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On the asymptotic decay of L2-solutions of one-body Schrödinger equations in unbounded domains*

Published online by Cambridge University Press:  14 November 2011

M. Hoffmann-Ostenhof
M. Hoffmann-Ostenhof
Affiliation:
Institut für Theoretische Physik, Universität Wien, Boltzmanng. 5, A-1090 Wien, Austria
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Synopsis

The asymptotic decay of L2-solutions of Schrödinger equations (-Δ+V)ψ=0 in ΔR= {x εRn∣∣x∣=r>R} is investigated, where V(x) = V1(r) + V2(x) with V1→ ∞ for r↑∞ and with some ε > 0 for large r. Under additional assumptions on the decay of V1, pointwise upper bounds to |ψ |and lower bounds to the spherical average of ψ are given showing the same asymptotics for r→ ∞. For the case V→ const. > 0 for r→ ℝ (investigated in [8] a simplified treatment is given.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 115 , Issue 1-2 , 1990 , pp. 65 - 86
Copyright
Copyright © Royal Society of Edinburgh 1990

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