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Brownian motion and a consequence of Harnack's inequality: nodes of quantum wave functions

Authors: M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and B. Simon
Journal: Proc. Amer. Math. Soc. 80 (1980), 301-305
MSC: Primary 81C20; Secondary 35B05, 35J10, 60G40, 60J65
MathSciNet review: 577764
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Abstract: Using Brownian motion ideas, we give two proofs that for a large class of V's, $ ( -\Delta + V)u = Eu$ and $ u({x_0}) = 0$ implies that u changes sign near $ {x_0}$.

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Keywords: Nodes, Brownian motion
Article copyright: © Copyright 1980 American Mathematical Society

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