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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Pointwise bounds on eigenfunctions and wave packets in $ N$-body quantum systems. I


Author: Barry Simon
Journal: Proc. Amer. Math. Soc. 42 (1974), 395-401
MSC: Primary 35P99; Secondary 81.47
Part II: Proc. Amer. Math. Soc. 45, no. 3 (1974), 454-456
MathSciNet review: 0417596
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Abstract: We provide a simple proof of (a modification of) Kato's theorem on the Hölder continuity of wave packets in N-body quantum systems. Using this method of proof and recent results of O'Connor, we prove a pointwise bound

$\displaystyle \vert\Psi (\zeta )\vert \leqq {D_\varepsilon }\exp [ - (1 - \varepsilon ){a_0}\vert x\vert]$

on discrete eigenfunctions of energy E. Here $ \varepsilon > 0,a_0^2 = 2$ (mass of the system) $ [{\text{dist}}(E,{\sigma _{{\text{ess}}}})]$ and $ \vert x\vert$ is the radius of gyration.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0417596-0
PII: S 0002-9939(1974)0417596-0
Article copyright: © Copyright 1974 American Mathematical Society



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