JournalsjstVol. 1, No. 4pp. 363–387

Eigenvalue bounds for two-dimensional magnetic Schrödinger operators

  • Hynek Kovařík

    Università degli Studi di Brescia, Italy
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Abstract

We prove that the number of negative eigenvalues of two-dimensional magnetic Schrödinger 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.

Cite this article

Hynek Kovařík, Eigenvalue bounds for two-dimensional magnetic Schrödinger operators. J. Spectr. Theory 1 (2011), no. 4, pp. 363–387

DOI 10.4171/JST/16