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Large Order Perturbation Theory and Summation Methods in Quantum Mechanics

  • Book
  • © 1990

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Authors:
  1. G. A. Arteca

    1. División Química Teórica, Instituto de Investigaciones Fisicoquímicas, Teóricas y Aplicadas (INIFTA), Facultad de Ciencias Exactas, Universidad Nacional de La Plata, La Plata, Argentina

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  2. F. M. Fernández

    1. División Química Teórica, Instituto de Investigaciones Fisicoquímicas, Teóricas y Aplicadas (INIFTA), Facultad de Ciencias Exactas, Universidad Nacional de La Plata, La Plata, Argentina

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    You can also search for this author in PubMed   Google Scholar

  3. E. A. Castro

    1. División Química Teórica, Instituto de Investigaciones Fisicoquímicas, Teóricas y Aplicadas (INIFTA), Facultad de Ciencias Exactas, Universidad Nacional de La Plata, La Plata, Argentina

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Part of the book series: Lecture Notes in Chemistry (LNC, volume 53)

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Table of contents (21 chapters)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  2. Large Order Perturbation Theory and Summation Methods in Quantum Mechanics

    1. Large Order Perturbation Theory and Summation Methods in Quantum Mechanics

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 1-4

  3. Part A

    1. General Properties of the Eigenvalue Spectrum

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 5-22

    2. The Semiclassical Approximation and the JWKB Method

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 23-44

    3. Rayleigh-Schrodinger Perturbation Theory (RSPT)

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 45-71

    4. Divergence of the Perturbation Series

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 72-109

    5. Perturbation Series Summation Techniques

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 110-140

    6. Foundations of the Variational Functional Method (VFM)

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 141-164

    7. Application of the VFM to One-Dimensional Systems with Trivial Boundary Conditions

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 165-189

    8. Application of the VFM to One-Dimensional Systems with Boundary Conditions for Finite Values of the Coordinates

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 190-216

    9. Multidimensional Systems: The Problem of the Zeeman Effect in Hydrogen

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 217-253

    10. Application of the VFM to the Zeeman Effect in Hydrogen

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 254-271

    11. Combination of VFM with RSPT: Application to Anharmonic Oscillators

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 272-304

    12. Geometrical Connection Between the VFM and the JWKB Method

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 305-328

  4. A General Method for Summation of Perturbation Series

    1. Front Matter

      Pages 329-329
      Download chapter PDF

    2. Generalization of the Functional Method as a Summation Technique of Perturbation Series

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 330-380

    3. Properties of the FM: Series with Non-Zero Convergence RADII.

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 381-414

    4. Properties of the FM: Series with Zero Convergence RADII

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 415-454

    5. Application of the FM to the Anharmonic Oscillator

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 455-477

    6. Application of the FM to Models with Confining Potentials

      • G. A. Arteca, F. M. Fernández, E. A. Castro
      Pages 478-493
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Keywords

About this book

The book provides a general, broad approach to aspects of perturbation theory. The aim has been to cover all topics of interest, from construction, analysis, and summation of perturbation series to applications. Emphasis is placed on simple methods, as well as clear, intuitive ideas stemming from the physics of systems of interest.

Authors and Affiliations

  • División Química Teórica, Instituto de Investigaciones Fisicoquímicas, Teóricas y Aplicadas (INIFTA), Facultad de Ciencias Exactas, Universidad Nacional de La Plata, La Plata, Argentina

    G. A. Arteca, F. M. Fernández, E. A. Castro

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