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Perturbation theory for shape resonances and large barrier potentials

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Tennessee, 37916, Knoxville, TN, USA

    Mark S. Ashbaugh

  2. Department of Mathematics, The Johns Hopkins University, 21218, Baltimore, MD, USA

    Evans M. Harrell

Authors
  1. Mark S. Ashbaugh
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  2. Evans M. Harrell
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Additional information

Communicated by B. Simon

Partially supported by USNSF grant MCS 7801885 and a National Science Foundation Graduate Fellowship

Supported by USNSF grant MCS 7926408

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Ashbaugh, M.S., Harrell, E.M. Perturbation theory for shape resonances and large barrier potentials. Commun.Math. Phys. 83, 151–170 (1982). https://doi.org/10.1007/BF01976039

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  • DOI: https://doi.org/10.1007/BF01976039

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