Sharp Semiclassical Bounds for the Moments of Eigenvalues for Some Schrödinger Type Operators with Unbounded Potentials

Journal Article

2013

Permanent link to this Item
http://hdl.handle.net/11427/34559
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VougalterV_Sharp_Semiclass_2013.pdf (164.58 KB)
Authors
Vougalter, V
Journal Title

Mathematical Modelling of Natural Phenomena

Link to Journal
https://dx.doi.org/10.1051/mmnp/20138119
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Volume Title
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Publisher
Department
Department of Mathematics and Applied Mathematics
Faculty
Faculty of Science
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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 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.
Description
Keywords
semiclassical bounds
Lieb-Thirring inequalities
unbounded potentials
magnetic fields

Reference:

Vougalter, V. 2013. Sharp Semiclassical Bounds for the Moments of Eigenvalues for Some Schrödinger Type Operators with Unbounded Potentials. Mathematical Modelling of Natural Phenomena. 8(1):237 - 245. http://hdl.handle.net/11427/34559

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