Eigenvalue bounds for two-dimensional magnetic Schrödinger operators

@article{Kovark2011EigenvalueBF,
  title={Eigenvalue bounds for two-dimensional magnetic Schr{\"o}dinger operators},
  author={Hynek Kovar{\'i}k},
  journal={arXiv: Spectral Theory},
  year={2011},
  volume={1},
  pages={363-387}
}
  • H. Kovarík
  • Published 27 March 2011
  • Mathematics
  • arXiv: Spectral Theory
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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