We prove that the Schrödinger equation is approximately controllable in Sobolev spaces , , generically with respect to the potential. We give two applications of this result. First, in the case of one space dimension, combining our result with a local exact controllability property, we get the global exact controllability of the system in higher Sobolev spaces. Then we prove that the Schrödinger equation with a potential which has a random time-dependent amplitude admits at most one stationary measure on the unit sphere S in .
Cite this article
Vahagn Nersesyan, Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 3, pp. 901–915DOI 10.1016/J.ANIHPC.2010.01.004