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\(L^ 2\)-lower bounds to solutions of one-body Schrödinger equations. (English) Zbl 0547.35038

For one-particle potentials \(L^ 2\)-lower bounds for solutions of the Schrödinger equation \((-\Delta +V-E)\psi =0\) are shown; i.e. it is proven that under certain conditions for the potential either the solution \(\psi\) has compact support or that \(f^.\) fails to be square integrable outside a ball depending on the growth properties of f where f is the product of power of the distance to the origin times an exponential.
Reviewer: H.Siedentop

MSC:

35J10 Schrödinger operator, Schrödinger equation
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
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