Hansen, Wolfhard A note on solutions of the Schrödinger equation. (English) Zbl 0770.31008 Proc. Am. Math. Soc. 117, No. 2, 381-384 (1993). (Author’s abstract.) Using a suitable geometric series a simple proof for the continuity of \(L^ 1\)-solutions of the Schrödinger equation \(Lu:=\Delta u-Vu\) \((V\) being a Kato function) is obtained. It works as well for uniformly elliptic operators having Hölder continuous coefficients and Kato measures instead of Kato functions. Moreover, it is shown that results on singularities are immediate consequences of the local existence of continuous Green functions for \(L\). Reviewer: M.Dont (Praha) Cited in 2 Documents MSC: 31D05 Axiomatic potential theory 35J10 Schrödinger operator, Schrödinger equation Keywords:Schrödinger equation; isolated singularity; Kato function; Kato measure PDFBibTeX XMLCite \textit{W. Hansen}, Proc. Am. Math. Soc. 117, No. 2, 381--384 (1993; Zbl 0770.31008) Full Text: DOI