Froese, R.; Herbst, I.; Hoffmann-Ostenhof, Maria; Hoffmann-Ostenhof, Thomas \(L^ 2\)-lower bounds to solutions of one-body Schrödinger equations. (English) Zbl 0547.35038 Proc. R. Soc. Edinb., Sect. A 95, 25-38 (1983). 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 Cited in 19 Documents 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 Keywords:Schrödinger operator; eigenfunction; lower bounds; compact support PDF BibTeX XML Cite \textit{R. Froese} et al., Proc. R. Soc. Edinb., Sect. A, Math. 95, 25--38 (1983; Zbl 0547.35038) Full Text: DOI OpenURL References: [1] DOI: 10.1007/BF01213596 · Zbl 0464.35085 [2] DOI: 10.1063/1.525023 · Zbl 0471.35011 [3] DOI: 10.5802/aif.843 · Zbl 0468.35017 [4] DOI: 10.1103/PhysRevA.23.2106 [5] DOI: 10.1007/BF02795485 · Zbl 0211.40703 [6] DOI: 10.1090/S0273-0979-1982-15041-8 · Zbl 0524.35002 [7] Reed, Methods of modem mathematical physics (1975) [8] Reed, Methods of modem mathematical physics (1978) [9] DOI: 10.1016/0196-8858(80)90015-9 · Zbl 0482.35065 [10] Georgescu, Helv. Phys. Acta 52 pp 655– (1979) [11] Froese, J. Analyse Math. (1983) [12] DOI: 10.1007/BF01940758 · Zbl 0419.35079 [13] DOI: 10.1007/BF01218565 · Zbl 0514.35024 [14] DOI: 10.1112/blms/14.4.273 · Zbl 0525.35026 [15] Bardos, Proc. Roy. Soc. Edinburgh Sect. A 76 pp 323– (1977) · Zbl 0351.35009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.