Communications in Mathematical Physics

, Volume 134, Issue 1, pp 209–212 | Cite as

Absence of ballistic motion

  • Barry Simon


For large classes of Schrödinger operators and Jacobi matrices we prove that ifh has only one point spectrum then for φ0 of compact support
$$\mathop {\lim }\limits_{t \to \infty } t^{ - 2} \left\| {xe^{ - ith} \phi _0 } \right\|^2 = 0.$$


Neural Network Statistical Physic Complex System Nonlinear Dynamics Large Classis 
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  1. 1.
    Cycon, H., Froese, R., Kirsch, W., Simon, B.: Schrödinger Operators. Berlin, Heidelberg, New York: Springer 1987Google Scholar
  2. 2.
    Radin, C., Simon, B.: Invariant domains for the time-dependent Schrödinger equation. J. Diff. Eq.29, 289–296 (1978)Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Barry Simon
    • 1
  1. 1.Division of Physics, Mathematics, and AstronomyCalifornia Institute of TechnologyPasadenaUSA

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