Second International Workshop On Harmonic Oscillators

Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

The following topics are discussed in this volume: recent developments in operator theory, coherent states and wavelet analysis, geometric and topological methods in theoretical physics and quantum field theory, and applications of these methods of mathematical physics to problems in atomic and molecular physics as well as the world of the elementary particles and their fundamental interactions. Two extensive sets of lecture notes on quantization techniques in general, and quantum gauge theories and strings as an avenue towards quantum geometry, are also included. The volume should be of interest to anyone working in a field using the mathematical methods associated with any of these topics. Contents:Quantization Techniques: A Quick Overview (S T Ali)The Quantum Geometer's Universe: Particles, Interactions and Topology (J Govaerts)Theoretical Methods of Modern Classical and Quantum Physics:Do Cross-Sections Determine Phase Shifts Uniquely? (D Atkinson)Hilbert Transform or Kramers-Kronig Relations Applied to Some Aspects of Linear and Nonlinear Physics (G Debiais)Application of the Gibbs Sampler to the Conditional Simulation of Rain Fields (H Onibon et al.)The Mathematics of an Algebraic Approach to the Physics of Hadrons (M D Slaughter)Coherent States, Wavelets and Geometric Methods in Theoretical Physics:Phase Space Geometry in Classical and Quantum Mechanics (J R Klauder)Functional Analysis Special Functions and Orthogonal Polynomials:On Generalized Continuous D Semi-Classical Hermite and Chebychev Orthogonal Polynomials of Class One (E Azatassou & M N Hounkonnou)On a Generalization of the Method by Barbaroux et al. for the Improvement on the Rate of Decay of an Operator Resolvent (G Honnouvo & M N Hounkonnou)and other papers Readership: Researchers in mathematical physics, theoretical physics, physical chemistry, analysis and differential equations, atomic and quantum physics. Keywords:

The following topics are discussed in this volume: recent developments in operator theory, coherent states and wavelet analysis, geometric and topological methods in theoretical physics and quantum field theory, and applications of these methods of mathematical physics to problems in atomic and molecular physics as well as the world of the elementary particles and their fundamental interactions. Two extensive sets of lecture notes on quantization techniques in general, and quantum gauge theories and strings as an avenue towards quantum geometry, are also included. The volume should be of interest to anyone working in a field using the mathematical methods associated with any of these topics.

This volume, recording the 10th international symposium honoring noted French mathematical physicist Jean-Pierre Vigier surveys and continues to develop Unified Field Mechanics (UFM) from the perspective of Multiverse cosmology and Topological Field Theory. UFM represents a developing paradigm shift with many new parameters extending the Standard Model to a 3rd regime of Natural Science beyond Quantum Mechanics. UFM is now experimentally testable, thus putatively able to demonstrate the existence of large-scale additional dimensionality (LSXD), test for QED violating phenomena and surmount the quantum uncertainty principle leading to a new 'Age of Discovery' paling all prior ages in the historical progression: Classical Mechanics (3D) to Quantum Mechanics (4D) and now to the birth of the 3rd regime of UFM in additional dimensionality correlating with M-Theory. Many still consider the Planck-scale as the 'basement of reality'. This could only be considered true under the limitations of the Standard Model. As we methodically enter the new regime a profound understanding of the multiverse and additional dimensionality beckons.