Regularity of the Schrödinger equation for the harmonic oscillator

Abstract

We consider the Schrödinger equation for the harmonic oscillator $i \partial_t u = Hu$, where $H = -\Delta + |x|^2$, with initial data in the Hermite-Sobolev space $H^{-s/2} L^2(\real^n)$. We obtain smoothing and maximal estimates and apply these to perturbations of the equation and almost everywhhere convergence problems.

Accepted: Arkiv för matematik