Dirac Kets, Gamow Vectors and Gel¿fand Triplets

The Rigged Hilbert Space Formulation of Quantum Mechanics. Lectures in Mathematical Physics at the University of Texas at Austin
Softcover Nachdruck of the original 1. Auflage 1989
ISBN: 978-3-662-13751-2
Verlag: Springer

Buch, Englisch, Band 348, 120 Seiten, Paperback, Format (B × H): 170 mm x 244 mm, Gewicht: 242 g

Reihe: Lecture Notes in Physics

Dirac's formalism of quantum mechanics was always praised for its elegance. This book introduces the student to its mathematical foundations and demonstrates its ease of applicability to problems in quantum physics. The book starts by describing in detail the concept of Gel'fand triplets and how one can make use of them to make the Dirac heuristic approach rigorous. The results are then deepened by giving the analytic tools, such as the Hardy class function and Hilbert and Mellin transforms, needed in applications to physical problems. Next, the RHS model for decaying states based on the concept of Gamow vectors is presented. Applications are given to physical theories of such phenomena as decaying states and resonances.

Zielgruppe

Research

Autoren/Hrsg.

Gadella, Manuel

Bohm, Arno

Dollard, J. D.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Naturwissenschaften Physik Quantenphysik Teilchenphysik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

I. The algebraic structure of the space of states.- II. The topological structure of the space of states.- III. The conjugate space of ?.- IV. Generalized eigenvectors and the nuclear spectral theorem.- V. A remark concerning generalization.- References on chapter I.- II. The Moller wave operators.- III. The Hardy class functions on a half plane.- References for chapter II.- I. Rigged Hilbert spaces of Hardy class functions.- II. The spaces ?+ and ??.- III. Functional for Ho and Hl.- References for chapter III.- I. The RHS model for decaying states.- II. Dynamical semigroups.- III. Virtual states.- References for chapter IV.