Physics – Mathematical Physics
Scientific paper
2005-01-10
J. Math. Phys. A: Math and Theor. 39, 389 (2006)
Physics
Mathematical Physics
Scientific paper
10.1088/0305-4470/39/2/009
This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, 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.
Garcia Stephan R.
Prodan Emil
Putinar Mihai
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