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


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.


Neural Network Statistical Physic Complex System Perturbation Theory Nonlinear Dynamics 
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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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