3 research outputs found
Norm estimates of complex symmetric operators applied to quantum systems
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