Math. Model. Nat. Phenom.
Volume 8, Number 1, 2013Harmonic analysis
|Page(s)||237 - 245|
|Published online||28 January 2013|
Sharp Semiclassical Bounds for the Moments of Eigenvalues for Some Schrödinger Type Operators with Unbounded Potentials
University of Cape Town, Department of
Corresponding author. E-mail: Vitali.Vougalter@uct.ac.za
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.
Mathematics Subject Classification: 35P15 / 35J10 / 35J25 / 81Q10
Key words: semiclassical bounds / Lieb-Thirring inequalities / unbounded potentials / magnetic fields
© EDP Sciences, 2013
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