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Eigenvalue bounds for two-dimensional magnetic Schroedinger operators

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.

preprint2011arXivOpen access
Hynek Kovarik
math-phmath.MPmath.SP
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Hynek Kovarik

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