Norm estimates of complex symmetric opera- tors applied to quantum systems

نویسندگان

  • Stephan R. Garcia
  • Emil Prodan
چکیده

Following an old and simple idea of Takagi we propose a formula for computing the norm of a compact complex symmetric operator. This observation is applied to two concrete problems related to quantum mechanical systems. First, we give sharp estimates on the exponential decay of the resolvent and the single-particle density matrix for Schrödinger operators with spectral gaps. Second, we provide new ways of evaluating the resolvent norm for Schrödinger operators appearing in the complex scaling theory of resonances. Mathematics Subject Classification (2000). Primary 47B25; Secondary 35J10, 35P15.

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تاریخ انتشار 2005