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L2-lower bounds to solutions of one-body Schrödinger equations

Published online by Cambridge University Press:  14 November 2011

R. Froese ,
I. Herbst ,
M. Hoffmann-Ostenhof  and
T. Hoffmann-Ostenhof
R. Froese
Affiliation:
Institut Mittag-Leffler, Auravägen 17, S-182 62 Djursholm, Sweden
I. Herbst
Affiliation:
Institut Mittag-Leffler, Auravägen 17, S-182 62 Djursholm, Sweden
M. Hoffmann-Ostenhof
Affiliation:
Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, 1090 Wien, Austria
T. Hoffmann-Ostenhof
Affiliation:
Institut für Theoretische Chemie und Strahlenchemie, Universität Wien, Währingerstrasse 17, 1090 Wien, Austria
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Extract

The asymptotic behaviour of L2-solutions of one-body Schrödinger equations (–δ+V–E)ψ = 0 in ΩR = {x ∊ Rn||x|>R} is investigated. We show, for example, that if V tends to zero in a certain sense for |x|→∞, then either |x|γ exp for some γ>0 or ψ has compact support. Related results are given for potentials tending to infinity for |x|→∞.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 95 , Issue 1-2 , 1983 , pp. 25 - 38
Copyright
Copyright © Royal Society of Edinburgh 1983

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