Conceptual Aspects of PT-Symmetry and Pseudo-Hermiticity: A status report

Details Conceptual Aspects of PT-Symmetry and Pseudo-Hermiticity: A status report Conceptual Aspects of PT-Symmetry and Pseudo-Hermiticity: A status report

2010-08-27

arxiv.org/abs/1008.4680v1

Phys. Scr.82:038110, 2010

Physics

Quantum Physics

11 pages

Scientific paper

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.

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