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Communications in Mathematical Physics

, Volume 83, Issue 2, pp 151–170 | Cite as

Perturbation theory for shape resonances and large barrier potentials

  • Mark S. Ashbaugh
  • Evans M. Harrell
Article

Abstract

We develop a systematic perturbation and resonance theory for the one-dimensional Schrödinger equation of the form
$$( - d^2 /dx^2 + U(x) + \lambda V(x) - E)\psi (x) = 0,0 \leqq x< \infty ,$$
where the barrier potentialV(x) is supported only wherex≧1 and is non-negative there, and λ is a real parameter tending to infinity. We prove that every λ=∞ eigenvalue turns into a resonance or an eigenvalue for finite λ.

Keywords

Neural Network Statistical Physic Complex System Perturbation Theory Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Mark S. Ashbaugh
    • 1
  • Evans M. Harrell
    • 2
  1. 1.Department of MathematicsUniversity of TennesseeKnoxvilleUSA
  2. 2.Department of MathematicsThe Johns Hopkins UniversityBaltimoreUSA

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