V. Ya. Ivrii, “Magnetic Schrödinger operator: geometry, classical and quantum dynamics and spectral asymptotics”, Mosc. Math. J., 2007, Volume 7, Number 3,Pages <nobr>461

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Magnetic Schrödinger operator: geometry, classical and quantum dynamics and spectral asymptotics

V. Ya. Ivrii

Department of Mathematics, University of Toronto

Abstract: I study the Schrödinger operator with the strong magnetic field, considering links between geometry of magnetic field, classical and quantum dynamics associated with operator and spectral asymptotics. In particular, I will discuss the role of short periodic trajectories.

Key words and phrases: Magnetic Schrödinger operator, dynamics, periodic trajectories logarithmic uncertainty principle.

MSC: 35P20

Received: May 22, 2006

Language: English

DOI: 10.17323/1609-4514-2007-7-3-461-479