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Asymptotics for Optimal Design Problems for the Schrödinger Equation with a Potential

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  • Alden Waters
  • Ekaterina Merkurjev

Abstract

We study the problem of optimal observability and prove time asymptotic observability estimates for the Schrödinger equation with a potential in , with , using spectral theory. An elegant way to model the problem using a time asymptotic observability constant is presented. For certain small potentials, we demonstrate the existence of a nonzero asymptotic observability constant under given conditions and describe its explicit properties and optimal values. Moreover, we give a precise description of numerical models to analyze the properties of important examples of potentials wells, including that of the modified harmonic oscillator.

Suggested Citation

  • Alden Waters & Ekaterina Merkurjev, 2018. "Asymptotics for Optimal Design Problems for the Schrödinger Equation with a Potential," Journal of Optimization, Hindawi, vol. 2018, pages 1-16, October.
    • Handle: RePEc:hin:jjopti:8162845
    DOI: 10.1155/2018/8162845
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