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

Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Simon, B.

doi:10.1090/S0002-9939-1980-0577764-7

Brownian motion and a consequence of Harnack’s inequality: nodes of quantum wave functions
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by M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and B. Simon PDF

Proc. Amer. Math. Soc. 80 (1980), 301-305 Request permission

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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