A note on solutions of the Schrödinger equation

Hansen, Wolfhard

doi:10.1090/S0002-9939-1993-1107921-1

A note on solutions of the Schrödinger equation
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by Wolfhard Hansen PDF

Proc. Amer. Math. Soc. 117 (1993), 381-384 Request permission

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 $L$.

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Valeurs propres pour l’opérateur de Schrödinger

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