Geodesic
Sharp Semiclassical Bounds for the Moments of Eigenvalues for Some Schrödinger Type Operators with Unbounded Potentials
V. Vougalter1
1 University 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 
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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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