. , Prian M. L. H. , Méndez-Sánchez R. A. , Hernández-Saldaña H.
Published: September 2005

We present an experimental setup based on the normal modes of vibrating soap films which shows quantum features of integrable and chaotic billiards. In particular, we obtain the so-called scars—narrow linear regions with high probability along classical periodic orbits—for the classically chaotic billiards. We show that these scars are also visible at low frequencies. Finally, we suggest some applications of our experimental setup in other related two-dimensional wave phenomena.
An exhaustive analysis of the asymptotic time dependence of wave packets in one dimension
Authors: Unnikrishnan K.
Published: September 2005

It is shown that the amplitude of a square-integrable wave packet in one dimension must decrease with time asymptotically as either t−1/2+μ, 0⩽μ<1/4, or as t−1/2 ln t. The different patterns reflect the different ways in which the wave function at t=0 falls off at large |x|; μ=0 corresponds to a decrease faster than |x|−1, the logarithmic form to a decrease exactly as |x|−1, and μ>0 to a decrease as |x|−1+2μ.
Materials physics: A new contemporary undergraduate laboratory
Authors: Jaeger Herbert , Pechan Michael J. , Lottis Daniel K.
Published: September 2005

We have developed a laboratory course focusing on the physics of materials. This course, taught in place of a “conventional” lecture-only solid state or condensed matter physics course, helps to prepare students for the technical work force and also serves as a solid, broad-based foundation for students bound for graduate school. In addition, the course illustrates the increasingly interdisciplinary nature of physics. Classroom activities and experiments concentrate on four materials classes: metals, ceramics, semiconductors, and polymers. Experiments include electrical conductivity of metals and semiconductors; ionic conductivity of ceramics; superconductivity in metals, alloys, and ceramics; preparation and characterizations of metallic thin films; scanning tunneling microscopy; magnetic properties of materials; impedance spectroscopy of solid electrolytes; phase diagram determination by differential thermal analysis and x-ray diffractometry; Hall effect in pure and doped semiconductors; dielectric response of polymers; and mechanical properties of polymers.
Electromagnetic angular momentum and quantum mechanics
Authors: Singleton D.
Published: September 2005

A quick way of arriving at the Dirac quantization condition between electric and magnetic charges is to require that the electromagnetic field angular momentum of a Thomson dipole (a magnetic monopole and an electric charge) equal some integer multiple of the fundamental unit of quantum mechanical angular momentum, ℏ/2. Applying this same type of argument to the electromagnetic field angular momentum carried by a magnetic dipole–electric charge system leads to an infinite number of different quantization conditions, and an apparent incompatibility between quantum mechanics and the dipole–charge system. However, a more careful analysis shows that the particle plus field angular momentum of this system does satisfy the standard angular momentum commutation relationships and is therefore a good quantum mechanical angular momentum. This emphasizes that caution must be taken when applying such semiclassical quantization arguments. Finally, a possible connection between this dipole–charge field angular momentum and the nucleon spin crisis is given.
Atomic hyperfine structure studies using temperature/current tuning of diode lasers: An undergraduate experiment
Authors: Rao G. N. , Reddy M. N. , Hecht E.
Published: September 2005

We present a simple and inexpensive experimental arrangement for hyperfine structure studies in atoms using commercially available laser diodes and hollow cathode lamps. The experiment is highly suitable for the undergraduate laboratory. This technique can be employed to investigate the hyperfine structure of rare earth and other elements such as Ta and Nb which have large nuclear magnetic and or quadrupole moments. In this paper, we report well-resolved hyperfine structure spectra recorded for holmium employing optogalvanic spectroscopy. We also report Doppler limited hyperfine structure measurements on the ground state of rubidium using injection current/temperature tuning of the diode laser. This involves a simple experimental arrangement suitable for undergraduate laboratories. The hyperfine coupling constants for the level at 31 443.26 cm−1 in Ho I are reported for the first time. Details of the data analysis to obtain accurate hyperfine structure coupling constants from the observed spectra are presented. A number of commercially available diode lasers in the visible and the near infrared regions and simple in-house developed or commercially available low cost current and temperature controllers can be employed for the present studies. We employ simple cooling/heating or current modulation for tuning the output wavelength of the diode laser. The presently proposed experimental arrangement can be assembled easily and requires no machine/glass shop facilities.
What is quantum mechanics trying to tell us?
Authors: Mermin N. David
Published: September 2005

I explore whether it is possible to make sense of the quantum mechanical description of physical reality by taking the proper subject of physics to be correlation and only correlation, and by separating the problem of understanding the nature of quantum mechanics from the hard problem of understanding the nature of objective probability in individual systems, and the even harder problem of understanding the nature of conscious awareness. The resulting perspective on quantum mechanics is supported by some elementary but insufficiently emphasized theorems. Whether or not it is adequate as a new Weltanschauung, this point of view toward quantum mechanics provides a different perspective from which to teach the subject or explain its peculiar character to people in other fields.
Time-frequency analysis with the continuous wavelet transform
Authors: Lang W. Christopher , Forinash Kyle
Published: September 2005

The continuous wavelet transform can be used to produce spectrograms which show the frequency content of sounds (or other signals) as a function of time in a manner analogous to sheet music. While this technique is commonly used in the engineering community for signal analysis, the physics community has, in our opinion, remained relatively unaware of this development. Indeed, some find the very notion of frequency as a function of time troublesome. Here spectrograms will be displayed for familiar sounds whose pitches change with time, demonstrating the usefulness of the continuous wavelet transform.
Propagation of a Feynman error on real and inertial forces in rotating systems
Authors: Tiersten Martin S. , Soodak Harry
Published: September 2005

Serious errors and misleading statements concerning real and inertial forces in rotating coordinate systems in The Feynman Lectures on Physics are pointed out and corrected.
Simple nonlinear jerk functions with periodic solutions
Authors: Gottlieb H. P. W.
Published: September 2005

The appearances of jerk, the third time derivative of displacement, in several papers of mathematical and physical content are reviewed. Two simple nonlinear jerk functions, all of whose solutions are periodic, are introduced and solved. The first has period dependent on initial acceleration but independent of amplitude, and is related to the second-order cubic oscillator. The second, with intrinsically third-order dynamics, has period dependent also on initial displacement. A possible bearing on chaotic jerk functions is mooted.
Example of mass–energy relation: Classical hydrogen atom accelerated or supported in a gravitational field
Authors: Boyer Timothy H.
Published: September 2005

A simple example of the mass–energy relation is given by using electromagnetic calculations for a classical hydrogen atom, a point mass electron moving under the Coulomb force in a uniform circular orbit around a heavy point mass proton when the radiation-reaction self-force is neglected. The system mass is determined by calculating the ratio of the total external force to the system acceleration in the limit of small acceleration, and is shown to be equal to c−2 times the total system energy including the particle rest-mass energies, the particle kinetic energies, and the electrostatic potential energy. From the equivalence principle, the external forces can be regarded either as accelerating the atom relative to an inertial frame or else as supporting the atom in a gravitational field. The calculations are carried out for two different models. In the first case, the atom is regarded as accelerated by a frictionless surface which applies forces to both the electron and the proton. In the second case, the atom is accelerated by a single external force applied to the proton, and the electron orbit is displaced relative to the proton. In both cases the accelerating forces are constant forces and there are no external forces stabilizing the system.
Development and assessment of a research-based tutorial on light and shadow
Authors: Wosilait Karen , Heron Paula R. L. , Shaffer Peter S. , McDermott Lillian C.
Published: September 2005

This article describes an investigation of student understanding of geometrical optics and illustrates the use of research as a basis for the development of curriculum. Evidence is presented that university students who have studied physics at the introductory level and beyond often cannot apply basic concepts from geometrical optics to account for the pattern produced on a screen when an aperture or obstacle is placed between a light source and the screen. Identification and analysis of student difficulties guided the initial design of a tutorial to supplement instruction in a typical calculus-based or algebra-based course. Development of a laboratory-based, inquiry-oriented curriculum for precollege teachers took place concurrently. Ongoing assessment was an integral part of the curriculum development process. The instructional materials that evolved from this iterative cycle have proved to be effective with the target populations.
Body motion in a one-dimensional resistive medium
Authors: Molina M. I.
Published: September 2005

A simple, one-dimensional, microscopic model of a moving body undergoing multiple collisions with particles composing a medium is introduced and solved in closed form, using energy and momentum conservation. It leads to the well-known regime of quadratic dependence on speed for the resistive force on the body.
Noether’s theorem, rotating potentials, and Jacobi’s integral of motion
Authors: Giordano C. M. , Plastino A. R.
Published: September 2005

We consider the derivation of Jacobi’s integral of motion for a particle moving in a uniformly rotating potential, as a simple illustrative application of Noether’s theorem. We also provide some examples of Jacobi’s integral. In particular, we show that some elementary problems usually discussed in texts of classical mechanics can be interpreted in terms of Jacobi’s integral.
Use of the Fokker–Planck equation in high-field transport problems
Authors: Bringuier E.
Published: September 2005

The Fokker–Planck drift-diffusion equation is often used to describe Brownian motion of a particle in thermal equilibrium with the surrounding medium. The present paper shows that the equation has the ability to describe charged particle transport far from equilibrium, such as occurs in the presence of a high electric field in a neutral gas or a semiconducting solid. These transport problems are usually tackled by means of the Boltzmann transport equation, but the Fokker–Planck approach is mathematically simpler, and gives insight into the statistics of energy-exchange processes and their thermalization capacity.
Ole Ro/mer, the speed of light, the apparent period of Io, the Doppler effect, and the dynamics of Earth and Jupiter
Authors: Shea James H.
Published: September 2005

Ole Rømer’s (1676) method of using variations in the apparent period of Jupiter’s moon, Io, to demonstrate that the speed of light is finite made use of what we would today call a “Doppler” method. He did this 166 years before Christian Doppler described what we now call the Doppler effect and the mechanism in 1842. Although the method Rømer conceived is unquestionably valid, his original and only paper on the subject left out much of the detail necessary to determine whether his measurements were adequate to the task of demonstrating the effect he claimed to have observed. Unfortunately, the timekeeping available to Rømer and his colleagues Picard and Cassini, each of whom made some of the observations involved, was, at best, not quite up to the task of measuring the necessary times with sufficient accuracy. Mathematical analysis of the dynamics of the Earth/Jupiter synodic system allows a more thorough analysis of Rømer’s work than has previously been made. Rømer’s case was built on four “observations,” one of which clearly failed, one of which was successful, and two of which were quite questionable.
Approximate trajectories for projectile motion with air resistance
Authors: Deakin Michael A. B. , Troup G. J.
Published: September 2005

To remarkable accuracy and under a wide variety of conditions, the trajectories of projectiles under various laws of resistance may be approximated by cubic curves. This allows for the relatively simple calculation of many details of the flight.
The sweet spot of a baseball bat
Authors: Cross Rod
Published: September 2005

The sweet spot of a baseball bat, like that of a tennis racket, can be defined either in terms of a vibration node or a centre of percussion. In order to determine how each of the sweet spots influences the “feel” of the bat, measurements were made of the impact forces transmitted to the hands. Measurements of the bat velocity, and results for a freely suspended bat, were also obtained in order to assist in the interpretation of the force waveforms. The results show that both sweet spots contribute to the formation of a sweet spot zone where the impact forces on the hands are minimised. The free bat results are also of interest since they provided particularly elegant examples of wave excitation and propagation, suitable for a student demonstration or experiment.
Eddy current damping of a magnet moving through a pipe
Authors: Hahn Kenneth D. , Johnson Erik M. , Brokken Allen , Baldwin Steven
Published: September 2005

A harmonic oscillator consisting of a neodymium magnet attached inside a spring is driven through resonance. Eddy currents, induced in pipes surrounding the magnet, result in a damping of the motion of the magnet. Our experiment makes precise measurements of the motion and damping of the magnet as we vary pipe composition, length, thickness, radius, and position. A theoretical analysis combining the standard differential equation for a damped, driven harmonic oscillator and Faraday’s law of electromagnetic induction gives excellent agreement with the experimental results. This analysis allows for the calculation of electromagnetic damping for any pipe configuration which is coaxial with the magnet’s motion and provides strong evidence for the eddy current damping analysis of the common demonstration of dropping a magnet down a conducting tube.
Angle states in quantum mechanics
Authors: de la Torre A. C. , Iguain J. L.
Published: September 2005

Angle states and angle operators are defined for a system with arbitrary angular momentum. They provide a reasonable formalization of the concept of angle provided that we accept that the angular orientation is quantized. The angle operator is the generator of boosts in angular momentum and is, almost everywhere, linearly related to the logarithm of the shift operator. Angle states for fermions and bosons behave differently under parity transformation.
On the formation of white-light interference fringes
Authors: Kovács A. P. , Varjú K. , Osvay K. , Bor Zsolt
Published: September 2005

We describe an experiment in which the white-light interference fringes appearing at the output of a Michelson interferometer are observed through a spectrograph. In this manner the relative positions of monochromatic interference fringes come into sight and it allows a better understanding of the formation of the white-light fringes. A simple model is described for determining the shape of the spectrally resolved white-light interference fringes. An expression for the relationship between the slope of the fringes and the arm length difference of the interferometer is derived and is demonstrated experimentally. In addition, an intuitive explanation based on this experiment is given for the washing out of the white-light fringes.
Student Performance in a Keller-Plan Course in Introductory Electricity and Magnetism
Authors: Austin Sam M. , Gilbert K. E.
Published: September 2005

A group of 25 students chosen at random from a larger class was taught in a Keller-plan (self-paced) format following the method of Green. The performance of these students was compared with that of the students in the lecture-recitation section through a common final examination and through a retest taken approximately two months after the end of the course. In each case the Keller-plan students did substantially better. Suggestions are made for improvements in the usual Keller-plan format.