Table of contents

The nuclear liquid drop model is applied to describe some basic properties of a negative hydrogen ion in the strong electric field of a laser. The equilibrium ionic size, energy and polarizability of the ion are calculated. Collective modes of the dipole oscillations are considered. A barrier which arises in a strong electric field is studied. The barrier vanishes at some large value of the electric field, which is defined as a critical value. The dependence of the critical field on frequency is studied. At frequencies  ω⩾(ω_d/2^1/2) (ω_d is the frequency of the dipole oscillations of the electronic cloud relative to the nucleus) the barrier remains for any field. At high frequencies a `stripping' mechanism for instability arises. At the resonant frequency a rather low amplitude of the electric field causes the `stripping' instability.

The equation of motion of the simple pendulum is derived in the framework of special relativity. The relativistic effect on the motion of the simple pendulum is investigated through numerical simulation. We present a discussion of the relativistic effects on the pendulum's period and on the dynamics of the phase space. We find that, although negligibly small, there exist calculable differences between the periods of the relativistic and non-relativistic pendulum if one implements a high-order precision during the evaluation. Furthermore, the discrepancy increases, first nonlinearly and then linearly, with the amplitude. The period for the non-relativistic case is always shorter than that for the relativistic case. While the general characteristics of the relativistic phase space remain the same as for the non-relativistic case, constant-energy-level curves conform to the relativistic limit.

The tautochrone problem consists of the determination of a curve in the (x,y) plane such that the time required for a particle to slide down the curve to its lowest point under gravity is independent of its initial position on the curve. Using the fractional derivation method, we determine the tautochrone curve for a rotating system, as well as the tautochrone under non-rotating and rotating Newtonian gravitational fields.

The Gibbs function, which depends on the intensive variables T and P, is easier to obtain experimentally than any other thermodynamical potential. However, textbooks usually first introduce the internal energy, as a function of the extensive variables V and S, and then proceed, by Legendre transformations, to obtain the Gibbs function. Here, taking liquid water as an example, we show how to obtain the internal energy from the Gibbs function. The two fundamental equations (Gibbs function and internal energy) are examined and their output compared. In both cases complete thermodynamical information is obtained and shown to be practically the same, emphasizing the equivalence of the two equations. The formalism of the Gibbs function is entirely analytical, while that based on the internal energy is, in this case, numerical. Although it is well known that all thermodynamic potentials contain the same information, usually only the ideal gas is given as an example. The study of real systems, such as liquid water, using numerical methods, may help students to obtain a deeper insight into thermodynamics.

The technique of importance sampling can lead to a considerable reduction in the uncertainties (variance) inherent in random sampling. The technique is explained, and is illustrated by simple examples. It is shown that the variance may be reduced by weighting so that each sample makes an almost equal contribution to the estimate: this is shown graphically. A BASIC program demonstrating importance sampling is available with and may be downloaded from the online version of this paper.

The force acting on a point charge inside a grounded conducting cavity is discussed. This is a situation relevant to some quantum dot devices. We emphasize that care must be taken when applying the image-charge method to this problem.

The properties of discrete random walks on a circle are contrasted with those of the more familiar (infinite) straight-line random-walk problem. Differences between these systems illustrate the kinetic-theory explanation of thermodynamic irreversibility. Results of circular random walk simulations are presented; these confirm the theoretical predictions of the mean recurrence interval.

A philosopher (WR) and a physicist (KF) have been team teaching a history and philosophy of science course every other year over the past twelve years at Indiana University Southeast. Our approach has been to spend about half the semester talking about the development of the Sun-centred system of Copernicus, covering some important developments in astronomy and physics during the period from Copernicus until Newton's death. The second half of the course examines modern views of scientific method, the scope of scientific knowledge, and observations about science and values put forth by various philosophers (for example, Popper, Ziman, Thagard, Carnap, Hempel, Quine and others). Students are asked to write essays critiquing these philosophical views using historical examples from the earlier readings as support for their arguments. The last time we ran the course we placed the papers (anonymously) on the web and had participants in the class make suggestions to each other on improving the essays of their fellow students. We feel this was a valuable exercise and intend to try it again. Our paper includes a discussion of our method and a sample of issues raised.

A self-contained discussion of non-relativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three dimensions. The present discussion illustrates in a simple way the concepts of partial-wave decomposition, phase shift, optical theorem and effective-range expansion.

In order to visualize equipotential and electric field lines in a medium with an applied direct current voltage, one needs to sample potential values from uniform grids in the medium. The equipotential lines are then constructed by locating points with equal potential and connecting them together. Finally, electric field lines are obtained by drawing lines perpendicular to these equipotential lines. These experimental procedures take time and are prone to errors when performed in a student laboratory. To integrate computers and microcontroller systems with physics experiments, we have developed a prototype `automatic sampling system'. The system consists of a microcontroller and its peripherals to control mechanical parts which move the probe to locations within the sampling area, read potential values from those locations and send them back to a computer for analysis. The system together with a computer program can be effectively used to experimentally study an electric field mapping in different configurations of electrodes.

A simple computer experiment is described for measuring the shape of a free hanging chain or catenary. The two ends of a chain are attached to a computer screen. The (x,y) coordinates of points of the chain are measured using a pointing device (mouse). The data are compared with the catenary equation. Such an experiment requires only a personal computer and needs no additional hardware. The experiment is appropriate for students. It includes all stages of `big' experiments - theory, planning, data acquisition and data processing. The idea of using the computer screen and mouse as measuring devices can also be applied to other physical phenomena.

The electrical properties of ferroelectric substances are investigated and related to the Curie-Weiss law. A cryogenic experiment suitable for students measures the electrical susceptibility of strontium titanate in the 90-300 K temperature range. By measuring the electrical susceptibility of a modified barium titanate ceramic between 273 K and 343 K a phase transition is clearly observed at 304 K.

A clear and simple physical approach to the explanation of exact particular solutions of the classical many-body problem is suggested. When the motion of individual bodies coupled by mutual gravitational forces in a many-body system occurs along conic sections, each body can be treated as moving not under the pull of the other moving bodies, but rather under a stationary central inverse-square gravitational field. These solutions describing possible amazingly simple (Keplerian) many-body motions are illustrated by computer simulations. Some pedagogical and philosophical aspects of the problem are discussed.