Geodesic
Sharp Semiclassical Bounds for the Moments of Eigenvalues for Some Schrödinger Type Operators with Unbounded Potentials
V. Vougalter1
1University of Cape Town, Department of Mathematics, Private Bag, Rondebosch 7701, South Africa
Mathematical modelling of natural phenomena, Tome 8 (2013) no. 1, pp. 237-245

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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 Schrödinger 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.
DOI : 10.1051/mmnp/20138119

V. Vougalter  1

1 University of Cape Town, Department of Mathematics, Private Bag, Rondebosch 7701, South Africa 
V. Vougalter. Sharp Semiclassical Bounds for the Moments of Eigenvalues for Some Schrödinger Type Operators with Unbounded Potentials. Mathematical modelling of natural phenomena, Tome 8 (2013) no. 1, pp. 237-245. doi: 10.1051/mmnp/20138119
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