Pavel Exner, Ari Laptev, Muhammad Usman
On some sharp spectral inequalities for Schr\"odinger operators on semi-axis
(340K, pdf)

ABSTRACT.  In this paper we obtain sharp Lieb-Thirring inequalities for a Schr\"odinger operator on semi-axis with a matrix potential and show how they can be used to other related problems. Among them are spectral inequalities on star graphs and spectral inequalities for Schr\"odinger operators on half-spaces with Robin boundary conditions.