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Smoothing Property for Schrödinger Equations¶with Potential Superquadratic at Infinity

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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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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan, , , , , , JP

    Kenji Yajima & Guoping Zhang

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  1. Kenji Yajima
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  2. Guoping Zhang
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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

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