Perturbation Series

  • Carl M. Bender
  • Steven A. Orszag


Perturbation theory is a large collection of iterative methods for obtaining approximate solutions to problems involving a small parameter ε. These methods are so powerful that sometimes it is actually advisable to introduce a parameter e temporarily into a difficult problem having no small parameter, and then finally to set ε = 1 to recover the original problem. This apparently artificial conversion to a perturbation problem may be the only way to make progress.


Branch Point Perturbation Method Perturbation Series Singular Perturbation Problem Matched Asymptotic Expansion 
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  1. 29.
    For general discussions of perturbation methods see Ref. 16 and: Nayfeh, A. H., Perturbation Methods, John Wiley and Sons, Inc., New York, 1973.zbMATHGoogle Scholar
  2. 30.
    Merzbacher, E., Quantum Mechanics, John Wiley and Sons, Inc., New York, 1970.Google Scholar
  3. 31.
    Perturbation methods for eigenvalue problems are discussed in Ref. 22 (vol. I) and: Landau, L. D., and Lifshitz, E. M., Quantum Mechanics, Non-Relativistic Theory, Pergamon Press, London, 1965.zbMATHGoogle Scholar
  4. 32.
    See also: Reed, M, and Simon, B., Methods of Modern Mathematical Physics, vols. I and II, Academic Press, Inc., New York, 1972.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Carl M. Bender
    • 1
  • Steven A. Orszag
    • 2
  1. 1.Department of PhysicsWashington UniversitySt. LouisUSA
  2. 2.Department of MathematicsYale UniversityNew HavenUSA

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