Semiclassical Quantization in Many Dimensions

We examine the semiclassical limit of the quantum energy spectrum in many dimensions: by means of a WKB-like ansatz leading to Einstein-Brillouin-Keller (EBK) quantization, by means of a path integral, hence associating a bound state with a particular classical periodic trajectory, and by the Birkhoff-Gustavson (BG) transformation to action-angle variables. We extend the EBK method to many-fermion systems using coherent states; and apply both EBK using surfaces of section, and the BG transformation to an SU(3) schematic nuclear shell model. We describe a new algorithm for finding periodic trajectories of a Lagrangian system with polynomial potential. It is applied to the Henon-Heiles system with good results, and these trajectories are used to quantize the system. The EBK and BG methods have some success, while periodic trajectory quantization fails. We discuss possible reasons for this failure and future approaches to these problems.</p

Molecular machinery and manufacturing with applications to computation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, 1991.Vita.Includes bibliographical references (p. 469-487).by K. Eric Drexler.Ph.D

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Publications of Goddard Space Flight Center, 1964. Volume I - Space sciences

This publication is a collection of articles, papers, talks, and reports generated by the scientific and engineering staff of Goddard Space Flight Center in the year 1964. Many of these articles were originally published in scientific or engineering Journals or as official NASA technical publications, while other are documents of a more informal nature. All are reprinted here as nearly verbatim as typography and format will permit. These articles are grouped into broad subject categories, but no detailed subdivision has been made. Within each category, the articles are arranged alphabetically by author. An overall author index is given in the back of the volume. The years 1963, 1964, and 1965 are being published as whole-year issues, and the resulting size dictates the use of two volumes; the first volume is titled Space Sciences, and the second Space Technology. It is anticipated, however, that future issues will be quarterly single volumes