The Schrödinger equation with spatial white noise: the average wave function
نویسندگان
چکیده
We prove a representation for the average wave function of the Schrödinger equation with a white noise potential in d = 1, 2, in terms of the renormalized self-intersection local time of a Brownian motion.
منابع مشابه
The Schrödinger equation with spatial white noise potential
We consider the linear and nonlinear Schrödinger equation with a spatial white noise as a potential in dimension 2. We prove existence and uniqueness of solutions thanks to a change of unknown originally used in [8] and conserved quantities. 2010 Mathematics Subject Classification AMS:
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