PT Symmetry as a Generalization of Hermiticity
Quantum Physics
2015-05-18 v2
Abstract
The Hilbert space in PT-symmetric quantum mechanics is formulated as a linear vector space with a dynamic inner product. The most general PT-symmetric matrix Hamiltonians are constructed for 2*2 and 3*3 cases. In the former case, the PT-symmetric Hamiltonian represents the most general matrix Hamiltonian with a real spectrum. In both cases, Hermitian matrices are shown to be special cases of PT-symmetric matrices. This finding confirms and strengthens the early belief that the PT-symmetric quantum mechanics is a generalization of the conventional Hermitian quantum mechanics.
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Cite
@article{arxiv.1002.2676,
title = {PT Symmetry as a Generalization of Hermiticity},
author = {Qing-hai Wang and Song-zhi Chia and Jie-hong Zhang},
journal= {arXiv preprint arXiv:1002.2676},
year = {2015}
}
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13 pages