Resonance theory for Schrödinger operators

O. Costin, A. Soffer

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

Resonances which result from perturbation of embedded eigenvalues are studied by time dependent methods. A general theory is developed, with new and weaker conditions, allowing for perturbations of threshold eigenvalues and relaxed Fermi Golden rule. The exponential decay rate of resonances is addressed; its uniqueness in the time dependent picture is shown in certain cases. The relation to the existence of meromorphic continuation of the properly weighted Green's function to time dependent resonance is further elucidated, by giving an equivalent time dependent asymptotic expansion of the solutions of the Schrödinger equation.

Original languageEnglish (US)
Pages (from-to)133-152
Number of pages20
JournalCommunications In Mathematical Physics
Volume224
Issue number1
DOIs
StatePublished - 2001

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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