Norm Estimates of Complex Symmetric Operators Applied to Quantum Systems
complex symmetric operators, Schrödinger operators, quantum mechanical systems
This paper communicates recent results in the theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schrödinger 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 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.
© 2006 IOP Publishing
Prodan, E., Garcia, S.R., Putinar, M., Norm estimates of complex symmetric operators applied to quantum systems, J. Phys. A: Math. Gen. 39, no. 2, (2006), 389–400. MR2198968 (2006j:81064). doi: 10.1088/0305-4470/39/2/009