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arXiv · 1706.01351

The Schr\"odinger equation with spatial white noise: the average wave function

Yu Gu·Tomasz Komorowski·Lenya Ryzhik
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Abstract

We prove a representation for the average wave function of the Schr\"odinger equation with a white noise potential in $d=1,2$, in terms of the renormalized self-intersection local time of a Brownian motion.

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Yu Gu, Tomasz Komorowski, Lenya Ryzhik. 2017-06-05. The Schr\"odinger equation with spatial white noise: the average wave function. https://arxiv.org/abs/1706.01351

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