Ronald L. Greene

Advances in plasma broadening of atomic hydrogen

The Stark broadening tables for hydrogen Lyman, Balmer and Paschen lines published in the early seventies give accurate results for the widths of the β lines down to relatively low electron densities, and for the far line wings in general. However, the half-widths of the α lines can be in error by as much as a factor of 30, particularly at intermediate densities. Modern theoretical methods are capable of producing accurate values over the entire density range. Recent developments in the Stark broadening of non-hydrogenic species are also considered.

Shallow impurity centers in semiconductor quantum well structures

Abstract Interest in the study of the behavior of shallow impurity centers in superlattices and quantum well structures is fairly recent. This paper reviews briefly both the theoretical and experimental work done in this field in the last few years. Several recent calculations of the energy levels of hydrogenic impurity states in quantum well structures, such as Ga1−xAlxAsGaAsGa1−xAlxAs, are reviewed. The behavior of these levels as a function of the quantum well size is discussed. Recent experimental data concerning the variations of the binding energies of shallow donors and acceptors as a function of the GaAs quantum well size are reviewed. A comparison between these experimental measurements and the results of recent calculations is presented.

Connectionist hashed associative memory

Abstract This paper proposes the use of simple connectionist networks as hashing functions for sparse associative or content addressable memory. The robustness of such networks in the presence of noisy inputs, and the property that “similar inputs lead to similar outputs” permits (in a probabilistic sense) faster-than-linear retrieval of data which best fits the input. The input may be noisy or have partially specified feature vectors. Mathematical analysis is presented for the Boolean feature case using a network with randomly selected connection strengths.

Efficient retrieval from sparse associative memory

Abstract Best-match retrieval of data from memory which is sparse in feature space is a time-consuming process for sequential machines. Previous work on this problem has shown that a connectionist network used as a hashing function can allow faster-than-linear probabilistic retrieval from such memory when presented with probing feature vectors which are noisy or partially specified. This paper introduces two simple modifications to the basic Connectionist-Hashed Associative Memory which together can improve the retrieval efficiency by an order of magnitude or more. Theoretical results are presented for storage/retrieval of memory items represented by feature vectors made up of 1000 randomly selected bivalent components. Experimental results on correlated feature vectors are presented in the context of a spelling correction application.

Introduction to Maple V

Maple V is an extensive software system capable of computing and manipulating data symbolically, numerically, and graphically. It is often generically referred to as a Computer Algebra System (CAS). Although it is a very powerful tool for mathematical manipulations, the sheer size of the program can be intimidating to someone considering using it in science or engineering. However, as will be seen in this text, even a small subset of Maple can be quite useful to the study of physics. Maple’s symbolic abilities can reduce the amount of tedious algebra that is often necessary in solving physics problems. Furthermore, its numeric and graphical abilities allow us to go further into a given problem and extract physical understanding that is otherwise difficult to obtain. This book considers Maple’s application specifically to the study of classical mechanics, but much of what is discussed is also applicable to other disciplines.

Systems of Particles

Let us consider a system of two particles, masses m1 and m2, which interact with each other through a central force; that is, m1 is acted upon by a force whose magnitude depends only upon the distance between the two particles, and whose center is at the position of m2. The force on m2 has the same form, with its center at m1. The distance between the two particles is given by \(r = \left| {{r_1}} \right. - {r_2}\left| , \right.\), where r1 and r2 are the positions of the two masses with respect to some inertial reference system. If we let \({\rm{\hat r = (}}{{\rm{r}}_{\rm{1}}}{\rm{ - }}{{\rm{r}}_{\rm{2}}}{\rm{)/r}}\) be the unit vector pointing from m2 to m1, the force acting on m1 due to m2 is of the form \({{\rm{F}}_{{\rm{12}}}}{\rm{ = f}}\left( r \right)\hat r\). Similarly, the force on m1 due to m2 is \({{\rm{F}}_{{\rm{21}}}}{\rm{ = - f}}\left( r \right)\hat r\).

Review of Introductory Mechanics

Classical mechanics has traditionally been broken into three subdisciplines: kinematics, dynamics, and statics. Kinematics is the study of how motion is described in general, and thus has to be discussed before examining dynamics, the study of the laws which determine what motion actually occurs. In this text statics is treated as a special case of dynamics.

The Harmonic Oscillator

As an extended example of Newtonian dynamics, let us examine the motion of a particle under the influence of a force whose magnitude is proportional to the displacement of the particle from an equilibrium position, and whose direction is toward that equilibrium position. If we choose the coordinate system so that the origin is at the point of equilibrium, the force may be written

On integrating computers into the physics curriculum

{\rm{F = - kr,}}