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
Böhm, Arno
1936-
creator
Gadella, M. (Manuel)
1949-
Dollard, John D.
text
bibliography
Electronic books.
gw
Berlin
New York
Springer-Verlag
©1989
1989
monographic
eng
1 online resource (vi, 119 pages) : illustrations
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.
A. Bohm, M. Gadella ; edited by A. Bohm and J.D. Dollard.
Includes bibliographical references.
Hilbert space
Quantum theory
Hilbert space
Quantum theory
QC174.17.H55 B62 1989
530.1/2
Dirac Kets, Gamow Vectors, and Gel'fand triplets
Berlin ; New York : Springer-Verlag, ©1989
(DLC) 89028963
(OCoLC)20595295
Lecture notes in physics ; 348
9783540468592
3540468595
https://link-springer-com.libraryproxy.ist.ac.at/10.1007/3-540-51916-5
https://link-springer-com.libraryproxy.ist.ac.at/10.1007/3-540-51916-5
SPLNP
080713
20200625171155.0
ocn233810203
eng