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

  • D'Ancona P
  • Selberg S
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We prove a sharp dispersive estimate|Pacu(t,x)|≤C|t|-1/2{dot operator}{norm of matrix}u(0){norm of matrix}L1(R) for the one dimensional Schrödinger equationiut-uxx+V(x)u+V0(x)u=0, where (1+x2)V∈L1(R) and V0 is a step function, real valued and constant on the positive and negative real axes. © 2011 Elsevier Inc.

Author-supplied keywords

  • 35J10
  • 35Q40
  • 58J45
  • Dispersive estimate
  • Schrödinger equation
  • Steplike potentials

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