Vitali Vougalter Sharp semiclassical bounds for the moments of eigenvalues for some Schroedinger type operators with unbounded potentials (157K, pdf) ABSTRACT. We establish sharp semiclassical upper bounds for the moments of some negative powers for the eigenvalues of the Dirichlet Laplacian. When a constant magnetic field is incorporated in the problem, we obtain sharp lower bounds for the moments of positive powers not exceeding one for such eigenvalues. When considering a Schroedinger operator with the relativistic kinetic energy and a smooth, nonnegative, unbounded potential, we prove the sharp Lieb-Thirring estimate for the moments of some negative powers of its eigenvalues.