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

Arno Bohm, Manuel Gadella (Autoren)

Arno Bohm, J.D. Dollard (Herausgeber)

Buch | Softcover

VIII, 120 Seiten

2014 | 1. Softcover reprint of the original 1st ed. 1989
Springer Berlin (Verlag)
978-3-662-13751-2 (ISBN)

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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.

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.

Erscheint lt. Verlag	23.8.2014
Reihe/Serie	Lecture Notes in Physics
Zusatzinfo	VIII, 120 p.
Verlagsort	Berlin
Sprache	englisch
Maße	170 x 244 mm
Gewicht	241 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Hochenergiephysik / Teilchenphysik
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Analysis • Hardy space • hilbert space • Mathematical Physics • Mechanics • quantum mechanics • Quantum Physics • transform theory
ISBN-10	3-662-13751-8 / 3662137518
ISBN-13	978-3-662-13751-2 / 9783662137512
Zustand	Neuware