For the Schrödinger equation with potential |x|, the authors establish that sets whose complements are α-thin with α > 1/2 are observable at any time, while half-lines are never observable.
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Quantitative observability for the Schr\"{o}dinger equation with an anharmonic oscillator
For the Schrödinger equation with potential |x|, the authors establish that sets whose complements are α-thin with α > 1/2 are observable at any time, while half-lines are never observable.