A multiscale reduced basis method with quasi-Monte Carlo sampling solves the semiclassical Schrödinger equation with random potentials, achieving spatial resolution proportional to the semiclassical parameter and sample count inversely proportional to it.
Owhadi, Bayesian numerical homogenization, Multiscale Modeling & Simulation, 13 (2015), pp
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A multiscale reduced basis method for Schr\"{o}dinger equation with multiscale and random potentials
A multiscale reduced basis method with quasi-Monte Carlo sampling solves the semiclassical Schrödinger equation with random potentials, achieving spatial resolution proportional to the semiclassical parameter and sample count inversely proportional to it.