Discreteness of spectrum for the magnetic Schrödinger operators. I

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We provide sufficient conditions for the discreteness of spectrum for magnetic Schrödinger operators. They generalize the classical result by K.Friedrichs (1934) and earlier results by J.Avron, I.Herbst and B.Simon (1978), A.Dufresnoy (1983) and A.Iwatsuka (1990) which were obtained in the absence of electric field. Our conditions are formulated as conditions of growth at infinity for some effective potentials. More precise sufficient conditions are formulated by use of the Wiener capacity and extend earlier work by A.M.Molchanov (1953) and V.Kondratiev and M.Shubin (1999) who considered the case of the operator without magnetic field. These conditions become necessary and sufficient in case when there is no magnetic field and the electric potential is semi-bounded below.
43 pages

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Spectral Theory, Mathematical Physics, 35J10, 81Q10

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http://salesiana.dossiersoluciones.com/handle/123456789/59591

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0007111
 http://arxiv.org/abs/math/0007111

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arXiv