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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

  • Book
  • © 1989

Overview

Editors:
  1. A. Bohm
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  2. J. D. Dollard
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  3. M. Gadella
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Part of the book series: Lecture Notes in Physics (LNP, volume 348)

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Table of contents (19 chapters)

  1. Front Matter

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  2. Introduction

    Pages 1-3

  3. I. The algebraic structure of the space of states

    Pages 4-8

  4. II. The topological structure of the space of states

    Pages 9-17

  5. III. The conjugate space of Φ

    Pages 18-21

  6. IV. Generalized eigenvectors and the nuclear spectral theorem

    Pages 22-30

  7. V. A remark concerning generalization

    Pages 31-32

  8. References on chapter I

    Pages 33-34

  9. Introduction

    Pages 35-37

  10. II. The Moller wave operators

    Pages 38-39

  11. III. The Hardy class functions on a half plane

    Pages 40-51

  12. References for chapter II

    Pages 51-52

  13. I. Rigged Hilbert spaces of Hardy class functions

    Pages 53-60

  14. II. The spaces Φ+ and Φ−

    Pages 61-62

  15. III. Functional for Ho and Hl

    Pages 63-69

  16. References for chapter III

    Pages 70-70

  17. I. The RHS model for decaying states

    Pages 71-78

  18. II. Dynamical semigroups

    Pages 79-90

  19. III. Virtual states

    Pages 91-96

  20. References for chapter IV

    Pages 97-97
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About this book

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.

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