05-8 Stephan R. Garcia, Emil Prodan and Mihai Putinar

Norm estimates of complex symmetric operators applied to quantum systems (322K, pdf) Jan 7, 05

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Abstract. 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 Schr\"odinger operators with spectral gaps. Second, we provide new ways of evaluating the resolvent norm for Schr\"odinger operators appearing in the complex scaling theory of resonances.

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