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We study the problem of optimal observability and prove time asymptotic observability estimates for the Schrodinger 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.

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