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