Dispersive estimate for the 1D Schrödinger equation with a steplike potential

Details Dispersive estimate for the 1D Schrödinger equation with a steplike potential Dispersive estimate for the 1D Schrödinger equation with a steplike potential

2010-10-17

arxiv.org/abs/1010.3433v1

Mathematics

Analysis of PDEs

25 pages

Scientific paper

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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