Asymptotics for Optimal Design Problems for the Schrödinger Equation with a Potential
Keyword(s):
We study the problem of optimal observability and prove time asymptotic observability estimates for the Schrödinger equation with a potential in L∞Ω, with Ω⊂Rd, 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.
2005 ◽
Vol 11
(8)
◽
pp. 779-782
◽
Keyword(s):
1974 ◽
Vol 22
(2)
◽
pp. 167-186
◽
2019 ◽
Vol 84
(3)
◽
pp. 269-288
◽