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

Abstract

We prove a sharp dispersive estimate $$|P_{ac}u(t,x)|\le C|t{|}^{-1/2}\Vert u(0){\Vert }_{L^1(R)}$$ for the one dimensional Schrödinger equation $$i{u}_t-u_{xx}+V(x)u+V_{0}u=0,$$ 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.

25 pages

References in corpus (1)

• Dispersive estimate for the Schroedinger equation with point interactions