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

Alden Waters and Ekaterina Merkurjev

Journal of Optimization, 2018, vol. 2018, 1-16

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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjopti:8162845

DOI: 10.1155/2018/8162845

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