Conceptual Aspects of PT-Symmetry and Pseudo-Hermiticity: A status report
Physica Scripta, 82 (3):
038110+ (Aug 27, 2010)DOI: 10.1088/0031-8949/82/03/038110
Abstract
We survey some of the main conceptual developments in the study of
PT-symmetric and pseudo-Hermitian Hamiltonian operators that have taken place
during the past ten years or so. We offer a precise mathematical description of
a quantum system and its representations that allows us to describe the idea of
unitarization of a quantum system by modifying the inner product of the Hilbert
space. We discuss the role and importance of the quantum-to-classical
correspondence principle that provides the physical interpretation of the
observables in quantum mechanics. Finally, we address the problem of
constructing an underlying classical Hamiltonian for a unitary quantum system
defined by an a priori non-Hermitian Hamiltonian.