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arXiv · 1810.03403

Asymptotics for optimal design problems for the Schr\"odinger equation with a potential

Alden Waters·Ekaterina Merkurjev
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Abstract

We study the problem of optimal observability and prove time asymptotic observability estimates for the Schr\"odinger equation with a potential in $L^{\infty}(\Omega)$, with $\Omega\subset \mathbb{R}^d$, 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.

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Alden Waters, Ekaterina Merkurjev. 2018-10-08. Asymptotics for optimal design problems for the Schr\"odinger equation with a potential. https://arxiv.org/abs/1810.03403

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