We consider the Schrödinger equation for the harmonic oscillator i∂tu=Hu, where H=−Δ+|x|2, with initial data in the Hermite–Sobolev space H−s/2L2(ℝn). We obtain smoothing and maximal estimates and apply these to perturbations of the equation and almost everywhere convergence problems.
"Regularity of the Schrödinger equation for the harmonic oscillator." Ark. Mat. 49 (2) 217 - 238, October 2011. https://doi.org/10.1007/s11512-009-0111-7