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Exponential lower bounds to solutions of the Schrödinger equation: Lower bounds for the spherical average

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Abstract

For a large class of generalizedN-body-Schrödinger operators,H, we show that ifE<Σ=infσess(H) and ψ is an eigenfunction ofH with eigenvalueE, then

$$\begin{array}{*{20}c} {\lim } \\ {R \to \infty } \\ \end{array} R^{ - 1} \ln \left( {\int\limits_{S^{n - 1} } {|\psi (R\omega )|} ^2 d\omega } \right)^{1/2} = - \alpha _0 ,$$

with α 20 +E a threshold. Similar results are given forE≧Σ.

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Authors and Affiliations

  1. Department of Mathematics, University of Virginia, 22903, Charlottesville, VA, USA

    Richard Froese & Ira Herbst

Authors
  1. Richard Froese
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  2. Ira Herbst
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Additional information

Communicated by B. Simon

Research in partial fulfillment of the requirements for a Ph.D. degree at the University of Virginia

Research partially supported by N.S.F. grant No. MCS-81-01665

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Froese, R., Herbst, I. Exponential lower bounds to solutions of the Schrödinger equation: Lower bounds for the spherical average. Commun.Math. Phys. 92, 71–80 (1983). https://doi.org/10.1007/BF01206314

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