The Schr\"odinger equation with spatial white noise: the average wave function
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🧮 math.PR
math-phmath.APmath.MP
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averageequationfunctionnoiseodingerschrwavewhite
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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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