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Springer Tracts in Natural Philosophy

Phase-Integral Method

Allowing Nearlying Transition Points

Authors: Fröman, Nanny, Fröman, Per O.

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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.

Table of contents (11 chapters)

Table of contents (11 chapters)
  • Phase-Integral Approximation of Arbitrary Order Generated from an Unspecified Base Function

    Pages 1-36

    Fröman, Nanny (et al.)

  • Technique of the Comparison Equation Adapted to the Phase-Integral Method

    Pages 37-71

    Fröman, Nanny (et al.)

  • Problem Involving One Transition Zero

    Pages 75-84

    Fröman, Nanny (et al.)

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

    Pages 85-108

    Dzieciol, Aleksander (et al.)

  • Cluster of Two Simple Transition Zeros

    Pages 109-147

    Fröman, Nanny (et al.)

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-1-4612-2342-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-0-387-94520-0
  • Free shipping for individuals worldwide
  • This title is currently reprinting. You can pre-order your copy now.
Softcover $89.99
price for USA in USD
  • ISBN 978-1-4612-7511-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Phase-Integral Method
Book Subtitle
Allowing Nearlying Transition Points
Authors
Series Title
Springer Tracts in Natural Philosophy
Series Volume
40
Copyright
1996
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York, Inc.
eBook ISBN
978-1-4612-2342-9
DOI
10.1007/978-1-4612-2342-9
Hardcover ISBN
978-0-387-94520-0
Softcover ISBN
978-1-4612-7511-4
Series ISSN
0081-3877
Edition Number
1
Number of Pages
X, 250
Topics