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arXiv · 1103.5194

Eigenvalue bounds for two-dimensional magnetic Schroedinger operators

Hynek Kovarik
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Abstract

We prove that the number of negative eigenvalues of two-dimensional magnetic Schroedinger operators is bounded from above by the strength of the corresponding electric potential. Such estimates fail in the absence of a magnetic field. We also show how the corresponding upper bounds depend on the properties of the magnetic field and discuss their connection with Hardy-type inequalities.

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Hynek Kovarik. 2011-03-27. Eigenvalue bounds for two-dimensional magnetic Schroedinger operators. https://doi.org/10.4171/jst%2F16

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