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December  2010, 28(4): 1381-1412. doi: 10.3934/dcds.2010.28.1381

A general description of quantum dynamical spreading over an orthonormal basis and applications to Schrödinger operators

David Damanik 1, and  Serguei Tcheremchantsev 2,

1. 

Department of Mathematics, Rice University, Houston, TX 77005
2. 

UMR 6628–MAPMO, Université d’Orléans, B.P. 6759, F-45067 Orléans Cedex, France

Received  October 2009 Revised  February 2010 Published  June 2010

We discuss the long-time behavior of solutions to the Schrödinger equation in some separable Hilbert space, with particular emphasis on the spreading over some orthonormal basis. Various ways of studying wavepacket spreading from this perspective are described and their inter-relations investigated. We also state and discuss known results for concrete quantum systems relative to this general framework.
Keywords: Schrödinger equation, Schrödinger operators., Quantum dynamics.
Mathematics Subject Classification: Primary: 81Q10; Secondary: 47B36, 47N5.
Citation: David Damanik, Serguei Tcheremchantsev. A general description of quantum dynamical spreading over an orthonormal basis and applications to Schrödinger operators. Discrete & Continuous Dynamical Systems, 2010, 28 (4) : 1381-1412. doi: 10.3934/dcds.2010.28.1381
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