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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

  • Editors
  • A. Bohm
  • J. D. Dollard
  • M. Gadella

Part of the Lecture Notes in Physics book series (LNP, volume 348)

About this book

Introduction

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.

Keywords

Hardy space Hilbert space mathematical physics mechanics quantum mechanics quantum physics transform theory

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-51916-5
  • Copyright Information Springer-Verlag 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-51916-4
  • Online ISBN 978-3-540-46859-2
  • Series Print ISSN 0075-8450
  • Series Online ISSN 1616-6361
  • Buy this book on publisher's site