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2007•arXiv (Cornell University)Open access

Analytic criteria in the qualitative spectral analysis of the Schroedinger operator

Vladimir Gilelevich Maz'ya

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Abstract

A number of topics in the qualitative spectral analysis of the Schrödinger operator $-Δ+ V$ are surveyed. In particular, some old and new results concerning the positivity and semiboundedness of this operator as well as the structure of different parts of its spectrum are considered. The attention is focused on conditions both necessary and sufficient, as well as on their sharp corollaries.

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A number of topics in the qualitative spectral analysis of the Schrödinger operator $-Δ+ V$ are surveyed. In particular, some old and new results concerning the positivity and semiboundedness of this operator as well as the structure of different parts of its spectrum are considered. The attention is focused on conditions both necessary and sufficient, as well as on their sharp corollaries.

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Available abstract

A number of topics in the qualitative spectral analysis of the Schrödinger operator $-Δ+ V$ are surveyed. In particular, some old and new results concerning the positivity and semiboundedness of this operator as well as the structure of different parts of its spectrum are considered. The attention is focused on conditions both necessary and sufficient, as well as on their sharp corollaries.

Key concepts: Schrödinger's cat, Operator (biology), Qualitative analysis, Mathematics, Applied mathematics, Mathematical physics, Qualitative research, Sociology

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