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Phase-Integral Method

Allowing Nearlying Transition Points

  • Book
  • © 1996

Overview

Authors:
  1. Nanny Fröman

    1. Department of Theoretical Physics, University of Uppsala, Uppsala, Sweden

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  2. Per Olof Fröman

    1. Department of Theoretical Physics, University of Uppsala, Uppsala, Sweden

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Springer Tracts in Natural Philosophy (STPHI, volume 40)

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Table of contents (11 chapters)

  1. Front Matter

    Pages ii-x
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  2. Phase-Integral Approximation of Arbitrary Order Generated from an Unspecified Base Function

    1. Phase-Integral Approximation of Arbitrary Order Generated from an Unspecified Base Function

      • Nanny Fröman, Per Olof Fröman
      Pages 1-36

  3. Technique of the Comparison Equation Adapted to the Phase-Integral Method

    1. Technique of the Comparison Equation Adapted to the Phase-Integral Method

      • Nanny Fröman, Per Olof Fröman
      Pages 37-71

  4. Adjoined Papers

    1. Front Matter

      Pages 73-73
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    2. Problem Involving One Transition Zero

      • Nanny Fröman, Per Olof Fröman
      Pages 75-84

    3. Relations Between Different Nonoscillating Solutions of the q-Equation Close to a Transition Zero

      • Aleksander Dzieciol, Per Olof Fröman, Nanny Fröman
      Pages 85-108

    4. Cluster of Two Simple Transition Zeros

      • Nanny Fröman, Per Olof Fröman, Bengt Lundborg
      Pages 109-147

    5. Phase-Integral Formulas for the Regular Wave Function When There Are Turning Points Close to a Pole of the Potential

      • Nanny Fröman, Per Olof Fröman, Staffan Linnaeus
      Pages 149-182

    6. Normalized Wave Function of the Radial Schrödinger Equation Close to the Origin

      • Nanny Fröman, Per Olof Fröman, Erik Walles, Staffan Linnaeus
      Pages 183-200

    7. Phase-Amplitude Method Combined with Comparison Equation Technique Applied to an Important Special Problem

      • Per Olof Fröman, Anders Hökback, Nanny Fröman
      Pages 201-210

    8. Improved Phase-Integral Treatment of the Combined Linear and Coulomb Potential

      • Staffan Linnaeus
      Pages 211-222

    9. High-Energy Scattering from a Yukawa Potential

      • Staffan Linnaeus
      Pages 223-232

    10. Probabilities for Transitions Between Bound States in a Yukawa Potential, Calculated with Comparison Equation Technique

      • Staffan Linnaeus
      Pages 233-241

  5. Back Matter

    Pages 243-252
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Keywords

About this book

The efficiency of the phase-integral method developed by the present au­ thors has been shown both analytically and numerically in many publica­ tions. With the inclusion of supplementary quantities, closely related to new Stokes constants and obtained with the aid of comparison equation technique, important classes of problems in which transition points may approach each other become accessible to accurate analytical treatment. The exposition in this monograph is of a mathematical nature but has important physical applications, some examples of which are found in the adjoined papers. Thus, we would like to emphasize that, although we aim at mathematical rigor, our treatment is made primarily with physical needs in mind. To introduce the reader into the background of this book, we start by de­ scribing the phase-integral approximation of arbitrary order generated from an unspecified base function. This is done in Chapter 1, which is reprinted, after minor changes, from a review article. Chapter 2 is the result of re­ search work that was pursued during more than two decades, interrupted at times. It started in the sixties, when we were still using a phase-integral approximation, which in our present terminology corresponds to a special choice of the base function. At the time our primary aim was to derive expressions for the supplementary quantities needed in order to obtain an accurate connection formula for a real potential barrier, when the energy lies in the neighborhood of the top of the barrier.

Authors and Affiliations

  • Department of Theoretical Physics, University of Uppsala, Uppsala, Sweden

    Nanny Fröman, Per Olof Fröman

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