Norm Estimates of Complex Symmetric Operators Applied to Quantum Systems

Authors

Emil Prodan, Princeton University
Stephan Ramon Garcia, Pomona CollegeFollow
Mihai Putinar, University of California - Santa Barbara

Document Type

Article

Department

Mathematics (Pomona)

Publication Date

2006

Keywords

complex symmetric operators, Schrödinger operators, quantum mechanical systems

Abstract

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.

Rights Information

© 2006 IOP Publishing

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1088/0305-4470/39/2/009

Recommended Citation

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