Reconstruction of singularities for solutions of Schrödinger's equation

Steven Zelditch*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

51 Scopus citations

Abstract

We determine the behavior in time of singularities of solutions to some Schrödinger equations on Rn. We assume the Hamiltonians are of the form H0+V, where {Mathematical expression}, and where V is bounded and smooth with decaying derivatives. When all ωk=0, the kernel k(t, x, y) of exp (-itH) is smooth in x for every fixed (t, y). When all ω1 are equal but non-zero, the initial singularity "reconstructs" at times {Mathematical expression} and positions x=(-1)my, just as if V=0;k is otherwise regular. In the general case, the singular support is shown to be contained in the union of the hyperplanes {Mathematical expression}, when ωjt/π=lj for j=j1,..., jr.

Original languageEnglish (US)
Pages (from-to)1-26
Number of pages26
JournalCommunications in Mathematical Physics
Volume90
Issue number1
DOIs
StatePublished - Mar 1 1983

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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