Abstract
The purpose of this note is to investigate the high-frequency behavior of solutions to linear Schrödinger equations. More precisely, Bourgain (1997) and Anantharaman and Macià (2011) proved that any weak- limit of the square density of solutions to the time-dependent homogeneous Schrödinger equation is absolutely continuous with respect to the Lebesgue measure on . The contribution of this article is that the same result automatically holds for nonhomogeneous Schrödinger equations, which allows for abstract potential type perturbations of the Laplace operator.
Citation
Nicolas Burq. "Semiclassical measures for inhomogeneous Schrödinger equations on tori." Anal. PDE 6 (6) 1421 - 1427, 2013. https://doi.org/10.2140/apde.2013.6.1421
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