Abstract:
We prove a smoothing property for one dimensional time dependent Schrödinger equations with potentials which satisfy at infinity, k≥ 2. As an application, we show that the initial value problem for certain nonlinear Schrödinger equations with such potentials is L 2 well-posed. We also prove a sharp asymptotic estimate of the L p-norm of the normalized eigenfunctions of H=−Δ+V for large energy.
Dedicated to Jean-Michel Combes on the occasion of his Sixtieth Birthday
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Received: 10 October 2000 / Accepted: 29 March 2001
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Yajima, K., Zhang, G. Smoothing Property for Schrödinger Equations¶with Potential Superquadratic at Infinity. Commun. Math. Phys. 221, 573–590 (2001). https://doi.org/10.1007/s002200100483
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DOI: https://doi.org/10.1007/s002200100483