The 1D Schrödinger equation with a spacetime white noise: the average wave function

Abstract

For the 1D Schrödinger equation with a mollified spacetime white noise, we show that the average wave function converges to the Schrödinger equation with an effective potential after an appropriate renormalization.

10 pages, minor revision

References in corpus (2)

• The continuous Anderson hamiltonian in dimension two
• The continuous Anderson hamiltonian in $d\le 3$