Includes bibliographical references (p. 185-188) and index.
|Statement||by Willi-Hans Steeb.|
|LC Classifications||QA322.4 .S74 1991|
|The Physical Object|
|Pagination||192 p. ;|
|Number of Pages||192|
|LC Control Number||92177555|
Additional Physical Format: Online version: Steeb, W.-H. Hilbert spaces, generalized functions and quantum mechanics. Mannheim: BI-Wissenschaftsverlag, © 1 Hilbert Spaces Fourier Transform and Wavelets Linear Operators in Hilbert Spaces Generalized Functions Classical Mechanics and Hamilton Systems Postulates of Quantum Mechanics Interaction Picture Eigenvalue Problem Eigenvalue Equation Applications Spin Matrices and Kronecker Product Parity and. The Hilbert space of a composite system is the Hilbert space tensor product of the state spaces associated with the component systems (for instance, J. M. Jauch, Foundations of quantum mechanics, section ). For a non-relativistic system consisting of a finite number of distinguishable particles, the component systems are the individual. Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics. Authors (view affiliations) Willi-Hans Steeb Linear Operators in Hilbert Spaces. Willi-Hans Steeb. Pages Generalized Functions. Algebra Eigenvalue Fourier transform Hilbert space Potential Soliton Wavelet mathematics mechanics operator quantum mechanics.
Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics. Authors: Steeb, W.-H. Free Preview. This book gives a comprehensive introduction to modern quantum mechanics, emphasising the underlying Hilbert space theory and generalised function theory. All the major modern techniques and approaches used in quantum mechanics are introduced, such as Berry phase, coherent and squeezed states, quantum computing, solitons and quantum mechanics. The theory of rigged Hilbert spaces plays a decisive role in the mathematical formulation of quantum mechanics [Ant98]. All of the above mentioned applications of S Author: Jean-Pierre Antoine. Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory and functional acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs.
Besides Hilbert spaces generalized functions (Gelfand and Shilov , Vladimorov ) play an important role in quantum mechanics. In this chapter we . All RHS's are is, basically Hilbert spaces with distribution theory/generalized functions stitched on. Which is why the word Rigged is used - it not meant to mean rigged like a card game but like the scaffolding or rigging on a ship. The existence of the limit follows from the theory of almost-periodic functions. This space is completed to the class of Besicovitch almost-periodic functions.. The spaces and were introduced and studied by D. Hilbert in his fundamental work on the theory of integral equations and infinite quadratic forms. The definition of a Hilbert space was given by J. von Neumann, F. Riesz and . "Generalized functions volume 4" by Gelʹfand, Vilenkin, (Math review number ) has a long an detailed discussion of rigged Hilbert spaces and nuclear spaces. The book by Glimm and Jaffe has a brief summary of the theory.