© 1996

Phase-Integral Method

Allowing Nearlying Transition Points


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

Table of contents

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

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

  4. Adjoined Papers

    1. Front Matter
      Pages 73-73
    2. Nanny Fröman, Per Olof Fröman
      Pages 75-84
    3. Aleksander Dzieciol, Per Olof Fröman, Nanny Fröman
      Pages 85-108
    4. Nanny Fröman, Per Olof Fröman, Bengt Lundborg
      Pages 109-147
    5. Nanny Fröman, Per Olof Fröman, Erik Walles, Staffan Linnaeus
      Pages 183-200
    6. Staffan Linnaeus
      Pages 223-232
  5. Back Matter
    Pages 243-252

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.


Approximation Potential Theoretical physics electromagnetic wave quantum mechanics

Authors and affiliations

  1. 1.Department of Theoretical PhysicsUniversity of UppsalaUppsalaSweden

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