Integrability, Supersymmetry and Coherent States

1. Front Matter

   Pages i-xi

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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

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.

• supersymmetric quantum mechanics
• New Challenges in Quantum Mechanics 2017
• coherent states and quantum optics
• New Challenges in Quantum Mechanics Valladolid
• Casimir Effect
• Véronique Hussin

• 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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