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arXiv · 1010.3433

Dispersive estimate for the 1D Schr\"odinger equation with a steplike potential

Piero D'Ancona·Sigmund Selberg
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Abstract

We prove a sharp dispersive estimate $$ |P_{ac}u(t,x)|\le C|t|^{-1/2}\|u(0)\|_{L^1(R)} $$ for the one dimensional Schr\"odinger equation $$ iu_{t}-u_{xx}+V(x)u+V_0 u=0, $$ where $(1+x^2)V\in L^1(R)$ and $V_0$ is a step function, real valued and consant on the positive and negative real axes.

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Piero D'Ancona, Sigmund Selberg. 2010-10-17. Dispersive estimate for the 1D Schr\"odinger equation with a steplike potential. https://arxiv.org/abs/1010.3433

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