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Integrability, Supersymmetry and Coherent States

A Volume in Honour of Professor Véronique Hussin

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  • © 2019

Overview

Editors:
  1. Şengül Kuru

    1. Department of Physics, Ankara University, Ankara, Turkey

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  2. Javier Negro

    1. Department of Theoretical Physics, Atomic Physics and Optics, University of Valladolid, Valladolid, Spain

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  3. Luis M. Nieto

    1. Department of Theoretical Physics, Atomic Physics and Optics, University of Valladolid, Valladolid, Spain

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  • Features rigorously reviewed contributions from leaders in each field?
  • Groups topics that can be dealt with using the same mathematical tools, allowing the reader to appreciate the applications in a comprehensive way
  • Shows a wide set of applications of mathematical physics to integrability, supersymmetric quantum mechanics and coherent states
  • Starts the volume with review papers on each topic, followed by a second part devoted to the contributions of recent research by other authors

Part of the book series: CRM Series in Mathematical Physics (CRM)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Curvature as an Integrable Deformation

    • Ángel Ballesteros, Alfonso Blasco, Francisco J. Herranz
    Pages 1-35

  3. Trends in Supersymmetric Quantum Mechanics

    • David J. Fernández C.
    Pages 37-68

  4. Coherent States in Quantum Optics: An Oriented Overview

    • Jean-Pierre Gazeau
    Pages 69-101

  5. Higher Order Quantum Superintegrability: A New “Painlevé Conjecture”

    • Ian Marquette, Pavel Winternitz
    Pages 103-131

  6. Supersymmetries in Schrödinger–Pauli Equations and in Schrödinger Equations with Position Dependent Mass

    • Anatoly G. Nikitin
    Pages 133-162

  7. Nonlinear Supersymmetry as a Hidden Symmetry

    • Mikhail S. Plyushchay
    Pages 163-186

  8. Coherent and Squeezed States: Introductory Review of Basic Notions, Properties, and Generalizations

    • Oscar Rosas-Ortiz
    Pages 187-230

  9. Trace Formulas Applied to the Riemann ζ-Function

    • Mark S. Ashbaugh, Fritz Gesztesy, Lotfi Hermi, Klaus Kirsten, Lance Littlejohn, Hagop Tossounian
    Pages 231-253

  10. Real- and Complex-Energy Non-conserving Particle Number Pairing Solution

    • Rodolfo M. Id Betan
    Pages 255-266

  11. Jacobi Polynomials as su(2, 2) Unitary Irreducible Representation

    • Enrico Celeghini, Mariano A. del Olmo, Miguel A. Velasco
    Pages 267-283

  12. Infinite Square-Well, Trigonometric Pöschl-Teller and Other Potential Wells with a Moving Barrier

    • Alonso Contreras-Astorga, Véronique Hussin
    Pages 285-299

  13. Variational Method Applied to Schrödinger-Like Equation

    • Elso Drigo Filho, Regina M. Ricotta, Natália F. Ribeiro
    Pages 301-308

  14. The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions

    • Fatih Erman, Manuel Gadella, Haydar Uncu
    Pages 309-322

  15. Hermite Coherent States for Quadratic Refractive Index Optical Media

    • Zulema Gress, Sara Cruz y Cruz
    Pages 323-339

  16. Analysis of \(\mathbb {C}P^{N-1}\) Sigma Models via Soliton Surfaces

    • P. P. Goldstein, A. M. Grundland
    Pages 341-357

  17. On the Equivalence Between Type I Liouville Dynamical Systems in the Plane and the Sphere

    • Miguel A.  González León, Juan Mateos Guilarte, Marina de la Torre Mayado
    Pages 359-373

  18. Construction of Partial Differential Equations with Conditional Symmetries

    • Decio Levi, Miguel A. Rodríguez, Zora Thomova
    Pages 375-386

  19. An Integro-Differential Equation of the Fractional Form: Cauchy Problem and Solution

    • Fernando Olivar-Romero, Oscar Rosas-Ortiz
    Pages 387-393

  20. Quasi-Integrability and Some Aspects of SU(3) Toda Field Theory

    • Wojtek Zakrzewski
    Pages 395-409
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Keywords

About this book

This volume shares and makes accessible new research lines and recent results in several branches of theoretical and mathematical physics, among them Quantum Optics, Coherent States, Integrable Systems, SUSY Quantum Mechanics, and Mathematical Methods in Physics. In addition to a selection of the contributions presented at the "6th International Workshop on New Challenges in Quantum Mechanics: Integrability and Supersymmetry", held in Valladolid, Spain, 27-30 June 2017, several high quality contributions from other authors are also included. The conference gathered 60 participants from many countries working in different fields of Theoretical Physics, and was dedicated to Prof. Véronique Hussin—an internationally recognized expert in many branches of Mathematical Physics who has been making remarkable contributions to this field since the 1980s. The reader will find interesting reviews on the main topics from internationally recognized experts in each field, as well as other original contributions, all of which deal with recent applications or discoveries in the aforementioned areas.

Editors and Affiliations

  • Department of Physics, Ankara University, Ankara, Turkey

    Şengül Kuru

  • Department of Theoretical Physics, Atomic Physics and Optics, University of Valladolid, Valladolid, Spain

    Javier Negro, Luis M. Nieto

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